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From mengxr <...@git.apache.org>
Subject [GitHub] incubator-spark pull request: Principal Component Analysis
Date Mon, 24 Feb 2014 08:42:14 GMT
Github user mengxr commented on a diff in the pull request:

    https://github.com/apache/incubator-spark/pull/564#discussion_r9983939
  
    --- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/PCA.scala ---
    @@ -0,0 +1,119 @@
    +/*
    + * 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.spark.mllib.linalg
    +
    +import org.apache.spark.SparkContext
    +import org.apache.spark.SparkContext._
    +import org.apache.spark.rdd.RDD
    +
    +import org.apache.spark.mllib.util._
    +
    +
    +/**
    + * Class used to obtain principal components
    + */
    +class PCA {
    +  private var k: Int = 1
    +
    +  /**
    +   * Set the number of top-k principle components to return
    +   */
    +  def setK(k: Int): PCA = {
    +    this.k = k
    +    this
    +  }
    +
    +   /**
    +   * Compute PCA using the current set parameters
    +   */
    +  def compute(matrix: DenseMatrix): DenseMatrix = {
    +    computePCA(matrix, k)
    +  }
    +
    +  /**
    +  * Principal Component Analysis.
    +  * Computes the top k principal component coefficients for the m-by-n data matrix X.
    +  * Rows of X correspond to observations and columns correspond to variables. 
    +  * The coefficient matrix is n-by-k. Each column of coeff contains coefficients
    +  * for one principal component, and the columns are in descending 
    +  * order of component variance.
    +  * This function centers the data and uses the 
    +  * singular value decomposition (SVD) algorithm. 
    +  *
    +  * All input and output is expected in DenseMatrix format
    +  *
    +  * @param matrix dense matrix to perform pca on
    +  * @param k Recover k principal components
    +  * @return An nxk matrix of principal components
    +  */
    +  def computePCA(matrix: DenseMatrix, k: Int): DenseMatrix = {
    +    val m = matrix.m
    +    val n = matrix.n
    +
    +    if (m <= 0 || n <= 0) {
    +      throw new IllegalArgumentException("Expecting a well-formed matrix")
    +    }
    +
    +    // compute column sums and normalize matrix
    +    val rawData = matrix.rows.flatMap{
    +      x => Array.tabulate(x.data.size)(idx => MatrixEntry(x.i, idx, x.data(idx)))
    +    }
    +    val colSums = rawData.map(entry => (entry.j, entry.mval)).reduceByKey(_ + _)
    +    val data = rawData.map(entry => (entry.j, (entry.i, entry.mval))).join(colSums).map{
    +      case (col, ((row, mval), colsum)) =>
    +        MatrixEntry(row, col, (mval - colsum / m.toDouble) / Math.sqrt(n-1)) }
    --- End diff --
    
    It creates many small objects and breaks the data continuity of each row. The following
code should be adequate for computing column sums:
    ~~~
    def addi(a: Array[Double], b: Array[Double]): Array[Double] = ...
    val colsums = matrix.rows.fold(new Array[Double](matrix.n))(addi)
    ~~~
    I ran a small test of size 1000000x100, where it is about 50x faster than flat-mapping
rows to entries and then reducing by column indices.


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