• PCA(主成分分析法，Principal Components Analysis)
• SVD(奇异值分解法，Singular Value Decomposition)

0 运行环境

export SPARK_HOME=/Users/erichan/Garden/spark-1.5.1-bin-hadoop2.6cd $SPARK_HOMEbin/spark-shell --name my_mlib --packages org.jblas:jblas:1.2.4-SNAPSHOT --driver-memory 4G --executor-memory 4G --driver-cores 2

1 抽取特征

1.1 载入脸部数据

val PATH = "/Users/erichan/sourcecode/book/Spark机器学习"val path = PATH+"/lfw/*"val rdd = sc.wholeTextFiles(path)val files = rdd.map { case (fileName, content) => fileName.replace("file:", "") }println(files.count)

1054

1.2 可视化脸部数据(python)

ipython -pylab

PATH = "/Users/erichan/sourcecode/book/Spark机器学习"path = PATH+"/lfw/Aaron_Eckhart/Aaron_Eckhart_0001.jpg"ae = imread(path)imshow(ae)

tmpPath = "/tmp/aeGray.jpg"aeGary = imread(tmpPath)imshow(aeGary, cmap=plt.cm.gray)

1.3 提取脸部图片作为向量

1.3.1 载入图片

import java.awt.image.BufferedImagedef loadImageFromFile(path: String): BufferedImage = {    import javax.imageio.ImageIO    import java.io.File    ImageIO.read(new File(path))}val aePath = PATH+"/lfw/Aaron_Eckhart/Aaron_Eckhart_0001.jpg"val aeImage = loadImageFromFile(aePath)

1.3.2 转换灰度、改变尺寸

def processImage(image: BufferedImage, width: Int, height: Int): BufferedImage = {    val bwImage = new BufferedImage(width, height, BufferedImage.TYPE_BYTE_GRAY)    val g = bwImage.getGraphics()    g.drawImage(image, 0, 0, width, height, null)    g.dispose()    bwImage}val grayImage = processImage(aeImage, 100, 100)import javax.imageio.ImageIOimport java.io.FileImageIO.write(grayImage, "jpg", new File("/tmp/aeGray.jpg"))

1.3.3 提取特征向量

def getPixelsFromImage(image: BufferedImage): Array[Double] = {    val width = image.getWidth    val height = image.getHeight    val pixels = Array.ofDim[Double](width * height)    image.getData.getPixels(0, 0, width, height, pixels)    // pixels.map(p => p / 255.0)         // optionally scale to [0, 1] domain}// put all the functions togetherdef extractPixels(path: String, width: Int, height: Int): Array[Double] = {    val raw = loadImageFromFile(path)    val processed = processImage(raw, width, height)    getPixelsFromImage(processed)}val pixels = files.map(f => extractPixels(f, 50, 50))println(pixels.take(10).map(_.take(10).mkString("", ",", ", ...")).mkString("\n"))

1.0,1.0,1.0,1.0,1.0,1.0,2.0,1.0,1.0,1.0, ...

247.0,173.0,159.0,144.0,139.0,155.0,32.0,7.0,4.0,5.0, ...

253.0,254.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0, ...242.0,242.0,246.0,239.0,238.0,239.0,225.0,165.0,140.0,167.0, ...47.0,221.0,205.0,46.0,41.0,154.0,127.0,214.0,232.0,232.0, ...0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, ...75.0,76.0,72.0,72.0,72.0,74.0,71.0,78.0,54.0,26.0, ...25.0,27.0,24.0,22.0,26.0,27.0,19.0,16.0,22.0,25.0, ...240.0,240.0,240.0,240.0,240.0,240.0,240.0,240.0,240.0,240.0, ...0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, ...

import org.apache.spark.mllib.linalg.Vectorsval vectors = pixels.map(p => Vectors.dense(p))vectors.setName("image-vectors")vectors.cache

1.4 正则化

import org.apache.spark.mllib.feature.StandardScalerval scaler = new StandardScaler(withMean = true, withStd = false).fit(vectors)val scaledVectors = vectors.map(v => scaler.transform(v))

2 训练降维模型

2.1 前k个主成分

import org.apache.spark.mllib.linalg.Matriximport org.apache.spark.mllib.linalg.distributed.RowMatrixval matrix = new RowMatrix(scaledVectors)val K = 10val pc = matrix.computePrincipalComponents(K)val rows = pc.numRowsval cols = pc.numColsprintln(rows, cols)

(2500,10)

2.2 可视化特征脸

import breeze.linalg.DenseMatrixval pcBreeze = new DenseMatrix(rows, cols, pc.toArray)import breeze.linalg.csvwriteimport java.io.Filecsvwrite(new File("/tmp/pc.csv"), pcBreeze)

pc = np.loadtxt("/tmp/pc.csv", delimiter=",")print(pc.shape)def plot_gallery(images, h, w, n_row=2, n_col=5):    """Helper function to plot a gallery of portraits"""    plt.figure(figsize=(1.8 * n_col, 2.4 * n_row))    plt.subplots_adjust(bottom=0, left=.01, right=.99, top=.90, hspace=.35)    for i in range(n_row * n_col):        plt.subplot(n_row, n_col, i + 1)        plt.imshow(images[:, i].reshape((h, w)), cmap=plt.cm.gray)        plt.title("Eigenface %d" % (i + 1), size=12)        plt.xticks(())        plt.yticks(())plot_gallery(pc, 50, 50)

3 使用降维模型

3.1 PCA投影（图像矩阵x主成分矩阵）

val projected = matrix.multiply(pc)println(projected.numRows, projected.numCols)println(projected.rows.take(5).mkString("\n"))

3.2 PCA与SVD

val svd = matrix.computeSVD(10, computeU = true)println(s"U dimension: (${svd.U.numRows}, ${svd.U.numCols})")println(s"S dimension: (${svd.s.size}, )")println(s"V dimension: (${svd.V.numRows}, ${svd.V.numCols})")

U dimension: (1054, 10)

S dimension: (10, )

V dimension: (2500, 10)

def approxEqual(array1: Array[Double], array2: Array[Double], tolerance: Double = 1e-6): Boolean = {    // note we ignore sign of the principal component / singular vector elements    val bools = array1.zip(array2).map { case (v1, v2) => if (math.abs(math.abs(v1) - math.abs(v2)) > 1e-6) false else true }    bools.fold(true)(_ & _)}println(approxEqual(Array(1.0, 2.0, 3.0), Array(1.0, 2.0, 3.0)))println(approxEqual(Array(1.0, 2.0, 3.0), Array(3.0, 2.0, 1.0)))println(approxEqual(svd.V.toArray, pc.toArray))

true

false

true

// compare projectionsval breezeS = breeze.linalg.DenseVector(svd.s.toArray)val projectedSVD = svd.U.rows.map { v =>    val breezeV = breeze.linalg.DenseVector(v.toArray)    val multV = breezeV :* breezeS    Vectors.dense(multV.data)}projected.rows.zip(projectedSVD).map { case (v1, v2) => approxEqual(v1.toArray, v2.toArray) }.filter(b => true).count

4 评价降维模型

4.1 评估SVD的k值

val sValues = (1 to 5).map { i => matrix.computeSVD(i, computeU = false).s }val svd300 = matrix.computeSVD(300, computeU = false)val sMatrix = new DenseMatrix(1, 300, svd300.s.toArray)csvwrite(new File("/tmp/s.csv"), sMatrix)

s = np.loadtxt("/tmp/s.csv", delimiter=",")print(s.shape)plot(s)

plot(cumsum(s))plt.yscale('log')