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From: trohrmann@apache.org
To: commits@flink.apache.org
Date: Fri, 08 May 2015 08:19:11 -0000
Message-Id: <e6d438df1e6348d89c9ac977a2621fe7@git.apache.org>
Subject: [1/2] flink git commit: [ml] [docs] Adds distance formulas to
 documentation. Automatically include latex_commands.html with mathjax
 markdown files.

Repository: flink
Updated Branches:
  refs/heads/master ce2163e6c -> f0b45c450


[ml] [docs] Adds distance formulas to documentation. Automatically include latex_commands.html with mathjax markdown files.


Project: http://git-wip-us.apache.org/repos/asf/flink/repo
Commit: http://git-wip-us.apache.org/repos/asf/flink/commit/778cda7a
Tree: http://git-wip-us.apache.org/repos/asf/flink/tree/778cda7a
Diff: http://git-wip-us.apache.org/repos/asf/flink/diff/778cda7a

Branch: refs/heads/master
Commit: 778cda7a57540a65b9f5e0c48e32bcadbc2022b7
Parents: ce2163e
Author: Till Rohrmann <trohrmann@apache.org>
Authored: Thu May 7 16:09:26 2015 +0200
Committer: Till Rohrmann <trohrmann@apache.org>
Committed: Fri May 8 10:18:55 2015 +0200

----------------------------------------------------------------------
 docs/_includes/latex_commands.html | 35 ++++++++++++++++++
 docs/_layouts/base.html            |  4 +++
 docs/libs/ml/distance_metrics.md   | 64 +++++++++++++++++++++++++++++----
 3 files changed, 96 insertions(+), 7 deletions(-)
----------------------------------------------------------------------


http://git-wip-us.apache.org/repos/asf/flink/blob/778cda7a/docs/_includes/latex_commands.html
----------------------------------------------------------------------
diff --git a/docs/_includes/latex_commands.html b/docs/_includes/latex_commands.html
new file mode 100644
index 0000000..a070b68
--- /dev/null
+++ b/docs/_includes/latex_commands.html
@@ -0,0 +1,35 @@
+<!--
+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.
+-->
+$$
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\x}{\mathbf{x}}
+\newcommand{\y}{\mathbf{y}}
+\newcommand{\wv}{\mathbf{w}}
+\newcommand{\av}{\mathbf{\alpha}}
+\newcommand{\bv}{\mathbf{b}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\id}{\mathbf{I}}
+\newcommand{\ind}{\mathbf{1}}
+\newcommand{\0}{\mathbf{0}}
+\newcommand{\unit}{\mathbf{e}}
+\newcommand{\one}{\mathbf{1}}
+\newcommand{\zero}{\mathbf{0}}
+\newcommand\rfrac[2]{^{#1}\!/_{#2}}
+$$
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/flink/blob/778cda7a/docs/_layouts/base.html
----------------------------------------------------------------------
diff --git a/docs/_layouts/base.html b/docs/_layouts/base.html
index e283354..b5a2e7b 100644
--- a/docs/_layouts/base.html
+++ b/docs/_layouts/base.html
@@ -51,6 +51,10 @@ under the License.
     {% comment %} Includes are found in the _includes directory. {% endcomment %}
     {% include navbar.html %}
 
+    {% if page.mathjax %}
+    {% include latex_commands.html %}
+    {% endif %}
+
     <!-- Main content. -->
     <div class="container">
       {% comment %}

http://git-wip-us.apache.org/repos/asf/flink/blob/778cda7a/docs/libs/ml/distance_metrics.md
----------------------------------------------------------------------
diff --git a/docs/libs/ml/distance_metrics.md b/docs/libs/ml/distance_metrics.md
index 9d87fa1..4dfd1af 100644
--- a/docs/libs/ml/distance_metrics.md
+++ b/docs/libs/ml/distance_metrics.md
@@ -1,4 +1,5 @@
 ---
+mathjax: include
 title: Distance Metrics
 ---
 <!--
@@ -31,13 +32,62 @@ use other distance metric by implementing `DistanceMetric` trait.
 
 ## Built-in Implementations
 
-* Euclidean Distance
-* Squared Euclidean Distance
-* Cosine Distance
-* Tanimoto Distance
-* Chebyshev Distance
-* Manhattan Distance
-* Minkowski Distance
+Currently, FlinkML supports the following metrics:
+
+<table class="table table-bordered">
+    <thead>
+      <tr>
+        <th class="text-left" style="width: 20%">Metric</th>
+        <th class="text-center">Description</th>
+      </tr>
+    </thead>
+
+    <tbody>
+      <tr>
+        <td><strong>Euclidean Distance</strong></td>
+        <td>
+          $$d(\x, \y) = \sqrt{\sum_{i=1}^n \left(x_i - y_i \right)^2}$$
+        </td>
+      </tr>
+      <tr>
+        <td><strong>Squared Euclidean Distance</strong></td>
+        <td>
+          $$d(\x, \y) = \sum_{i=1}^n \left(x_i - y_i \right)^2$$
+        </td>
+      </tr>
+      <tr>
+        <td><strong>Cosine Similarity</strong></td>
+        <td>
+          $$d(\x, \y) = 1 - \frac{\x^T \y}{\Vert \x \Vert \Vert \y \Vert}$$
+        </td>
+      </tr>
+      <tr>
+        <td><strong>Chebyshev Distance</strong></td>
+        <td>
+          $$d(\x, \y) = \max_{i}\left(\left \vert x_i - y_i \right\vert \right)$$
+        </td>
+      </tr>
+      <tr>
+        <td><strong>Manhattan Distance</strong></td>
+        <td>
+          $$d(\x, \y) = \sum_{i=1}^n \left\vert x_i - y_i \right\vert$$
+        </td>
+      </tr>
+      <tr>
+        <td><strong>Minkowski Distance</strong></td>
+        <td>
+          $$d(\x, \y) = \left( \sum_{i=1}^{n} \left( x_i - y_i \right)^p \right)^{\rfrac{1}{p}}$$
+        </td>
+      </tr>
+      <tr>
+        <td><strong>Tanimoto Distance</strong></td>
+        <td>
+          $$d(\x, \y) = 1 - \frac{\x^T\y}{\Vert \x \Vert^2 + \Vert \y \Vert^2 - \x^T\y}$$ 
+          with $\x$ and $\y$ being bit-vectors
+        </td>
+      </tr>
+    </tbody>
+  </table>
 
 ## Custom Implementation