Spark MLlib基本算法【相关性分析、卡方检验、总结器】

一.相关性分析

　　1.简介

　　　　计算两个系列数据之间的相关性是统计中的常见操作。在spark.ml中提供了很多算法用来计算两两的相关性。目前支持的相关性算法是Pearson和Spearman。Correlation使用指定的方法计算输入数据集的相关矩阵。输出是一个DataFrame，其中包含向量列的相关矩阵。

　　2.代码实现

package ml

import org.apache.log4j.{Level, Logger}
import org.apache.spark.ml.linalg.{Matrix, Vectors}
import org.apache.spark.ml.stat.Correlation
import org.apache.spark.sql.{Row, SparkSession}
/**
  * Created by Administrator on 2019/11/28.
  */
object CorrelationDemo {
  Logger.getLogger("org").setLevel(Level.WARN)
  def main(args: Array[String]) {
    val spark = SparkSession.builder().appName(s"${this.getClass.getSimpleName}").master("local[2]").getOrCreate()
    import spark.implicits._ // 导入，否则无法使用toDF算子

    val data = Seq(
      Vectors.sparse(4, Seq((0, 1.0), (3, -2.0))),
      Vectors.dense(4.0, 5.0, 0.0, 3.0),
      Vectors.dense(6.0, 7.0, 0.0, 8.0),
      Vectors.sparse(4, Seq((0, 9.0), (3, 1.0)))
    )

    val df = data.map(Tuple1.apply).toDF("features")
    val Row(coeff : Matrix) = Correlation.corr(df, "features").head
    println(s"Pearson correlation matrix:
 $coeff")

    df.cache()
    val Row(coeff2 : Matrix) = Correlation.corr(df, "features", "spearman").head
    println(s"Spearman correlation matrix:
 $coeff2")
  }
}

　　3.源码分析

package org.apache.spark.ml.stat

import scala.collection.JavaConverters._

import org.apache.spark.annotation.{Experimental, Since}
import org.apache.spark.ml.linalg.{SQLDataTypes, Vector}
import org.apache.spark.mllib.linalg.{Vectors => OldVectors}
import org.apache.spark.mllib.stat.{Statistics => OldStatistics}
import org.apache.spark.sql.{DataFrame, Dataset, Row}
import org.apache.spark.sql.types.{StructField, StructType}

/**
 * API for correlation functions in MLlib, compatible with DataFrames and Datasets.
 *
 * The functions in this package generalize the functions in [[org.apache.spark.sql.Dataset#stat]]
 * to spark.ml's Vector types.
 */
@Since("2.2.0")
@Experimental
object Correlation {

  /**
   * :: Experimental ::
   * Compute the correlation matrix for the input Dataset of Vectors using the specified method.
   * Methods currently supported: `pearson` (default), `spearman`.
   *
   * @param dataset A dataset or a dataframe
   * @param column The name of the column of vectors for which the correlation coefficient needs
   *               to be computed. This must be a column of the dataset, and it must contain
   *               Vector objects.
   * @param method String specifying the method to use for computing correlation.
   *               Supported: `pearson` (default), `spearman`
   * @return A dataframe that contains the correlation matrix of the column of vectors. This
   *         dataframe contains a single row and a single column of name
   *         '$METHODNAME($COLUMN)'.
   * @throws IllegalArgumentException if the column is not a valid column in the dataset, or if
   *                                  the content of this column is not of type Vector.
   *
   *  Here is how to access the correlation coefficient:
   *  {{{
   *    val data: Dataset[Vector] = ...
   *    val Row(coeff: Matrix) = Correlation.corr(data, "value").head
   *    // coeff now contains the Pearson correlation matrix.
   *  }}}
   *
   * @note For Spearman, a rank correlation, we need to create an RDD[Double] for each column
   * and sort it in order to retrieve the ranks and then join the columns back into an RDD[Vector],
   * which is fairly costly. Cache the input Dataset before calling corr with `method = "spearman"`
   * to avoid recomputing the common lineage.
   */
  @Since("2.2.0")
  def corr(dataset: Dataset[_], column: String, method: String): DataFrame = {
    val rdd = dataset.select(column).rdd.map {
      case Row(v: Vector) => OldVectors.fromML(v)
    }
    val oldM = OldStatistics.corr(rdd, method)
    val name = s"$method($column)"
    val schema = StructType(Array(StructField(name, SQLDataTypes.MatrixType, nullable = false)))
    dataset.sparkSession.createDataFrame(Seq(Row(oldM.asML)).asJava, schema)
  }

  /**
   * Compute the Pearson correlation matrix for the input Dataset of Vectors.
   */
  @Since("2.2.0")
  def corr(dataset: Dataset[_], column: String): DataFrame = {
    corr(dataset, column, "pearson")
  }
}

　　4.执行结果

　　

二.卡方检验

　　1.简介

　　　　ChiSquareTest针对标签上的每个功能进行Pearson独立性检验。对于每个特征，将（特征，标签）对转换为列矩阵，针对该列矩阵计算卡方统计量。所有标签和特征必须是分类数据。

　　2.代码实现

package ml

import org.apache.log4j.{Level, Logger}
import org.apache.spark.ml.linalg.Vectors
import org.apache.spark.ml.stat.ChiSquareTest
import org.apache.spark.sql.SparkSession

/**
  * Created by Administrator on 2019/11/28.
  */
object ChiSquare {
  Logger.getLogger("org").setLevel(Level.WARN)
  def main(args: Array[String]) {
    val spark = SparkSession.builder().appName(s"${this.getClass.getSimpleName}").master("local[2]").getOrCreate()
    import spark.implicits._// 导入，否则无法使用toDF算子

    val data = Seq(
      (0.0, Vectors.dense(0.5, 10.0)),
      (0.0, Vectors.dense(1.5, 20.0)),
      (1.0, Vectors.dense(1.5, 30.0)),
      (0.0, Vectors.dense(3.5, 30.0)),
      (0.0, Vectors.dense(3.5, 40.0)),
      (1.0, Vectors.dense(3.5, 40.0))
    )

    val df = data.toDF("label", "features")
    val chi = ChiSquareTest.test(df, "features", "label") // 卡方检验
    chi.show()
  }
}

　　3.源码分析

package org.apache.spark.ml.stat

import org.apache.spark.annotation.{Experimental, Since}
import org.apache.spark.ml.linalg.{Vector, Vectors, VectorUDT}
import org.apache.spark.ml.util.SchemaUtils
import org.apache.spark.mllib.linalg.{Vectors => OldVectors}
import org.apache.spark.mllib.regression.{LabeledPoint => OldLabeledPoint}
import org.apache.spark.mllib.stat.{Statistics => OldStatistics}
import org.apache.spark.sql.DataFrame
import org.apache.spark.sql.functions.col


/**
 * :: Experimental ::
 *
 * Chi-square hypothesis testing for categorical data.
 *
 * See <a href="http://en.wikipedia.org/wiki/Chi-squared_test">Wikipedia</a> for more information
 * on the Chi-squared test.
 */
@Experimental
@Since("2.2.0")
object ChiSquareTest {

  /** Used to construct output schema of tests */
  private case class ChiSquareResult(
      pValues: Vector,
      degreesOfFreedom: Array[Int],
      statistics: Vector)

  /**
   * Conduct Pearson's independence test for every feature against the label. For each feature, the
   * (feature, label) pairs are converted into a contingency matrix for which the Chi-squared
   * statistic is computed. All label and feature values must be categorical.
   *
   * The null hypothesis is that the occurrence of the outcomes is statistically independent.
   *
   * @param dataset  DataFrame of categorical labels and categorical features.
   *                 Real-valued features will be treated as categorical for each distinct value.
   * @param featuresCol  Name of features column in dataset, of type `Vector` (`VectorUDT`)
   * @param labelCol  Name of label column in dataset, of any numerical type
   * @return DataFrame containing the test result for every feature against the label.
   *         This DataFrame will contain a single Row with the following fields:
   *          - `pValues: Vector`
   *          - `degreesOfFreedom: Array[Int]`
   *          - `statistics: Vector`
   *         Each of these fields has one value per feature.
   */
  @Since("2.2.0")
  def test(dataset: DataFrame, featuresCol: String, labelCol: String): DataFrame = {
    val spark = dataset.sparkSession
    import spark.implicits._

    SchemaUtils.checkColumnType(dataset.schema, featuresCol, new VectorUDT)
    SchemaUtils.checkNumericType(dataset.schema, labelCol)
    val rdd = dataset.select(col(labelCol).cast("double"), col(featuresCol)).as[(Double, Vector)]
      .rdd.map { case (label, features) => OldLabeledPoint(label, OldVectors.fromML(features)) }
    val testResults = OldStatistics.chiSqTest(rdd)
    val pValues: Vector = Vectors.dense(testResults.map(_.pValue))
    val degreesOfFreedom: Array[Int] = testResults.map(_.degreesOfFreedom)
    val statistics: Vector = Vectors.dense(testResults.map(_.statistic))
    spark.createDataFrame(Seq(ChiSquareResult(pValues, degreesOfFreedom, statistics)))
  }
}

　　4.执行结果

　　

三.总结器

　　1.简介

　　　　其提供矢量列汇总统计DataFrame的Summarizer。可以度量按列的最大值、最小值、平均值、方差和非零个数，以及总数。

　　2.代码实现

package ml

import org.apache.log4j.{Level, Logger}
import org.apache.spark.ml.linalg.Vectors
import org.apache.spark.ml.stat.Summarizer._  // 导入总结器
import org.apache.spark.sql.SparkSession
import org.apache.spark.ml.linalg.Vector

/**
  * Created by Administrator on 2019/11/28.
  */
object Summary {
  Logger.getLogger("org").setLevel(Level.WARN)
  def main(args: Array[String]) {
    val spark = SparkSession.builder().appName(s"${this.getClass.getSimpleName}").master("local[2]").getOrCreate()
    import spark.implicits._// 导入，否则无法使用toDF算子

    /**
      * features数据个数不一致时报错：
      * Dimensions mismatch when merging with another summarizer. Expecting 3 but got 2.
      */
    val data = Seq(
      (Vectors.dense(2.0, 3.0, 5.0), 1.0),
      (Vectors.dense(4.0, 6.0, 8.0), 2.0)
    )

    val df = data.toDF("features", "weight")

    /**
      * 计算均值时考虑权重
      * [(2.0*1+4.0*2)/3,(3.0*1+6.0*2)/3,(5.0*1+8.0*2)/3) = [3.333333333333333,5.0,7.0]
      * 方差的计算不考虑权重
      */
    val (meanVal, varianceVal) = df.select(metrics("mean", "variance").summary($"features", $"weight").as("summary"))
      .select("summary.mean", "summary.variance")
      .as[(Vector, Vector)].first()

    println(s"with weight:mean = ${meanVal},variance = ${varianceVal}")

    /**
      * 计算均值，无权重
      * [(2.0+4.0)/2,(3.0+6.0)/2,(5.0+8.0)/2) = [3.0,4.5,6.5]
      */
    val (meanVal2, varianceVal2) = df.select(mean($"features"), variance($"features"))
      .as[(Vector, Vector)].first()

    println(s"with weight:mean = ${meanVal2}, variance = ${varianceVal2}")
  }
}

　　3.源码分析

/**
 * Tools for vectorized statistics on MLlib Vectors.
 *
 * The methods in this package provide various statistics for Vectors contained inside DataFrames.
 *
 * This class lets users pick the statistics they would like to extract for a given column. Here is
 * an example in Scala:
 * {{{
 *   import org.apache.spark.ml.linalg._
 *   import org.apache.spark.sql.Row
 *   val dataframe = ... // Some dataframe containing a feature column and a weight column
 *   val multiStatsDF = dataframe.select(
 *       Summarizer.metrics("min", "max", "count").summary($"features", $"weight")
 *   val Row(Row(minVec, maxVec, count)) = multiStatsDF.first()
 * }}}
 *
 * If one wants to get a single metric, shortcuts are also available:
 * {{{
 *   val meanDF = dataframe.select(Summarizer.mean($"features"))
 *   val Row(meanVec) = meanDF.first()
 * }}}
 *
 * Note: Currently, the performance of this interface is about 2x~3x slower than using the RDD
 * interface.
 */
@Experimental
@Since("2.3.0")
object Summarizer extends Logging {

  import SummaryBuilderImpl._

  /**
   * Given a list of metrics, provides a builder that it turns computes metrics from a column.
   *
   * See the documentation of [[Summarizer]] for an example.
   *
   * The following metrics are accepted (case sensitive):
   *  - mean: a vector that contains the coefficient-wise mean.
   *  - variance: a vector tha contains the coefficient-wise variance.
   *  - count: the count of all vectors seen.
   *  - numNonzeros: a vector with the number of non-zeros for each coefficients
   *  - max: the maximum for each coefficient.
   *  - min: the minimum for each coefficient.
   *  - normL2: the Euclidean norm for each coefficient.
   *  - normL1: the L1 norm of each coefficient (sum of the absolute values).
   * @param metrics metrics that can be provided.
   * @return a builder.
   * @throws IllegalArgumentException if one of the metric names is not understood.
   *
   * Note: Currently, the performance of this interface is about 2x~3x slower then using the RDD
   * interface.
   */
  @Since("2.3.0")
  @scala.annotation.varargs
  def metrics(metrics: String*): SummaryBuilder = {
    require(metrics.size >= 1, "Should include at least one metric")
    val (typedMetrics, computeMetrics) = getRelevantMetrics(metrics)
    new SummaryBuilderImpl(typedMetrics, computeMetrics)
  }

  @Since("2.3.0")
  def mean(col: Column, weightCol: Column): Column = {
    getSingleMetric(col, weightCol, "mean")
  }

  @Since("2.3.0")
  def mean(col: Column): Column = mean(col, lit(1.0))

  @Since("2.3.0")
  def variance(col: Column, weightCol: Column): Column = {
    getSingleMetric(col, weightCol, "variance")
  }

  @Since("2.3.0")
  def variance(col: Column): Column = variance(col, lit(1.0))
...

　　4.执行结果