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From isap...@apache.org
Subject [4/4] ignite git commit: IGNITE-5218: First version of decision trees. This closes #2936
Date Fri, 10 Nov 2017 15:07:13 GMT
IGNITE-5218: First version of decision trees.
This closes #2936


Project: http://git-wip-us.apache.org/repos/asf/ignite/repo
Commit: http://git-wip-us.apache.org/repos/asf/ignite/commit/db7697b1
Tree: http://git-wip-us.apache.org/repos/asf/ignite/tree/db7697b1
Diff: http://git-wip-us.apache.org/repos/asf/ignite/diff/db7697b1

Branch: refs/heads/master
Commit: db7697b17cf6eb94754edb2b5e200655a3610dc1
Parents: 6579e69
Author: Artem Malykh <amalykh@gridgain.com>
Authored: Fri Nov 10 18:03:33 2017 +0300
Committer: Igor Sapego <isapego@gridgain.com>
Committed: Fri Nov 10 18:03:33 2017 +0300

----------------------------------------------------------------------
 .gitignore                                      |   2 +
 examples/pom.xml                                |   5 +
 .../examples/ml/math/trees/MNISTExample.java    | 261 +++++++++
 .../examples/ml/math/trees/package-info.java    |  22 +
 modules/ml/licenses/netlib-java-bsd3.txt        |  51 ++
 modules/ml/pom.xml                              |  12 +-
 .../main/java/org/apache/ignite/ml/Model.java   |   4 +-
 .../main/java/org/apache/ignite/ml/Trainer.java |  30 +
 .../clustering/KMeansDistributedClusterer.java  |  19 +-
 .../apache/ignite/ml/estimators/Estimators.java |  50 ++
 .../ignite/ml/estimators/package-info.java      |  22 +
 .../ignite/ml/math/distributed/CacheUtils.java  | 178 +++++-
 .../math/distributed/keys/MatrixCacheKey.java   |   6 +-
 .../distributed/keys/impl/BlockMatrixKey.java   |  17 +-
 .../distributed/keys/impl/SparseMatrixKey.java  |  59 +-
 .../ignite/ml/math/functions/Functions.java     |  38 ++
 .../ml/math/functions/IgniteBinaryOperator.java |  29 +
 .../math/functions/IgniteCurriedBiFunction.java |  29 +
 .../ml/math/functions/IgniteSupplier.java       |  30 +
 .../math/functions/IgniteToDoubleFunction.java  |  25 +
 .../matrix/SparseBlockDistributedMatrix.java    |   4 +-
 .../impls/matrix/SparseDistributedMatrix.java   |   3 +-
 .../storage/matrix/BlockMatrixStorage.java      |  12 +-
 .../matrix/SparseDistributedMatrixStorage.java  |  17 +-
 .../ignite/ml/structures/LabeledVector.java     |  63 +++
 .../ml/structures/LabeledVectorDouble.java      |  46 ++
 .../ignite/ml/structures/package-info.java      |  22 +
 .../ignite/ml/trees/CategoricalRegionInfo.java  |  72 +++
 .../ignite/ml/trees/CategoricalSplitInfo.java   |  68 +++
 .../ignite/ml/trees/ContinuousRegionInfo.java   |  74 +++
 .../ml/trees/ContinuousSplitCalculator.java     |  50 ++
 .../org/apache/ignite/ml/trees/RegionInfo.java  |  62 +++
 .../ml/trees/models/DecisionTreeModel.java      |  44 ++
 .../ignite/ml/trees/models/package-info.java    |  22 +
 .../ml/trees/nodes/CategoricalSplitNode.java    |  50 ++
 .../ml/trees/nodes/ContinuousSplitNode.java     |  56 ++
 .../ignite/ml/trees/nodes/DecisionTreeNode.java |  33 ++
 .../org/apache/ignite/ml/trees/nodes/Leaf.java  |  49 ++
 .../apache/ignite/ml/trees/nodes/SplitNode.java | 100 ++++
 .../ignite/ml/trees/nodes/package-info.java     |  22 +
 .../apache/ignite/ml/trees/package-info.java    |  22 +
 .../ml/trees/trainers/columnbased/BiIndex.java  | 113 ++++
 ...exedCacheColumnDecisionTreeTrainerInput.java |  57 ++
 .../CacheColumnDecisionTreeTrainerInput.java    | 142 +++++
 .../columnbased/ColumnDecisionTreeTrainer.java  | 557 +++++++++++++++++++
 .../ColumnDecisionTreeTrainerInput.java         |  55 ++
 .../MatrixColumnDecisionTreeTrainerInput.java   |  82 +++
 .../trainers/columnbased/RegionProjection.java  | 109 ++++
 .../trainers/columnbased/TrainingContext.java   | 166 ++++++
 .../columnbased/caches/ContextCache.java        |  68 +++
 .../columnbased/caches/FeaturesCache.java       | 151 +++++
 .../columnbased/caches/ProjectionsCache.java    | 284 ++++++++++
 .../trainers/columnbased/caches/SplitCache.java | 206 +++++++
 .../ContinuousSplitCalculators.java             |  34 ++
 .../contsplitcalcs/GiniSplitCalculator.java     | 234 ++++++++
 .../contsplitcalcs/VarianceSplitCalculator.java | 179 ++++++
 .../contsplitcalcs/package-info.java            |  22 +
 .../trainers/columnbased/package-info.java      |  22 +
 .../columnbased/regcalcs/RegionCalculators.java |  85 +++
 .../columnbased/regcalcs/package-info.java      |  22 +
 .../vectors/CategoricalFeatureProcessor.java    | 211 +++++++
 .../vectors/ContinuousFeatureProcessor.java     | 111 ++++
 .../vectors/ContinuousSplitInfo.java            |  54 ++
 .../columnbased/vectors/FeatureProcessor.java   |  81 +++
 .../vectors/FeatureVectorProcessorUtils.java    |  57 ++
 .../columnbased/vectors/SampleInfo.java         |  80 +++
 .../trainers/columnbased/vectors/SplitInfo.java | 106 ++++
 .../columnbased/vectors/package-info.java       |  22 +
 .../org/apache/ignite/ml/util/MnistUtils.java   | 121 ++++
 .../java/org/apache/ignite/ml/util/Utils.java   |  53 ++
 .../org/apache/ignite/ml/IgniteMLTestSuite.java |   4 +-
 .../java/org/apache/ignite/ml/TestUtils.java    |  15 +
 .../SparseDistributedBlockMatrixTest.java       |   1 +
 .../ignite/ml/trees/BaseDecisionTreeTest.java   |  70 +++
 .../ml/trees/ColumnDecisionTreeTrainerTest.java | 190 +++++++
 .../ignite/ml/trees/DecisionTreesTestSuite.java |  33 ++
 .../ml/trees/GiniSplitCalculatorTest.java       | 141 +++++
 .../ignite/ml/trees/SplitDataGenerator.java     | 390 +++++++++++++
 .../ml/trees/VarianceSplitCalculatorTest.java   |  84 +++
 .../ColumnDecisionTreeTrainerBenchmark.java     | 455 +++++++++++++++
 .../trees/columntrees.manualrun.properties      |   5 +
 81 files changed, 6538 insertions(+), 114 deletions(-)
----------------------------------------------------------------------


http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/.gitignore
----------------------------------------------------------------------
diff --git a/.gitignore b/.gitignore
index d8dd951..18146f8 100644
--- a/.gitignore
+++ b/.gitignore
@@ -89,3 +89,5 @@ packages
 /modules/platforms/cpp/odbc-test/ignite-odbc-tests
 /modules/platforms/cpp/stamp-h1
 
+#Files related to ML manual-runnable tests
+/modules/ml/src/test/resources/manualrun/trees/columntrees.manualrun.properties
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/examples/pom.xml
----------------------------------------------------------------------
diff --git a/examples/pom.xml b/examples/pom.xml
index 30d23ae..2b95e65 100644
--- a/examples/pom.xml
+++ b/examples/pom.xml
@@ -248,6 +248,11 @@
                     <artifactId>ignite-ml</artifactId>
                     <version>${project.version}</version>
                 </dependency>
+                <dependency>
+                    <groupId>commons-cli</groupId>
+                    <artifactId>commons-cli</artifactId>
+                    <version>1.2</version>
+                </dependency>
             </dependencies>
         </profile>
 

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/MNISTExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/MNISTExample.java b/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/MNISTExample.java
new file mode 100644
index 0000000..6aaadd9
--- /dev/null
+++ b/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/MNISTExample.java
@@ -0,0 +1,261 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.examples.ml.math.trees;
+
+import java.io.IOException;
+import java.util.HashMap;
+import java.util.Iterator;
+import java.util.Random;
+import java.util.function.Function;
+import java.util.stream.Stream;
+import org.apache.commons.cli.BasicParser;
+import org.apache.commons.cli.CommandLine;
+import org.apache.commons.cli.CommandLineParser;
+import org.apache.commons.cli.Option;
+import org.apache.commons.cli.OptionBuilder;
+import org.apache.commons.cli.Options;
+import org.apache.commons.cli.ParseException;
+import org.apache.ignite.Ignite;
+import org.apache.ignite.IgniteCache;
+import org.apache.ignite.IgniteDataStreamer;
+import org.apache.ignite.Ignition;
+import org.apache.ignite.cache.CacheAtomicityMode;
+import org.apache.ignite.cache.CacheMode;
+import org.apache.ignite.cache.CacheWriteSynchronizationMode;
+import org.apache.ignite.configuration.CacheConfiguration;
+import org.apache.ignite.examples.ExampleNodeStartup;
+import org.apache.ignite.internal.util.IgniteUtils;
+import org.apache.ignite.lang.IgniteBiTuple;
+import org.apache.ignite.ml.Model;
+import org.apache.ignite.ml.estimators.Estimators;
+import org.apache.ignite.ml.math.Vector;
+import org.apache.ignite.ml.math.functions.IgniteTriFunction;
+import org.apache.ignite.ml.math.impls.vector.DenseLocalOnHeapVector;
+import org.apache.ignite.ml.trees.models.DecisionTreeModel;
+import org.apache.ignite.ml.trees.trainers.columnbased.BiIndex;
+import org.apache.ignite.ml.trees.trainers.columnbased.BiIndexedCacheColumnDecisionTreeTrainerInput;
+import org.apache.ignite.ml.trees.trainers.columnbased.ColumnDecisionTreeTrainer;
+import org.apache.ignite.ml.trees.trainers.columnbased.contsplitcalcs.ContinuousSplitCalculators;
+import org.apache.ignite.ml.trees.trainers.columnbased.contsplitcalcs.GiniSplitCalculator;
+import org.apache.ignite.ml.trees.trainers.columnbased.regcalcs.RegionCalculators;
+import org.apache.ignite.ml.util.MnistUtils;
+import org.jetbrains.annotations.NotNull;
+
+/**
+ * <p>
+ * Example of usage of decision trees algorithm for MNIST dataset
+ * (it can be found here: http://yann.lecun.com/exdb/mnist/). </p>
+ * <p>
+ * Remote nodes should always be started with special configuration file which
+ * enables P2P class loading: {@code 'ignite.{sh|bat} examples/config/example-ignite.xml'}.</p>
+ * <p>
+ * Alternatively you can run {@link ExampleNodeStartup} in another JVM which will start node
+ * with {@code examples/config/example-ignite.xml} configuration.</p>
+ * <p>
+ * It is recommended to start at least one node prior to launching this example if you intend
+ * to run it with default memory settings.</p>
+ * <p>
+ * This example should with program arguments, for example
+ * -ts_i /path/to/train-images-idx3-ubyte
+ * -ts_l /path/to/train-labels-idx1-ubyte
+ * -tss_i /path/to/t10k-images-idx3-ubyte
+ * -tss_l /path/to/t10k-labels-idx1-ubyte
+ * -cfg examples/config/example-ignite.xml.</p>
+ * <p>
+ * -ts_i specifies path to training set images of MNIST;
+ * -ts_l specifies path to training set labels of MNIST;
+ * -tss_i specifies path to test set images of MNIST;
+ * -tss_l specifies path to test set labels of MNIST;
+ * -cfg specifies path to a config path.</p>
+ */
+public class MNISTExample {
+    /** Name of parameter specifying path to training set images. */
+    private static final String MNIST_TRAINING_IMAGES_PATH = "ts_i";
+
+    /** Name of parameter specifying path to training set labels. */
+    private static final String MNIST_TRAINING_LABELS_PATH = "ts_l";
+
+    /** Name of parameter specifying path to test set images. */
+    private static final String MNIST_TEST_IMAGES_PATH = "tss_i";
+
+    /** Name of parameter specifying path to test set labels. */
+    private static final String MNIST_TEST_LABELS_PATH = "tss_l";
+
+    /** Name of parameter specifying path of Ignite config. */
+    private static final String CONFIG = "cfg";
+
+    /** Default config path. */
+    private static final String DEFAULT_CONFIG = "examples/config/example-ignite.xml";
+
+    /**
+     * Launches example.
+     *
+     * @param args Program arguments.
+     */
+    public static void main(String[] args) {
+        String igniteCfgPath;
+
+        CommandLineParser parser = new BasicParser();
+
+        String trainingImagesPath;
+        String trainingLabelsPath;
+
+        String testImagesPath;
+        String testLabelsPath;
+
+        try {
+            // Parse the command line arguments.
+            CommandLine line = parser.parse(buildOptions(), args);
+
+            trainingImagesPath = line.getOptionValue(MNIST_TRAINING_IMAGES_PATH);
+            trainingLabelsPath = line.getOptionValue(MNIST_TRAINING_LABELS_PATH);
+            testImagesPath = line.getOptionValue(MNIST_TEST_IMAGES_PATH);
+            testLabelsPath = line.getOptionValue(MNIST_TEST_LABELS_PATH);
+            igniteCfgPath = line.getOptionValue(CONFIG, DEFAULT_CONFIG);
+        }
+        catch (ParseException e) {
+            e.printStackTrace();
+            return;
+        }
+
+        try (Ignite ignite = Ignition.start(igniteCfgPath)) {
+            IgniteUtils.setCurrentIgniteName(ignite.configuration().getIgniteInstanceName());
+
+            int ptsCnt = 60000;
+            int featCnt = 28 * 28;
+
+            Stream<DenseLocalOnHeapVector> trainingMnistStream = MnistUtils.mnist(trainingImagesPath, trainingLabelsPath, new Random(123L), ptsCnt);
+            Stream<DenseLocalOnHeapVector> testMnistStream = MnistUtils.mnist(testImagesPath, testLabelsPath, new Random(123L), 10_000);
+
+            IgniteCache<BiIndex, Double> cache = createBiIndexedCache(ignite);
+
+            loadVectorsIntoBiIndexedCache(cache.getName(), trainingMnistStream.iterator(), featCnt + 1, ignite);
+
+            ColumnDecisionTreeTrainer<GiniSplitCalculator.GiniData> trainer =
+                new ColumnDecisionTreeTrainer<>(10, ContinuousSplitCalculators.GINI.apply(ignite), RegionCalculators.GINI, RegionCalculators.MOST_COMMON, ignite);
+
+            System.out.println(">>> Training started");
+            long before = System.currentTimeMillis();
+            DecisionTreeModel mdl = trainer.train(new BiIndexedCacheColumnDecisionTreeTrainerInput(cache, new HashMap<>(), ptsCnt, featCnt));
+            System.out.println(">>> Training finished in " + (System.currentTimeMillis() - before));
+
+            IgniteTriFunction<Model<Vector, Double>, Stream<IgniteBiTuple<Vector, Double>>, Function<Double, Double>, Double> mse = Estimators.errorsPercentage();
+            Double accuracy = mse.apply(mdl, testMnistStream.map(v -> new IgniteBiTuple<>(v.viewPart(0, featCnt), v.getX(featCnt))), Function.identity());
+            System.out.println(">>> Errs percentage: " + accuracy);
+        }
+        catch (IOException e) {
+            e.printStackTrace();
+        }
+    }
+
+    /**
+     * Build cli options.
+     */
+    @NotNull private static Options buildOptions() {
+        Options options = new Options();
+
+        Option trsImagesPathOpt = OptionBuilder.withArgName(MNIST_TRAINING_IMAGES_PATH).withLongOpt(MNIST_TRAINING_IMAGES_PATH).hasArg()
+            .withDescription("Path to the MNIST training set.")
+            .isRequired(true).create();
+
+        Option trsLabelsPathOpt = OptionBuilder.withArgName(MNIST_TRAINING_LABELS_PATH).withLongOpt(MNIST_TRAINING_LABELS_PATH).hasArg()
+            .withDescription("Path to the MNIST training set.")
+            .isRequired(true).create();
+
+        Option tssImagesPathOpt = OptionBuilder.withArgName(MNIST_TEST_IMAGES_PATH).withLongOpt(MNIST_TEST_IMAGES_PATH).hasArg()
+            .withDescription("Path to the MNIST test set.")
+            .isRequired(true).create();
+
+        Option tssLabelsPathOpt = OptionBuilder.withArgName(MNIST_TEST_LABELS_PATH).withLongOpt(MNIST_TEST_LABELS_PATH).hasArg()
+            .withDescription("Path to the MNIST test set.")
+            .isRequired(true).create();
+
+        Option configOpt = OptionBuilder.withArgName(CONFIG).withLongOpt(CONFIG).hasArg()
+            .withDescription("Path to the config.")
+            .isRequired(false).create();
+
+        options.addOption(trsImagesPathOpt);
+        options.addOption(trsLabelsPathOpt);
+        options.addOption(tssImagesPathOpt);
+        options.addOption(tssLabelsPathOpt);
+        options.addOption(configOpt);
+
+        return options;
+    }
+
+    /**
+     * Creates cache where data for training is stored.
+     *
+     * @param ignite Ignite instance.
+     * @return cache where data for training is stored.
+     */
+    private static IgniteCache<BiIndex, Double> createBiIndexedCache(Ignite ignite) {
+        CacheConfiguration<BiIndex, Double> cfg = new CacheConfiguration<>();
+
+        // Write to primary.
+        cfg.setWriteSynchronizationMode(CacheWriteSynchronizationMode.PRIMARY_SYNC);
+
+        // Atomic transactions only.
+        cfg.setAtomicityMode(CacheAtomicityMode.ATOMIC);
+
+        // No eviction.
+        cfg.setEvictionPolicy(null);
+
+        // No copying of values.
+        cfg.setCopyOnRead(false);
+
+        // Cache is partitioned.
+        cfg.setCacheMode(CacheMode.PARTITIONED);
+
+        cfg.setBackups(0);
+
+        cfg.setName("TMP_BI_INDEXED_CACHE");
+
+        return ignite.getOrCreateCache(cfg);
+    }
+
+    /**
+     * Loads vectors into cache.
+     *
+     * @param cacheName Name of cache.
+     * @param vectorsIterator Iterator over vectors to load.
+     * @param vectorSize Size of vector.
+     * @param ignite Ignite instance.
+     */
+    private static void loadVectorsIntoBiIndexedCache(String cacheName, Iterator<? extends Vector> vectorsIterator,
+        int vectorSize, Ignite ignite) {
+        try (IgniteDataStreamer<BiIndex, Double> streamer =
+                 ignite.dataStreamer(cacheName)) {
+            int sampleIdx = 0;
+
+            streamer.perNodeBufferSize(10000);
+
+            while (vectorsIterator.hasNext()) {
+                org.apache.ignite.ml.math.Vector next = vectorsIterator.next();
+
+                for (int i = 0; i < vectorSize; i++)
+                    streamer.addData(new BiIndex(sampleIdx, i), next.getX(i));
+
+                sampleIdx++;
+
+                if (sampleIdx % 1000 == 0)
+                    System.out.println("Loaded " + sampleIdx + " vectors.");
+            }
+        }
+    }
+}
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/package-info.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/package-info.java b/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/package-info.java
new file mode 100644
index 0000000..9b6867b
--- /dev/null
+++ b/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+/**
+ * <!-- Package description. -->
+ * Decision trees examples.
+ */
+package org.apache.ignite.examples.ml.math.trees;

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/licenses/netlib-java-bsd3.txt
----------------------------------------------------------------------
diff --git a/modules/ml/licenses/netlib-java-bsd3.txt b/modules/ml/licenses/netlib-java-bsd3.txt
new file mode 100644
index 0000000..d6b30c1
--- /dev/null
+++ b/modules/ml/licenses/netlib-java-bsd3.txt
@@ -0,0 +1,51 @@
+This product binaries redistribute netlib-java which is available under the following license:
+
+Copyright (c) 2013 Samuel Halliday
+Copyright (c) 1992-2011 The University of Tennessee and The University
+                        of Tennessee Research Foundation.  All rights
+                        reserved.
+Copyright (c) 2000-2011 The University of California Berkeley. All
+                        rights reserved.
+Copyright (c) 2006-2011 The University of Colorado Denver.  All rights
+                        reserved.
+
+$COPYRIGHT$
+
+Additional copyrights may follow
+
+$HEADER$
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+- Redistributions of source code must retain the above copyright
+  notice, this list of conditions and the following disclaimer.
+
+- Redistributions in binary form must reproduce the above copyright
+  notice, this list of conditions and the following disclaimer listed
+  in this license in the documentation and/or other materials
+  provided with the distribution.
+
+- Neither the name of the copyright holders nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+The copyright holders provide no reassurances that the source code
+provided does not infringe any patent, copyright, or any other
+intellectual property rights of third parties.  The copyright holders
+disclaim any liability to any recipient for claims brought against
+recipient by any third party for infringement of that parties
+intellectual property rights.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/pom.xml
----------------------------------------------------------------------
diff --git a/modules/ml/pom.xml b/modules/ml/pom.xml
index 94cfc51..c495f44 100644
--- a/modules/ml/pom.xml
+++ b/modules/ml/pom.xml
@@ -75,13 +75,6 @@
 
         <dependency>
             <groupId>org.springframework</groupId>
-            <artifactId>spring-beans</artifactId>
-            <version>${spring.version}</version>
-            <scope>test</scope>
-        </dependency>
-
-        <dependency>
-            <groupId>org.springframework</groupId>
             <artifactId>spring-context</artifactId>
             <version>${spring.version}</version>
             <scope>test</scope>
@@ -105,6 +98,11 @@
             <version>1.0</version>
         </dependency>
 
+        <dependency>
+            <groupId>com.zaxxer</groupId>
+            <artifactId>SparseBitSet</artifactId>
+            <version>1.0</version>
+        </dependency>
     </dependencies>
 
     <profiles>

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/Model.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/Model.java b/modules/ml/src/main/java/org/apache/ignite/ml/Model.java
index 3c60bfa..05ce774 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/Model.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/Model.java
@@ -24,7 +24,7 @@ import java.util.function.BiFunction;
 @FunctionalInterface
 public interface Model<T, V> extends Serializable {
     /** Predict a result for value. */
-    public V predict(T val);
+    V predict(T val);
 
     /**
      * Combines this model with other model via specified combiner
@@ -33,7 +33,7 @@ public interface Model<T, V> extends Serializable {
      * @param combiner Combiner.
      * @return Combination of models.
      */
-    public default <X, W> Model<T, X> combine(Model<T, W> other, BiFunction<V, W, X> combiner) {
+    default <X, W> Model<T, X> combine(Model<T, W> other, BiFunction<V, W, X> combiner) {
         return v -> combiner.apply(predict(v), other.predict(v));
     }
 }

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/Trainer.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/Trainer.java b/modules/ml/src/main/java/org/apache/ignite/ml/Trainer.java
new file mode 100644
index 0000000..795e218
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/Trainer.java
@@ -0,0 +1,30 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml;
+
+import org.apache.ignite.ml.trees.trainers.columnbased.ColumnDecisionTreeTrainer;
+
+/**
+ * Interface for Trainers. Trainer is just a function which produces model from the data.
+ * See for example {@link ColumnDecisionTreeTrainer}.
+ * @param <M> Type of produced model.
+ * @param <T> Type of data needed for model producing.
+ */
+public interface Trainer<M extends Model, T> {
+    M train(T data);
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/clustering/KMeansDistributedClusterer.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/clustering/KMeansDistributedClusterer.java b/modules/ml/src/main/java/org/apache/ignite/ml/clustering/KMeansDistributedClusterer.java
index d6a3fc3..6c25edc 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/clustering/KMeansDistributedClusterer.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/clustering/KMeansDistributedClusterer.java
@@ -21,6 +21,7 @@ import java.util.ArrayList;
 import java.util.List;
 import java.util.Map;
 import java.util.Random;
+import java.util.UUID;
 import java.util.concurrent.ConcurrentHashMap;
 import java.util.stream.Collectors;
 import javax.cache.Cache;
@@ -94,7 +95,7 @@ public class KMeansDistributedClusterer extends BaseKMeansClusterer<SparseDistri
         boolean converged = false;
         int iteration = 0;
         int dim = pointsCp.viewRow(0).size();
-        IgniteUuid uid = pointsCp.getUUID();
+        UUID uid = pointsCp.getUUID();
 
         // Execute iterations of Lloyd's algorithm until converged
         while (iteration < maxIterations && !converged) {
@@ -140,7 +141,7 @@ public class KMeansDistributedClusterer extends BaseKMeansClusterer<SparseDistri
         // to their squared distance from the centers. Note that only distances between points
         // and new centers are computed in each iteration.
         int step = 0;
-        IgniteUuid uid = points.getUUID();
+        UUID uid = points.getUUID();
 
         while (step < initSteps) {
             // We assume here that costs can fit into memory of one node.
@@ -180,7 +181,7 @@ public class KMeansDistributedClusterer extends BaseKMeansClusterer<SparseDistri
     }
 
     /** */
-    private List<Vector> getNewCenters(int k, ConcurrentHashMap<Integer, Double> costs, IgniteUuid uid,
+    private List<Vector> getNewCenters(int k, ConcurrentHashMap<Integer, Double> costs, UUID uid,
         double sumCosts, String cacheName) {
         return distributedFold(cacheName,
             (IgniteBiFunction<Cache.Entry<SparseMatrixKey, Map<Integer, Double>>,
@@ -200,7 +201,7 @@ public class KMeansDistributedClusterer extends BaseKMeansClusterer<SparseDistri
                 list1.addAll(list2);
                 return list1;
             },
-            new ArrayList<>()
+            ArrayList::new
         );
     }
 
@@ -219,11 +220,11 @@ public class KMeansDistributedClusterer extends BaseKMeansClusterer<SparseDistri
             (map1, map2) -> {
                 map1.putAll(map2);
                 return map1;
-            }, new ConcurrentHashMap<>());
+            }, ConcurrentHashMap::new);
     }
 
     /** */
-    private ConcurrentHashMap<Integer, Integer> weightCenters(IgniteUuid uid, List<Vector> distinctCenters, String cacheName) {
+    private ConcurrentHashMap<Integer, Integer> weightCenters(UUID uid, List<Vector> distinctCenters, String cacheName) {
         return distributedFold(cacheName,
             (IgniteBiFunction<Cache.Entry<SparseMatrixKey, Map<Integer, Double>>,
                 ConcurrentHashMap<Integer, Integer>,
@@ -249,7 +250,7 @@ public class KMeansDistributedClusterer extends BaseKMeansClusterer<SparseDistri
             key -> key.matrixId().equals(uid),
             (map1, map2) -> MapUtil.mergeMaps(map1, map2, (integer, integer2) -> integer2 + integer,
                 ConcurrentHashMap::new),
-            new ConcurrentHashMap<>());
+            ConcurrentHashMap::new);
     }
 
     /** */
@@ -258,7 +259,7 @@ public class KMeansDistributedClusterer extends BaseKMeansClusterer<SparseDistri
     }
 
     /** */
-    private SumsAndCounts getSumsAndCounts(Vector[] centers, int dim, IgniteUuid uid, String cacheName) {
+    private SumsAndCounts getSumsAndCounts(Vector[] centers, int dim, UUID uid, String cacheName) {
         return CacheUtils.distributedFold(cacheName,
             (IgniteBiFunction<Cache.Entry<SparseMatrixKey, Map<Integer, Double>>, SumsAndCounts, SumsAndCounts>)(entry, counts) -> {
                 Map<Integer, Double> vec = entry.getValue();
@@ -278,7 +279,7 @@ public class KMeansDistributedClusterer extends BaseKMeansClusterer<SparseDistri
                 return counts;
             },
             key -> key.matrixId().equals(uid),
-            SumsAndCounts::merge, new SumsAndCounts()
+            SumsAndCounts::merge, SumsAndCounts::new
         );
     }
 

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/estimators/Estimators.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/estimators/Estimators.java b/modules/ml/src/main/java/org/apache/ignite/ml/estimators/Estimators.java
new file mode 100644
index 0000000..13331d1
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/estimators/Estimators.java
@@ -0,0 +1,50 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.estimators;
+
+import java.util.concurrent.atomic.AtomicLong;
+import java.util.function.Function;
+import java.util.stream.Stream;
+import org.apache.ignite.lang.IgniteBiTuple;
+import org.apache.ignite.ml.Model;
+import org.apache.ignite.ml.math.functions.IgniteTriFunction;
+
+/** Estimators. */
+public class Estimators {
+    /** Simple implementation of mean squared error estimator. */
+    public static <T, V> IgniteTriFunction<Model<T, V>, Stream<IgniteBiTuple<T, V>>, Function<V, Double>, Double> MSE() {
+        return (model, stream, f) -> stream.mapToDouble(dp -> {
+            double diff = f.apply(dp.get2()) - f.apply(model.predict(dp.get1()));
+            return diff * diff;
+        }).average().orElse(0);
+    }
+
+    /** Simple implementation of errors percentage estimator. */
+    public static <T, V> IgniteTriFunction<Model<T, V>, Stream<IgniteBiTuple<T, V>>, Function<V, Double>, Double> errorsPercentage() {
+        return (model, stream, f) -> {
+            AtomicLong total = new AtomicLong(0);
+
+            long cnt = stream.
+                peek((ib) -> total.incrementAndGet()).
+                filter(dp -> !model.predict(dp.get1()).equals(dp.get2())).
+                count();
+
+            return (double)cnt / total.get();
+        };
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/estimators/package-info.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/estimators/package-info.java b/modules/ml/src/main/java/org/apache/ignite/ml/estimators/package-info.java
new file mode 100644
index 0000000..c03827f
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/estimators/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+/**
+ * <!-- Package description. -->
+ * Contains estimation algorithms.
+ */
+package org.apache.ignite.ml.estimators;
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/CacheUtils.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/CacheUtils.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/CacheUtils.java
index 8c8bba7..b9eb386 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/CacheUtils.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/CacheUtils.java
@@ -21,7 +21,11 @@ import java.util.Collection;
 import java.util.Collections;
 import java.util.Map;
 import java.util.Objects;
+import java.util.Set;
+import java.util.UUID;
+import java.util.concurrent.ConcurrentHashMap;
 import java.util.function.BinaryOperator;
+import java.util.stream.Stream;
 import javax.cache.Cache;
 import org.apache.ignite.Ignite;
 import org.apache.ignite.IgniteCache;
@@ -32,17 +36,21 @@ import org.apache.ignite.cluster.ClusterGroup;
 import org.apache.ignite.cluster.ClusterNode;
 import org.apache.ignite.internal.processors.cache.CacheEntryImpl;
 import org.apache.ignite.internal.util.typedef.internal.A;
+import org.apache.ignite.lang.IgniteBiTuple;
 import org.apache.ignite.lang.IgniteCallable;
 import org.apache.ignite.lang.IgnitePredicate;
 import org.apache.ignite.lang.IgniteRunnable;
 import org.apache.ignite.lang.IgniteUuid;
 import org.apache.ignite.ml.math.KeyMapper;
-import org.apache.ignite.ml.math.distributed.keys.RowColMatrixKey;
-import org.apache.ignite.ml.math.distributed.keys.impl.BlockMatrixKey;
+import org.apache.ignite.ml.math.distributed.keys.BlockMatrixKey;
+import org.apache.ignite.ml.math.distributed.keys.MatrixCacheKey;
 import org.apache.ignite.ml.math.functions.IgniteBiFunction;
+import org.apache.ignite.ml.math.functions.IgniteBinaryOperator;
 import org.apache.ignite.ml.math.functions.IgniteConsumer;
 import org.apache.ignite.ml.math.functions.IgniteDoubleFunction;
 import org.apache.ignite.ml.math.functions.IgniteFunction;
+import org.apache.ignite.ml.math.functions.IgniteSupplier;
+import org.apache.ignite.ml.math.functions.IgniteTriFunction;
 import org.apache.ignite.ml.math.impls.matrix.BlockEntry;
 
 /**
@@ -131,7 +139,7 @@ public class CacheUtils {
      * @return Sum obtained using sparse logic.
      */
     @SuppressWarnings("unchecked")
-    public static <K, V> double sparseSum(IgniteUuid matrixUuid, String cacheName) {
+    public static <K, V> double sparseSum(UUID matrixUuid, String cacheName) {
         A.notNull(matrixUuid, "matrixUuid");
         A.notNull(cacheName, "cacheName");
 
@@ -198,7 +206,7 @@ public class CacheUtils {
      * @return Minimum value obtained using sparse logic.
      */
     @SuppressWarnings("unchecked")
-    public static <K, V> double sparseMin(IgniteUuid matrixUuid, String cacheName) {
+    public static <K, V> double sparseMin(UUID matrixUuid, String cacheName) {
         A.notNull(matrixUuid, "matrixUuid");
         A.notNull(cacheName, "cacheName");
 
@@ -235,7 +243,7 @@ public class CacheUtils {
      * @return Maximum value obtained using sparse logic.
      */
     @SuppressWarnings("unchecked")
-    public static <K, V> double sparseMax(IgniteUuid matrixUuid, String cacheName) {
+    public static <K, V> double sparseMax(UUID matrixUuid, String cacheName) {
         A.notNull(matrixUuid, "matrixUuid");
         A.notNull(cacheName, "cacheName");
 
@@ -316,7 +324,7 @@ public class CacheUtils {
      * @param mapper Mapping {@link IgniteFunction}.
      */
     @SuppressWarnings("unchecked")
-    public static <K, V> void sparseMap(IgniteUuid matrixUuid, IgniteDoubleFunction<Double> mapper, String cacheName) {
+    public static <K, V> void sparseMap(UUID matrixUuid, IgniteDoubleFunction<Double> mapper, String cacheName) {
         A.notNull(matrixUuid, "matrixUuid");
         A.notNull(cacheName, "cacheName");
         A.notNull(mapper, "mapper");
@@ -350,12 +358,12 @@ public class CacheUtils {
      *
      * @param matrixUuid Matrix uuid.
      */
-    private static <K> IgnitePredicate<K> sparseKeyFilter(IgniteUuid matrixUuid) {
+    private static <K> IgnitePredicate<K> sparseKeyFilter(UUID matrixUuid) {
         return key -> {
-            if (key instanceof BlockMatrixKey)
-                return ((BlockMatrixKey)key).matrixId().equals(matrixUuid);
-            else if (key instanceof RowColMatrixKey)
-                return ((RowColMatrixKey)key).matrixId().equals(matrixUuid);
+            if (key instanceof MatrixCacheKey)
+                return ((MatrixCacheKey)key).matrixId().equals(matrixUuid);
+            else if (key instanceof IgniteBiTuple)
+                return ((IgniteBiTuple<Integer, UUID>)key).get2().equals(matrixUuid);
             else
                 throw new UnsupportedOperationException();
         };
@@ -404,6 +412,76 @@ public class CacheUtils {
     }
 
     /**
+     * @param cacheName Cache name.
+     * @param fun An operation that accepts a cache entry and processes it.
+     * @param ignite Ignite.
+     * @param keysGen Keys generator.
+     * @param <K> Cache key object type.
+     * @param <V> Cache value object type.
+     */
+    public static <K, V> void update(String cacheName, Ignite ignite,
+        IgniteBiFunction<Ignite, Cache.Entry<K, V>, Stream<Cache.Entry<K, V>>> fun, IgniteSupplier<Set<K>> keysGen) {
+        bcast(cacheName, ignite, () -> {
+            Ignite ig = Ignition.localIgnite();
+            IgniteCache<K, V> cache = ig.getOrCreateCache(cacheName);
+
+            Affinity<K> affinity = ig.affinity(cacheName);
+            ClusterNode locNode = ig.cluster().localNode();
+
+            Collection<K> ks = affinity.mapKeysToNodes(keysGen.get()).get(locNode);
+
+            if (ks == null)
+                return;
+
+            Map<K, V> m = new ConcurrentHashMap<>();
+
+            ks.parallelStream().forEach(k -> {
+                V v = cache.localPeek(k);
+                if (v != null)
+                    (fun.apply(ignite, new CacheEntryImpl<>(k, v))).forEach(ent -> m.put(ent.getKey(), ent.getValue()));
+            });
+
+            cache.putAll(m);
+        });
+    }
+
+    /**
+     * @param cacheName Cache name.
+     * @param fun An operation that accepts a cache entry and processes it.
+     * @param ignite Ignite.
+     * @param keysGen Keys generator.
+     * @param <K> Cache key object type.
+     * @param <V> Cache value object type.
+     */
+    public static <K, V> void update(String cacheName, Ignite ignite, IgniteConsumer<Cache.Entry<K, V>> fun,
+        IgniteSupplier<Set<K>> keysGen) {
+        bcast(cacheName, ignite, () -> {
+            Ignite ig = Ignition.localIgnite();
+            IgniteCache<K, V> cache = ig.getOrCreateCache(cacheName);
+
+            Affinity<K> affinity = ig.affinity(cacheName);
+            ClusterNode locNode = ig.cluster().localNode();
+
+            Collection<K> ks = affinity.mapKeysToNodes(keysGen.get()).get(locNode);
+
+            if (ks == null)
+                return;
+
+            Map<K, V> m = new ConcurrentHashMap<>();
+
+            for (K k : ks) {
+                V v = cache.localPeek(k);
+                fun.accept(new CacheEntryImpl<>(k, v));
+                m.put(k, v);
+            }
+
+            long before = System.currentTimeMillis();
+            cache.putAll(m);
+            System.out.println("PutAll took: " + (System.currentTimeMillis() - before));
+        });
+    }
+
+    /**
      * <b>Currently fold supports only commutative operations.<b/>
      *
      * @param cacheName Cache name.
@@ -463,11 +541,11 @@ public class CacheUtils {
      * @param folder Folder.
      * @param keyFilter Key filter.
      * @param accumulator Accumulator.
-     * @param zeroVal Zero value.
+     * @param zeroValSupp Zero value supplier.
      */
     public static <K, V, A> A distributedFold(String cacheName, IgniteBiFunction<Cache.Entry<K, V>, A, A> folder,
-        IgnitePredicate<K> keyFilter, BinaryOperator<A> accumulator, A zeroVal) {
-        return sparseFold(cacheName, folder, keyFilter, accumulator, zeroVal, null, null, 0,
+        IgnitePredicate<K> keyFilter, BinaryOperator<A> accumulator, IgniteSupplier<A> zeroValSupp) {
+        return sparseFold(cacheName, folder, keyFilter, accumulator, zeroValSupp, null, null, 0,
             false);
     }
 
@@ -478,17 +556,17 @@ public class CacheUtils {
      * @param folder Folder.
      * @param keyFilter Key filter.
      * @param accumulator Accumulator.
-     * @param zeroVal Zero value.
-     * @param defVal Def value.
-     * @param defKey Def key.
+     * @param zeroValSupp Zero value supplier.
+     * @param defVal Default value.
+     * @param defKey Default key.
      * @param defValCnt Def value count.
      * @param isNilpotent Is nilpotent.
      */
     private static <K, V, A> A sparseFold(String cacheName, IgniteBiFunction<Cache.Entry<K, V>, A, A> folder,
-        IgnitePredicate<K> keyFilter, BinaryOperator<A> accumulator, A zeroVal, V defVal, K defKey, long defValCnt,
-        boolean isNilpotent) {
+        IgnitePredicate<K> keyFilter, BinaryOperator<A> accumulator, IgniteSupplier<A> zeroValSupp, V defVal, K defKey,
+        long defValCnt, boolean isNilpotent) {
 
-        A defRes = zeroVal;
+        A defRes = zeroValSupp.get();
 
         if (!isNilpotent)
             for (int i = 0; i < defValCnt; i++)
@@ -504,7 +582,7 @@ public class CacheUtils {
             Affinity affinity = ignite.affinity(cacheName);
             ClusterNode locNode = ignite.cluster().localNode();
 
-            A a = zeroVal;
+            A a = zeroValSupp.get();
 
             // Iterate over all partitions. Some of them will be stored on that local node.
             for (int part = 0; part < partsCnt; part++) {
@@ -519,16 +597,54 @@ public class CacheUtils {
 
             return a;
         });
-        totalRes.add(defRes);
-        return totalRes.stream().reduce(zeroVal, accumulator);
+        return totalRes.stream().reduce(defRes, accumulator);
+    }
+
+    public static <K, V, A, W> A reduce(String cacheName, Ignite ignite,
+        IgniteTriFunction<W, Cache.Entry<K, V>, A, A> acc,
+        IgniteSupplier<W> supp,
+        IgniteSupplier<Iterable<Cache.Entry<K, V>>> entriesGen, IgniteBinaryOperator<A> comb,
+        IgniteSupplier<A> zeroValSupp) {
+
+        A defRes = zeroValSupp.get();
+
+        Collection<A> totalRes = bcast(cacheName, ignite, () -> {
+            // Use affinity in filter for ScanQuery. Otherwise we accept consumer in each node which is wrong.
+            A a = zeroValSupp.get();
+
+            W w = supp.get();
+
+            for (Cache.Entry<K, V> kvEntry : entriesGen.get())
+                a = acc.apply(w, kvEntry, a);
+
+            return a;
+        });
+
+        return totalRes.stream().reduce(defRes, comb);
+    }
+
+    public static <K, V, A, W> A reduce(String cacheName, IgniteTriFunction<W, Cache.Entry<K, V>, A, A> acc,
+        IgniteSupplier<W> supp,
+        IgniteSupplier<Iterable<Cache.Entry<K, V>>> entriesGen, IgniteBinaryOperator<A> comb,
+        IgniteSupplier<A> zeroValSupp) {
+        return reduce(cacheName, Ignition.localIgnite(), acc, supp, entriesGen, comb, zeroValSupp);
     }
 
     /**
      * @param cacheName Cache name.
      * @param run {@link Runnable} to broadcast to cache nodes for given cache name.
      */
+    public static void bcast(String cacheName, Ignite ignite, IgniteRunnable run) {
+        ignite.compute(ignite.cluster().forDataNodes(cacheName)).broadcast(run);
+    }
+
+    /**
+     * Broadcast runnable to data nodes of given cache.
+     * @param cacheName Cache name.
+     * @param run Runnable.
+     */
     public static void bcast(String cacheName, IgniteRunnable run) {
-        ignite().compute(ignite().cluster().forCacheNodes(cacheName)).broadcast(run);
+        bcast(cacheName, ignite(), run);
     }
 
     /**
@@ -537,6 +653,18 @@ public class CacheUtils {
      * @param <A> Type returned by the callable.
      */
     public static <A> Collection<A> bcast(String cacheName, IgniteCallable<A> call) {
-        return ignite().compute(ignite().cluster().forCacheNodes(cacheName)).broadcast(call);
+        return bcast(cacheName, ignite(), call);
+    }
+
+    /**
+     * Broadcast callable to data nodes of given cache.
+     * @param cacheName Cache name.
+     * @param ignite Ignite instance.
+     * @param call Callable to broadcast.
+     * @param <A> Type of callable result.
+     * @return Results of callable from each node.
+     */
+    public static <A> Collection<A> bcast(String cacheName, Ignite ignite, IgniteCallable<A> call) {
+        return ignite.compute(ignite.cluster().forDataNodes(cacheName)).broadcast(call);
     }
 }

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/MatrixCacheKey.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/MatrixCacheKey.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/MatrixCacheKey.java
index 669e9a4..0242560 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/MatrixCacheKey.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/MatrixCacheKey.java
@@ -17,7 +17,7 @@
 
 package org.apache.ignite.ml.math.distributed.keys;
 
-import org.apache.ignite.lang.IgniteUuid;
+import java.util.UUID;
 
 /**
  * Base matrix cache key.
@@ -26,10 +26,10 @@ public interface MatrixCacheKey {
     /**
      * @return matrix id.
      */
-    public IgniteUuid matrixId();
+    public UUID matrixId();
 
     /**
      * @return affinity key.
      */
-    public IgniteUuid affinityKey();
+    public Object affinityKey();
 }

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/BlockMatrixKey.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/BlockMatrixKey.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/BlockMatrixKey.java
index 2edd9cb..cc8c488 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/BlockMatrixKey.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/BlockMatrixKey.java
@@ -21,6 +21,7 @@ import java.io.Externalizable;
 import java.io.IOException;
 import java.io.ObjectInput;
 import java.io.ObjectOutput;
+import java.util.UUID;
 import org.apache.ignite.binary.BinaryObjectException;
 import org.apache.ignite.binary.BinaryRawReader;
 import org.apache.ignite.binary.BinaryRawWriter;
@@ -47,7 +48,7 @@ public class BlockMatrixKey implements org.apache.ignite.ml.math.distributed.key
     /** Block col ID */
     private long blockIdCol;
     /** Matrix ID */
-    private IgniteUuid matrixUuid;
+    private UUID matrixUuid;
     /** Block affinity key. */
     private IgniteUuid affinityKey;
 
@@ -64,7 +65,7 @@ public class BlockMatrixKey implements org.apache.ignite.ml.math.distributed.key
      * @param matrixUuid Matrix uuid.
      * @param affinityKey Affinity key.
      */
-    public BlockMatrixKey(long rowId, long colId,  IgniteUuid matrixUuid, @Nullable IgniteUuid affinityKey) {
+    public BlockMatrixKey(long rowId, long colId,  UUID matrixUuid, @Nullable IgniteUuid affinityKey) {
         assert rowId >= 0;
         assert colId >= 0;
         assert matrixUuid != null;
@@ -86,7 +87,7 @@ public class BlockMatrixKey implements org.apache.ignite.ml.math.distributed.key
     }
 
     /** {@inheritDoc} */
-    @Override public IgniteUuid matrixId() {
+    @Override public UUID matrixId() {
         return matrixUuid;
     }
 
@@ -97,7 +98,7 @@ public class BlockMatrixKey implements org.apache.ignite.ml.math.distributed.key
 
     /** {@inheritDoc} */
     @Override public void writeExternal(ObjectOutput out) throws IOException {
-        U.writeGridUuid(out, matrixUuid);
+        out.writeObject(matrixUuid);
         U.writeGridUuid(out, affinityKey);
         out.writeLong(blockIdRow);
         out.writeLong(blockIdCol);
@@ -105,7 +106,7 @@ public class BlockMatrixKey implements org.apache.ignite.ml.math.distributed.key
 
     /** {@inheritDoc} */
     @Override public void readExternal(ObjectInput in) throws IOException, ClassNotFoundException {
-        matrixUuid = U.readGridUuid(in);
+        matrixUuid = (UUID)in.readObject();
         affinityKey = U.readGridUuid(in);
         blockIdRow = in.readLong();
         blockIdCol = in.readLong();
@@ -115,7 +116,7 @@ public class BlockMatrixKey implements org.apache.ignite.ml.math.distributed.key
     @Override public void writeBinary(BinaryWriter writer) throws BinaryObjectException {
         BinaryRawWriter out = writer.rawWriter();
 
-        BinaryUtils.writeIgniteUuid(out, matrixUuid);
+        out.writeUuid(matrixUuid);
         BinaryUtils.writeIgniteUuid(out, affinityKey);
         out.writeLong(blockIdRow);
         out.writeLong(blockIdCol);
@@ -125,7 +126,7 @@ public class BlockMatrixKey implements org.apache.ignite.ml.math.distributed.key
     @Override public void readBinary(BinaryReader reader) throws BinaryObjectException {
         BinaryRawReader in = reader.rawReader();
 
-        matrixUuid = BinaryUtils.readIgniteUuid(in);
+        matrixUuid = in.readUuid();
         affinityKey = BinaryUtils.readIgniteUuid(in);
         blockIdRow = in.readLong();
         blockIdCol = in.readLong();
@@ -160,6 +161,4 @@ public class BlockMatrixKey implements org.apache.ignite.ml.math.distributed.key
     @Override public String toString() {
         return S.toString(BlockMatrixKey.class, this);
     }
-
-
 }

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/SparseMatrixKey.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/SparseMatrixKey.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/SparseMatrixKey.java
index 0c34c8b..aa5e0ad 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/SparseMatrixKey.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/distributed/keys/impl/SparseMatrixKey.java
@@ -21,30 +21,24 @@ import java.io.Externalizable;
 import java.io.IOException;
 import java.io.ObjectInput;
 import java.io.ObjectOutput;
-import org.apache.ignite.binary.BinaryObjectException;
-import org.apache.ignite.binary.BinaryRawReader;
-import org.apache.ignite.binary.BinaryRawWriter;
-import org.apache.ignite.binary.BinaryReader;
-import org.apache.ignite.binary.BinaryWriter;
-import org.apache.ignite.binary.Binarylizable;
-import org.apache.ignite.internal.binary.BinaryUtils;
+import java.util.UUID;
+import org.apache.ignite.cache.affinity.AffinityKeyMapped;
 import org.apache.ignite.internal.util.typedef.F;
 import org.apache.ignite.internal.util.typedef.internal.S;
-import org.apache.ignite.internal.util.typedef.internal.U;
-import org.apache.ignite.lang.IgniteUuid;
 import org.apache.ignite.ml.math.distributed.keys.RowColMatrixKey;
 import org.apache.ignite.ml.math.impls.matrix.SparseDistributedMatrix;
 
 /**
  * Key implementation for {@link SparseDistributedMatrix}.
  */
-public class SparseMatrixKey implements RowColMatrixKey, Externalizable, Binarylizable {
+public class SparseMatrixKey implements RowColMatrixKey, Externalizable {
     /** */
     private int idx;
     /** */
-    private IgniteUuid matrixId;
+    private UUID matrixId;
     /** */
-    private IgniteUuid affinityKey;
+    @AffinityKeyMapped
+    private Object affinityKey;
 
     /**
      * Default constructor (required by Externalizable).
@@ -56,7 +50,7 @@ public class SparseMatrixKey implements RowColMatrixKey, Externalizable, Binaryl
     /**
      * Build Key.
      */
-    public SparseMatrixKey(int idx, IgniteUuid matrixId, IgniteUuid affinityKey) {
+    public SparseMatrixKey(int idx, UUID matrixId, Object affinityKey) {
         assert idx >= 0 : "Index must be positive.";
         assert matrixId != null : "Matrix id can`t be null.";
 
@@ -71,54 +65,35 @@ public class SparseMatrixKey implements RowColMatrixKey, Externalizable, Binaryl
     }
 
     /** {@inheritDoc} */
-    @Override public IgniteUuid matrixId() {
+    @Override public UUID matrixId() {
         return matrixId;
     }
 
     /** {@inheritDoc} */
-    @Override public IgniteUuid affinityKey() {
+    @Override public Object affinityKey() {
         return affinityKey;
     }
 
     /** {@inheritDoc} */
     @Override public void writeExternal(ObjectOutput out) throws IOException {
-        U.writeGridUuid(out, matrixId);
-        U.writeGridUuid(out, affinityKey);
+//        U.writeGridUuid(out, matrixId);
+        out.writeObject(matrixId);
+        out.writeObject(affinityKey);
         out.writeInt(idx);
     }
 
     /** {@inheritDoc} */
     @Override public void readExternal(ObjectInput in) throws IOException, ClassNotFoundException {
-        matrixId = U.readGridUuid(in);
-        affinityKey = U.readGridUuid(in);
-        idx = in.readInt();
-    }
-
-    /** {@inheritDoc} */
-    @Override public void writeBinary(BinaryWriter writer) throws BinaryObjectException {
-        BinaryRawWriter out = writer.rawWriter();
-
-        BinaryUtils.writeIgniteUuid(out, matrixId);
-        BinaryUtils.writeIgniteUuid(out, affinityKey);
-        out.writeInt(idx);
-    }
-
-    /** {@inheritDoc} */
-    @Override public void readBinary(BinaryReader reader) throws BinaryObjectException {
-        BinaryRawReader in = reader.rawReader();
-
-        matrixId = BinaryUtils.readIgniteUuid(in);
-        affinityKey = BinaryUtils.readIgniteUuid(in);
+        matrixId = (UUID)in.readObject();
+        affinityKey = in.readObject();
         idx = in.readInt();
     }
 
     /** {@inheritDoc} */
     @Override public int hashCode() {
-        int res = 1;
-
-        res += res * 37 + matrixId.hashCode();
-        res += res * 37 + idx;
-
+        int res = idx;
+        res = 31 * res + (matrixId != null ? matrixId.hashCode() : 0);
+        res = 31 * res + (affinityKey != null ? affinityKey.hashCode() : 0);
         return res;
     }
 

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/Functions.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/Functions.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/Functions.java
index 022dd04..0b4ad12 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/Functions.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/Functions.java
@@ -17,7 +17,9 @@
 
 package org.apache.ignite.ml.math.functions;
 
+import java.util.Comparator;
 import java.util.List;
+import java.util.function.BiFunction;
 import org.apache.ignite.lang.IgniteBiTuple;
 
 /**
@@ -75,6 +77,30 @@ public final class Functions {
     /** Function that returns {@code max(abs(a), abs(b))}. */
     public static final IgniteBiFunction<Double, Double, Double> MAX_ABS = (a, b) -> Math.max(Math.abs(a), Math.abs(b));
 
+    /**
+     * Generic 'max' function.
+     * @param a First object to compare.
+     * @param b Second object to compare.
+     * @param f Comparator.
+     * @param <T> Type of objects to compare.
+     * @return Maximum between {@code a} and {@code b} in terms of comparator {@code f}.
+     */
+    public static <T> T MAX_GENERIC(T a, T b, Comparator<T> f) {
+        return f.compare(a, b) > 0 ? a : b;
+    }
+
+    /**
+     * Generic 'min' function.
+     * @param a First object to compare.
+     * @param b Second object to compare.
+     * @param f Comparator.
+     * @param <T> Type of objects to compare.
+     * @return Minimum between {@code a} and {@code b} in terms of comparator {@code f}.
+     */
+    public static <T> T MIN_GENERIC(T a, T b, Comparator<T> f) {
+        return f.compare(a, b) > 0 ? a : b;
+    }
+
     /** Function that returns {@code min(abs(a), abs(b))}. */
     public static final IgniteBiFunction<Double, Double, Double> MIN_ABS = (a, b) -> Math.min(Math.abs(a), Math.abs(b));
 
@@ -185,4 +211,16 @@ public final class Functions {
                 return Math.pow(a, b);
         };
     }
+
+    /**
+     * Curry bifunction.
+     * @param f Bifunction to curry.
+     * @param <A> Type of first argument of {@code f}.
+     * @param <B> Type of second argument of {@code f}.
+     * @param <C> Return type of {@code f}.
+     * @return Curried bifunction.
+     */
+    public static <A, B, C> IgniteCurriedBiFunction<A, B, C> curry(BiFunction<A, B, C> f) {
+        return a -> b -> f.apply(a, b);
+    }
 }

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteBinaryOperator.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteBinaryOperator.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteBinaryOperator.java
new file mode 100644
index 0000000..1170b67
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteBinaryOperator.java
@@ -0,0 +1,29 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.math.functions;
+
+import java.io.Serializable;
+import java.util.function.BinaryOperator;
+
+/**
+ * Serializable binary operator.
+ *
+ * @see java.util.function.BinaryOperator
+ */
+public interface IgniteBinaryOperator<A> extends BinaryOperator<A>, Serializable {
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteCurriedBiFunction.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteCurriedBiFunction.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteCurriedBiFunction.java
new file mode 100644
index 0000000..3dd8490
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteCurriedBiFunction.java
@@ -0,0 +1,29 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.math.functions;
+
+import java.io.Serializable;
+import java.util.function.BiFunction;
+
+/**
+ * Serializable binary function.
+ *
+ * @see BiFunction
+ */
+public interface IgniteCurriedBiFunction<A, B, T> extends IgniteFunction<A, IgniteFunction<B, T>>, Serializable {
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteSupplier.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteSupplier.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteSupplier.java
new file mode 100644
index 0000000..8c05b75
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteSupplier.java
@@ -0,0 +1,30 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.math.functions;
+
+import java.io.Serializable;
+import java.util.function.Supplier;
+
+/**
+ * Serializable supplier.
+ *
+ * @see java.util.function.Consumer
+ */
+@FunctionalInterface
+public interface IgniteSupplier<T> extends Supplier<T>, Serializable {
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteToDoubleFunction.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteToDoubleFunction.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteToDoubleFunction.java
new file mode 100644
index 0000000..59a8bf3
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/functions/IgniteToDoubleFunction.java
@@ -0,0 +1,25 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.math.functions;
+
+import java.io.Serializable;
+import java.util.function.ToDoubleFunction;
+
+@FunctionalInterface
+public interface IgniteToDoubleFunction<T> extends ToDoubleFunction<T>, Serializable {
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseBlockDistributedMatrix.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseBlockDistributedMatrix.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseBlockDistributedMatrix.java
index 3d542bc..e829168 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseBlockDistributedMatrix.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseBlockDistributedMatrix.java
@@ -20,13 +20,13 @@ package org.apache.ignite.ml.math.impls.matrix;
 import java.util.Collection;
 import java.util.List;
 import java.util.Map;
+import java.util.UUID;
 import org.apache.ignite.Ignite;
 import org.apache.ignite.IgniteCache;
 import org.apache.ignite.Ignition;
 import org.apache.ignite.cache.affinity.Affinity;
 import org.apache.ignite.cluster.ClusterNode;
 import org.apache.ignite.internal.util.lang.IgnitePair;
-import org.apache.ignite.lang.IgniteUuid;
 import org.apache.ignite.ml.math.Matrix;
 import org.apache.ignite.ml.math.StorageConstants;
 import org.apache.ignite.ml.math.Vector;
@@ -190,7 +190,7 @@ public class SparseBlockDistributedMatrix extends AbstractMatrix implements Stor
     }
 
     /** */
-    private IgniteUuid getUUID() {
+    private UUID getUUID() {
         return ((BlockMatrixStorage)getStorage()).getUUID();
     }
 

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseDistributedMatrix.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseDistributedMatrix.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseDistributedMatrix.java
index 9a18f8b..594aebc 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseDistributedMatrix.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/matrix/SparseDistributedMatrix.java
@@ -19,6 +19,7 @@ package org.apache.ignite.ml.math.impls.matrix;
 
 import java.util.Collection;
 import java.util.Map;
+import java.util.UUID;
 import org.apache.ignite.Ignite;
 import org.apache.ignite.IgniteCache;
 import org.apache.ignite.Ignition;
@@ -211,7 +212,7 @@ public class SparseDistributedMatrix extends AbstractMatrix implements StorageCo
     }
 
     /** */
-    public IgniteUuid getUUID() {
+    public UUID getUUID() {
         return ((SparseDistributedMatrixStorage)getStorage()).getUUID();
     }
 }

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/BlockMatrixStorage.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/BlockMatrixStorage.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/BlockMatrixStorage.java
index 0d5cf0a..cd76e5a 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/BlockMatrixStorage.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/BlockMatrixStorage.java
@@ -24,6 +24,7 @@ import java.util.HashSet;
 import java.util.LinkedList;
 import java.util.List;
 import java.util.Set;
+import java.util.UUID;
 import org.apache.ignite.IgniteCache;
 import org.apache.ignite.Ignition;
 import org.apache.ignite.cache.CacheAtomicityMode;
@@ -32,7 +33,6 @@ import org.apache.ignite.cache.CachePeekMode;
 import org.apache.ignite.cache.CacheWriteSynchronizationMode;
 import org.apache.ignite.configuration.CacheConfiguration;
 import org.apache.ignite.internal.util.lang.IgnitePair;
-import org.apache.ignite.internal.util.typedef.internal.U;
 import org.apache.ignite.lang.IgniteUuid;
 import org.apache.ignite.ml.math.MatrixStorage;
 import org.apache.ignite.ml.math.StorageConstants;
@@ -59,7 +59,7 @@ public class BlockMatrixStorage extends CacheUtils implements MatrixStorage, Sto
     /** Amount of columns in the matrix. */
     private int cols;
     /** Matrix uuid. */
-    private IgniteUuid uuid;
+    private UUID uuid;
     /** Block size about 8 KB of data. */
     private int maxBlockEdge = MAX_BLOCK_SIZE;
 
@@ -92,7 +92,7 @@ public class BlockMatrixStorage extends CacheUtils implements MatrixStorage, Sto
 
         cache = newCache();
 
-        uuid = IgniteUuid.randomUuid();
+        uuid = UUID.randomUUID();
     }
 
     /**
@@ -152,7 +152,7 @@ public class BlockMatrixStorage extends CacheUtils implements MatrixStorage, Sto
         out.writeInt(cols);
         out.writeInt(blocksInRow);
         out.writeInt(blocksInCol);
-        U.writeGridUuid(out, uuid);
+        out.writeObject(uuid);
         out.writeUTF(cache.getName());
     }
 
@@ -162,7 +162,7 @@ public class BlockMatrixStorage extends CacheUtils implements MatrixStorage, Sto
         cols = in.readInt();
         blocksInRow = in.readInt();
         blocksInCol = in.readInt();
-        uuid = U.readGridUuid(in);
+        uuid = (UUID)in.readObject();
         cache = ignite().getOrCreateCache(in.readUTF());
     }
 
@@ -201,7 +201,7 @@ public class BlockMatrixStorage extends CacheUtils implements MatrixStorage, Sto
      *
      * @return storage UUID.
      */
-    public IgniteUuid getUUID() {
+    public UUID getUUID() {
         return uuid;
     }
 

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/SparseDistributedMatrixStorage.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/SparseDistributedMatrixStorage.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/SparseDistributedMatrixStorage.java
index 95852b7..c40e73d 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/SparseDistributedMatrixStorage.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/impls/storage/matrix/SparseDistributedMatrixStorage.java
@@ -24,6 +24,7 @@ import java.io.ObjectInput;
 import java.io.ObjectOutput;
 import java.util.Map;
 import java.util.Set;
+import java.util.UUID;
 import java.util.stream.Collectors;
 import java.util.stream.IntStream;
 import org.apache.ignite.IgniteCache;
@@ -33,7 +34,6 @@ import org.apache.ignite.cache.CacheMode;
 import org.apache.ignite.cache.CachePeekMode;
 import org.apache.ignite.cache.CacheWriteSynchronizationMode;
 import org.apache.ignite.configuration.CacheConfiguration;
-import org.apache.ignite.lang.IgniteUuid;
 import org.apache.ignite.ml.math.MatrixStorage;
 import org.apache.ignite.ml.math.StorageConstants;
 import org.apache.ignite.ml.math.distributed.CacheUtils;
@@ -57,7 +57,7 @@ public class SparseDistributedMatrixStorage extends CacheUtils implements Matrix
     /** Random or sequential access mode. */
     private int acsMode;
     /** Matrix uuid. */
-    private IgniteUuid uuid;
+    private UUID uuid;
 
     /** Actual distributed storage. */
     private IgniteCache<
@@ -91,7 +91,7 @@ public class SparseDistributedMatrixStorage extends CacheUtils implements Matrix
 
         cache = newCache();
 
-        uuid = IgniteUuid.randomUuid();
+        uuid = UUID.randomUUID();
     }
 
     /**
@@ -115,6 +115,9 @@ public class SparseDistributedMatrixStorage extends CacheUtils implements Matrix
         // Cache is partitioned.
         cfg.setCacheMode(CacheMode.PARTITIONED);
 
+        // TODO: Possibly we should add a fix of https://issues.apache.org/jira/browse/IGNITE-6862 here commented below.
+        // cfg.setReadFromBackup(false);
+
         // Random cache name.
         cfg.setName(CACHE_NAME);
 
@@ -205,7 +208,7 @@ public class SparseDistributedMatrixStorage extends CacheUtils implements Matrix
 
     /** Build cache key for row/column. */
     public RowColMatrixKey getCacheKey(int idx) {
-        return new SparseMatrixKey(idx, uuid, null);
+        return new SparseMatrixKey(idx, uuid, idx);
     }
 
     /** {@inheritDoc} */
@@ -239,7 +242,7 @@ public class SparseDistributedMatrixStorage extends CacheUtils implements Matrix
         cols = in.readInt();
         acsMode = in.readInt();
         stoMode = in.readInt();
-        uuid = (IgniteUuid)in.readObject();
+        uuid = (UUID)in.readObject();
         cache = ignite().getOrCreateCache(in.readUTF());
     }
 
@@ -304,7 +307,7 @@ public class SparseDistributedMatrixStorage extends CacheUtils implements Matrix
     }
 
     /** */
-    public IgniteUuid getUUID() {
+    public UUID getUUID() {
         return uuid;
     }
 
@@ -312,7 +315,7 @@ public class SparseDistributedMatrixStorage extends CacheUtils implements Matrix
     @Override public Set<RowColMatrixKey> getAllKeys() {
         int range = stoMode == ROW_STORAGE_MODE ? rows : cols;
 
-        return IntStream.range(0, range).mapToObj(i -> new SparseMatrixKey(i, getUUID(), null)).collect(Collectors.toSet());
+        return IntStream.range(0, range).mapToObj(i -> new SparseMatrixKey(i, getUUID(), i)).collect(Collectors.toSet());
     }
 
     /** {@inheritDoc} */

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/structures/LabeledVector.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/structures/LabeledVector.java b/modules/ml/src/main/java/org/apache/ignite/ml/structures/LabeledVector.java
new file mode 100644
index 0000000..51b973a
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/structures/LabeledVector.java
@@ -0,0 +1,63 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.structures;
+
+import org.apache.ignite.ml.math.Vector;
+
+/**
+ * Class for vector with label.
+ *
+ * @param <V> Some class extending {@link Vector}.
+ * @param <T> Type of label.
+ */
+public class LabeledVector<V extends Vector, T> {
+    /** Vector. */
+    private final V vector;
+
+    /** Label. */
+    private final T lb;
+
+    /**
+     * Construct labeled vector.
+     *
+     * @param vector Vector.
+     * @param lb Label.
+     */
+    public LabeledVector(V vector, T lb) {
+        this.vector = vector;
+        this.lb = lb;
+    }
+
+    /**
+     * Get the vector.
+     *
+     * @return Vector.
+     */
+    public V vector() {
+        return vector;
+    }
+
+    /**
+     * Get the label.
+     *
+     * @return Label.
+     */
+    public T label() {
+        return lb;
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/structures/LabeledVectorDouble.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/structures/LabeledVectorDouble.java b/modules/ml/src/main/java/org/apache/ignite/ml/structures/LabeledVectorDouble.java
new file mode 100644
index 0000000..4ef9eae
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/structures/LabeledVectorDouble.java
@@ -0,0 +1,46 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.structures;
+
+import org.apache.ignite.ml.math.Vector;
+
+/**
+ * Labeled vector specialized to double label.
+ *
+ * @param <V> Type of vector.
+ */
+public class LabeledVectorDouble<V extends Vector> extends LabeledVector<V, Double> {
+    /**
+     * Construct LabeledVectorDouble.
+     *
+     * @param vector Vector.
+     * @param lb Label.
+     */
+    public LabeledVectorDouble(V vector, Double lb) {
+        super(vector, lb);
+    }
+
+    /**
+     * Get label as double.
+     *
+     * @return label as double.
+     */
+    public double doubleLabel() {
+        return label();
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/structures/package-info.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/structures/package-info.java b/modules/ml/src/main/java/org/apache/ignite/ml/structures/package-info.java
new file mode 100644
index 0000000..ec9d79e
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/structures/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+/**
+ * <!-- Package description. -->
+ * Contains some utility structures.
+ */
+package org.apache.ignite.ml.structures;
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/trees/CategoricalRegionInfo.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/trees/CategoricalRegionInfo.java b/modules/ml/src/main/java/org/apache/ignite/ml/trees/CategoricalRegionInfo.java
new file mode 100644
index 0000000..3ae474e
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/trees/CategoricalRegionInfo.java
@@ -0,0 +1,72 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.trees;
+
+import java.io.Externalizable;
+import java.io.IOException;
+import java.io.ObjectInput;
+import java.io.ObjectOutput;
+import java.util.BitSet;
+
+/**
+ * Information about categorical region.
+ */
+public class CategoricalRegionInfo extends RegionInfo implements Externalizable {
+    /**
+     * Bitset representing categories of this region.
+     */
+    private BitSet cats;
+
+    /**
+     * @param impurity Impurity of region.
+     * @param cats Bitset representing categories of this region.
+     */
+    public CategoricalRegionInfo(double impurity, BitSet cats) {
+        super(impurity);
+
+        this.cats = cats;
+    }
+
+    /**
+     * No-op constructor for serialization/deserialization.
+     */
+    public CategoricalRegionInfo() {
+        // No-op
+    }
+
+    /**
+     * Get bitset representing categories of this region.
+     *
+     * @return Bitset representing categories of this region.
+     */
+    public BitSet cats() {
+        return cats;
+    }
+
+    /** {@inheritDoc} */
+    @Override public void writeExternal(ObjectOutput out) throws IOException {
+        super.writeExternal(out);
+        out.writeObject(cats);
+    }
+
+    /** {@inheritDoc} */
+    @Override public void readExternal(ObjectInput in) throws IOException, ClassNotFoundException {
+        super.readExternal(in);
+        cats = (BitSet)in.readObject();
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/db7697b1/modules/ml/src/main/java/org/apache/ignite/ml/trees/CategoricalSplitInfo.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/trees/CategoricalSplitInfo.java b/modules/ml/src/main/java/org/apache/ignite/ml/trees/CategoricalSplitInfo.java
new file mode 100644
index 0000000..94cb1e8
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/trees/CategoricalSplitInfo.java
@@ -0,0 +1,68 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.trees;
+
+import java.util.BitSet;
+import org.apache.ignite.ml.trees.nodes.CategoricalSplitNode;
+import org.apache.ignite.ml.trees.nodes.SplitNode;
+import org.apache.ignite.ml.trees.trainers.columnbased.vectors.SplitInfo;
+
+/**
+ * Information about split of categorical feature.
+ *
+ * @param <D> Class representing information of left and right subregions.
+ */
+public class CategoricalSplitInfo<D extends RegionInfo> extends SplitInfo<D> {
+    /** Bitset indicating which vectors are assigned to left subregion. */
+    private final BitSet bs;
+
+    /**
+     * @param regionIdx Index of region which is split.
+     * @param leftData Data of left subregion.
+     * @param rightData Data of right subregion.
+     * @param bs Bitset indicating which vectors are assigned to left subregion.
+     */
+    public CategoricalSplitInfo(int regionIdx, D leftData, D rightData,
+        BitSet bs) {
+        super(regionIdx, leftData, rightData);
+        this.bs = bs;
+    }
+
+    /** {@inheritDoc} */
+    @Override public SplitNode createSplitNode(int featureIdx) {
+        return new CategoricalSplitNode(featureIdx, bs);
+    }
+
+    /**
+     * Get bitset indicating which vectors are assigned to left subregion.
+     */
+    public BitSet bitSet() {
+        return bs;
+    }
+
+    /** {@inheritDoc} */
+    @Override public String toString() {
+        return "CategoricalSplitInfo [" +
+            "infoGain=" + infoGain +
+            ", regionIdx=" + regionIdx +
+            ", leftData=" + leftData +
+            ", bs=" + bs +
+            ", rightData=" + rightData +
+            ']';
+    }
+}


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