主成分分析(Principal Component Analysis，PCA)， 將多個變數通過線性變換以選出較少個數重要變數的一種多

元統計分析方法.

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理論和資料見附錄

Spark 原始碼（mllib包）

實驗

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Spark 原始碼（mllib包）

/**
 * A feature transformer that projects vectors to a low-dimensional space using PCA.
 *	
 * @param k number of principal components
 */
@Since("1.4.0")
class PCA @Since("1.4.0") (@Since("1.4.0") val k: Int) {
  require(k > 0,
s"Number of principal components must be positive but got 
 
${k}")

  /**
   * Computes a [[PCAModel]] that contains the principal components of the input vectors.
   *
   * @param sources source vectors
   */
@Since("1.4.0")
  def fit(sources: RDD[Vector]): PCAModel = {
    require(k <= sources.first().size,
s"source vector size is ${sources.first().size} must be greater than k=
 
$k")

    val mat = new RowMatrix(sources)
    val (pc, explainedVariance) = mat.computePrincipalComponentsAndExplainedVariance(k)
    val densePC = pc match {
      case dm: DenseMatrix =>
        dm
      case sm: SparseMatrix =>
        /* Convert a sparse matrix to dense.
         *
         * RowMatrix.computePrincipalComponents always returns a dense matrix.
         * The following code is a safeguard.
         */
sm.toDense
      case m =>
        throw new IllegalArgumentException("Unsupported matrix format. Expected " +
          s"SparseMatrix or DenseMatrix. Instead got: ${m.getClass}")

    }
    val denseExplainedVariance = explainedVariance match {
      case dv: DenseVector =>
        dv
      case sv: SparseVector =>
        sv.toDense
    }
    new PCAModel(k, densePC, denseExplainedVariance)
  }

  /**
   * Java-friendly version of [[fit()]]
*/
@Since("1.4.0")
  def fit(sources: JavaRDD[Vector]): PCAModel = fit(sources.rdd)
}

/**
 * Model fitted by [[PCA]] that can project vectors to a low-dimensional space using PCA.
 *
 * @param k number of principal components.
 * @param pc a principal components Matrix. Each column is one principal component.
 */
@Since("1.4.0")
class PCAModel private[spark] (
    @Since("1.4.0") val k: Int,
@Since("1.4.0") val pc: DenseMatrix,
@Since("1.6.0") val explainedVariance: DenseVector) extends VectorTransformer {
  /**
   * Transform a vector by computed Principal Components.
   *
   * @param vector vector to be transformed.
   *               Vector must be the same length as the source vectors given to [[PCA.fit()]].
   * @return transformed vector. Vector will be of length k.
   */
@Since("1.4.0")
  override def transform(vector: Vector): Vector = {
    vector match {
      case dv: DenseVector =>
        pc.transpose.multiply(dv)
      case SparseVector(size, indices, values) =>
        /* SparseVector -> single row SparseMatrix */
val sm = Matrices.sparse(size, 1, Array(0, indices.length), indices, values).transpose
        val projection = sm.multiply(pc)
        Vectors.dense(projection.values)
      case _ =>
        throw new IllegalArgumentException("Unsupported vector format. Expected " +
          s"SparseVector or DenseVector. Instead got: ${vector.getClass}")
    }
  }
}

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SparkML實驗

import org.apache.log4j.{Level, Logger}
import org.apache.spark.mllib.feature.PCA
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.{SparkConf, SparkContext}


object myPCA {
  def main(args: Array[String]) {
    val conf = new SparkConf().setAppName("PCA example").setMaster("local")
    val sc = new SparkContext(conf)

    Logger.getLogger("org.apache.spark").setLevel(Level.ERROR)
    Logger.getLogger("org.eclipse.jetty.Server").setLevel(Level.OFF)

    val data = sc.textFile("/root/application/upload/pca2.data")
    //data.foreach(println)

    val parseData = data.map{ line =>
    val part = line.split(' ')
      Vectors.dense(part.map(_.toDouble))
    }

    val model = new PCA(3).fit(parseData)

    model.transform(parseData).foreach(println)
    //--------------------------------------------------------------------------
    /**
      * [-198.49935555431662,61.7455925014451,-33.61561582724634]
        [-142.6503762139188,42.83576581230462,-27.723300375043127]
        [-94.48444346449276,37.63137787042039,-18.467916687311757]
        [-93.78770648660057,53.13442729915277,-20.324679585348406]
        [-115.21309309209421,64.72629901491086,-24.068684431501]
        [-141.13717390563068,62.443549430022024,-32.15482042868974]
        [-139.84404002633448,85.49929177772042,-26.90430756804854]
        [-106.34627395862736,57.60589638943985,-23.47345414370614]
        [-254.30867520979697,40.87956572432333,-12.424267061380176]
        [-146.56200808994245,52.842236008590454,-16.703674457958243]
        [-170.42181527333886,63.27229377718993,-21.440842300235158]
        [-139.13974251002367,74.9052975468746,-12.130842693355147]
        [-131.03062483262897,72.29955746812841,-15.20705763790804]
        [-126.21628609915788,71.19600990352119,-11.411808043562743]
        [-120.23904415710874,39.83322827884836,-26.220672650471542]
        [-97.36990893617941,43.377395313806836,-17.568739657112463]
      */
    println("---------------------------------------------------")
    
    sc.stop()

  }
}

附錄

連結：http://pan.baidu.com/s/1dELByj3 密碼：wsnb