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SparkMLlibLogisticRegression实现逻辑回归算法

已有 5870 次阅读2016-5-9 19:37

1.2 Spark Mllib Logistic Regression源码分析1.2.1 LogisticRegressionWithSGD
Logistic回归算法的train方法，由LogisticRegressionWithSGD类的object定义了train函数，在train函数中新建了LogisticRegressionWithSGD对象。
package org.apache.spark.mllib.classification
// 1 类：LogisticRegressionWithSGD
class LogisticRegressionWithSGD private[mllib] (
    privatevar stepSize: Double,
    privatevar numIterations: Int,
    privatevar regParam: Double,
    privatevar miniBatchFraction: Double)
  extends GeneralizedLinearAlgorithm[LogisticRegressionModel] with Serializable {

  privateval gradient = new LogisticGradient()
  privateval updater = new SquaredL2Updater()
  overrideval optimizer = new GradientDescent(gradient, updater)
    .setStepSize(stepSize)
    .setNumIterations(numIterations)
    .setRegParam(regParam)
    .setMiniBatchFraction(miniBatchFraction)
  overrideprotectedval validators = List(DataValidators.binaryLabelValidator)

  /**
   * Construct a LogisticRegression object with default parameters: {stepSize: 1.0,
   * numIterations: 100, regParm: 0.01, miniBatchFraction: 1.0}.
   */
  defthis() = this(1.0, 100, 0.01, 1.0)

  overrideprotected[mllib] def createModel(weights: Vector, intercept: Double) = {
    new LogisticRegressionModel(weights, intercept)
}
LogisticRegressionWithSGD类中参数说明：
stepSize: 迭代步长，默认为1.0
numIterations: 迭代次数，默认为100
regParam: 正则化参数，默认值为0.0
miniBatchFraction: 每次迭代参与计算的样本比例，默认为1.0
gradient：LogisticGradient()，Logistic梯度下降；
updater：SquaredL2Updater()，正则化，L2范数；
optimizer：GradientDescent(gradient, updater)，梯度下降最优化计算。
// 2 train方法
object LogisticRegressionWithSGD {
  /**
   * Train a logistic regression model given an RDD of (label, features) pairs. We run a fixed
   * number of iterations of gradient descent using the specified step size. Each iteration uses
   * `miniBatchFraction` fraction of the data to calculate the gradient. The weights used in
   * gradient descent are initialized using the initial weights provided.
   * NOTE: Labels used in Logistic Regression should be {0, 1}
   *
   * @param input RDD of (label, array of features) pairs.
   * @param numIterations Number of iterations of gradient descent to run.
   * @param stepSize Step size to be used for each iteration of gradient descent.
   * @param miniBatchFraction Fraction of data to be used per iteration.
   * @param initialWeights Initial set of weights to be used. Array should be equal in size to
   *        the number of features in the data.
   */
  def train(
      input: RDD[LabeledPoint],
      numIterations: Int,
      stepSize: Double,
      miniBatchFraction: Double,
      initialWeights: Vector): LogisticRegressionModel = {
    new LogisticRegressionWithSGD(stepSize, numIterations, 0.0, miniBatchFraction)
      .run(input, initialWeights)
  }
}
train参数说明：
input：样本数据，分类标签lable只能是1.0和0.0两种,feature为double类型
numIterations: 迭代次数，默认为100
stepSize: 迭代步长，默认为1.0
miniBatchFraction: 每次迭代参与计算的样本比例，默认为1.0
initialWeights:初始权重，默认为0向量
run方法来自于继承父类GeneralizedLinearAlgorithm，实现方法如下。
1.2.2 GeneralizedLinearAlgorithm
LogisticRegressionWithSGD中run方法的实现。
package org.apache.spark.mllib.regression
/**
   * Run the algorithm with the configured parameters on an input RDD
   * of LabeledPoint entries starting from the initial weights provided.
   */
  def run(input: RDD[LabeledPoint], initialWeights: Vector): M = {
// 特征维度赋值。
    if (numFeatures < 0) {
      numFeatures = input.map(_.features.size).first()
    }
// 输入样本数据检测。
    if (input.getStorageLevel == StorageLevel.NONE) {
      logWarning("The input data is not directly cached, which may hurt performance if its"
        + " parent RDDs are also uncached.")
    }
// 输入样本数据检测。
    // Check the data properties before running the optimizer
    if (validateData && !validators.forall(func => func(input))) {
      thrownew SparkException("Input validation failed.")
    }
val scaler = if (useFeatureScaling) {
      new StandardScaler(withStd = true, withMean = false).fit(input.map(_.features))
    } else {
      null
    }
// 输入样本数据处理，输出data(label, features)格式。
// addIntercept：是否增加θ0常数项，若增加，则增加x0=1项。
    // Prepend an extra variable consisting of all 1.0's for the intercept.
    // TODO: Apply feature scaling to the weight vector instead of input data.
    val data =
      if (addIntercept) {
        if (useFeatureScaling) {
          input.map(lp => (lp.label, appendBias(scaler.transform(lp.features)))).cache()
        } else {
          input.map(lp => (lp.label, appendBias(lp.features))).cache()
        }
      } else {
        if (useFeatureScaling) {
          input.map(lp => (lp.label, scaler.transform(lp.features))).cache()
        } else {
          input.map(lp => (lp.label, lp.features))
        }
      }
//初始化权重。
// addIntercept：是否增加θ0常数项，若增加，则权重增加θ0。
    /**
     * TODO: For better convergence, in logistic regression, the intercepts should be computed
     * from the prior probability distribution of the outcomes; for linear regression,
     * the intercept should be set as the average of response.
     */
    val initialWeightsWithIntercept = if (addIntercept && numOfLinearPredictor == 1) {
      appendBias(initialWeights)
    } else {
      /** If `numOfLinearPredictor > 1`, initialWeights already contains intercepts. */
      initialWeights
    }
//权重优化，进行梯度下降学习，返回最优权重。
    val weightsWithIntercept = optimizer.optimize(data, initialWeightsWithIntercept)

    val intercept = if (addIntercept && numOfLinearPredictor == 1) {
      weightsWithIntercept(weightsWithIntercept.size - 1)
    } else {
      0.0
    }

    var weights = if (addIntercept && numOfLinearPredictor == 1) {
      Vectors.dense(weightsWithIntercept.toArray.slice(0, weightsWithIntercept.size - 1))
    } else {
      weightsWithIntercept
    }

    createModel(weights, intercept)
}
其中optimizer.optimize(data, initialWeightsWithIntercept)是逻辑回归实现的核心。
oprimizer的类型为GradientDescent，optimize方法中主要调用GradientDescent伴生对象的runMiniBatchSGD方法，返回当前迭代产生的最优特征权重向量。
GradientDescentd对象中optimize实现方法如下。
1.2.3 GradientDescent
optimize实现方法如下。
package org.apache.spark.mllib.optimization
/**
   * :: DeveloperApi ::
   * Runs gradient descent on the given training data.
   * @param data training data
   * @param initialWeights initial weights
   * @return solution vector
   */
  @DeveloperApi
  def optimize(data: RDD[(Double, Vector)], initialWeights: Vector): Vector = {
    val (weights, _) = GradientDescent.runMiniBatchSGD(
      data,
      gradient,
      updater,
      stepSize,
      numIterations,
      regParam,
      miniBatchFraction,
      initialWeights)
    weights
  }

}
在optimize方法中，调用了GradientDescent.runMiniBatchSGD方法，其runMiniBatchSGD实现方法如下：
/**
   * Run stochastic gradient descent (SGD) in parallel using mini batches.
   * In each iteration, we sample a subset (fraction miniBatchFraction) of the total data
   * in order to compute a gradient estimate.
   * Sampling, and averaging the subgradients over this subset is performed using one standard
   * spark map-reduce in each iteration.
   *
   * @param data - Input data for SGD. RDD of the set of data examples, each of
   *               the form (label, [feature values]).
   * @param gradient - Gradient object (used to compute the gradient of the loss function of
   *                   one single data example)
   * @param updater - Updater function to actually perform a gradient step in a given direction.
   * @param stepSize - initial step size for the first step
   * @param numIterations - number of iterations that SGD should be run.
   * @param regParam - regularization parameter
   * @param miniBatchFraction - fraction of the input data set that should be used for
   *                            one iteration of SGD. Default value 1.0.
   *
   * @return A tuple containing two elements. The first element is a column matrix containing
   *         weights for every feature, and the second element is an array containing the
   *         stochastic loss computed for every iteration.
   */
  def runMiniBatchSGD(
      data: RDD[(Double, Vector)],
      gradient: Gradient,
      updater: Updater,
      stepSize: Double,
      numIterations: Int,
      regParam: Double,
      miniBatchFraction: Double,
      initialWeights: Vector): (Vector, Array[Double]) = {
//历史迭代误差数组
    val stochasticLossHistory = new ArrayBuffer[Double](numIterations)
//样本数据检测，若为空，返回初始值。
    val numExamples = data.count()

    // if no data, return initial weights to avoid NaNs
    if (numExamples == 0) {
      logWarning("GradientDescent.runMiniBatchSGD returning initial weights, no data found")
      return (initialWeights, stochasticLossHistory.toArray)
    }
// miniBatchFraction值检测。
    if (numExamples * miniBatchFraction < 1) {
      logWarning("The miniBatchFraction is too small")
    }
// weights权重初始化。
    // Initialize weights as a column vector
    var weights = Vectors.dense(initialWeights.toArray)
    val n = weights.size

    /**
     * For the first iteration, the regVal will be initialized as sum of weight squares
     * if it's L2 updater; for L1 updater, the same logic is followed.
     */
    var regVal = updater.compute(
      weights, Vectors.dense(new Array[Double](weights.size)), 0, 1, regParam)._2
// weights权重迭代计算。
    for (i <- 1 to numIterations) {
      val bcWeights = data.context.broadcast(weights)
      // Sample a subset (fraction miniBatchFraction) of the total data
      // compute and sum up the subgradients on this subset (this is one map-reduce)
// 采用treeAggregate的RDD方法，进行聚合计算，计算每个样本的权重向量、误差值，然后对所有样本权重向量及误差值进行累加。
// sample是根据miniBatchFraction指定的比例随机采样相应数量的样本。
      val (gradientSum, lossSum, miniBatchSize) = data.sample(false, miniBatchFraction, 42 + i)
        .treeAggregate((BDV.zeros[Double](n), 0.0, 0L))(
          seqOp = (c, v) => {
            // c: (grad, loss, count), v: (label, features)
            val l = gradient.compute(v._2, v._1, bcWeights.value, Vectors.fromBreeze(c._1))
            (c._1, c._2 + l, c._3 + 1)
          },
          combOp = (c1, c2) => {
            // c: (grad, loss, count)
            (c1._1 += c2._1, c1._2 + c2._2, c1._3 + c2._3)
          })
// 保存本次迭代误差值，以及更新weights权重向量。
      if (miniBatchSize > 0) {
        /**
         * NOTE(Xinghao): lossSum is computed using the weights from the previous iteration
         * and regVal is the regularization value computed in the previous iteration as well.
         */
// updater.compute更新weights矩阵和regVal（正则化项）。根据本轮迭代中的gradient和loss的变化以及正则化项计算更新之后的weights和regVal。
        stochasticLossHistory.append(lossSum / miniBatchSize + regVal)
        val update = updater.compute(
          weights, Vectors.fromBreeze(gradientSum / miniBatchSize.toDouble), stepSize, i, regParam)
        weights = update._1
        regVal = update._2
      } else {
        logWarning(s"Iteration ($i/$numIterations). The size of sampled batch is zero")
      }
    }

    logInfo("GradientDescent.runMiniBatchSGD finished. Last 10 stochastic losses %s".format(
      stochasticLossHistory.takeRight(10).mkString(", ")))

    (weights, stochasticLossHistory.toArray)

  }
runMiniBatchSGD的输入、输出参数说明：
data 样本输入数据，格式 (label, [feature values])
gradient 梯度对象，用于对每个样本计算梯度及误差
updater 权重更新对象，用于每次更新权重
stepSize 初始步长
numIterations 迭代次数
regParam 正则化参数
miniBatchFraction 迭代因子，每次迭代参与计算的样本比例
返回结果(Vector, Array[Double])，第一个为权重，每二个为每次迭代的误差值。
在MiniBatchSGD中主要实现对输入数据集进行迭代抽样，通过使用LogisticGradient作为梯度下降算法，使用SquaredL2Updater作为更新算法，不断对抽样数据集进行迭代计算从而找出最优的特征权重向量解。在LinearRegressionWithSGD中定义如下：
  privateval gradient = new LogisticGradient()
  privateval updater = new SquaredL2Updater()
  overrideval optimizer = new GradientDescent(gradient, updater)
    .setStepSize(stepSize)
    .setNumIterations(numIterations)
    .setRegParam(regParam)
    .setMiniBatchFraction(miniBatchFraction)
runMiniBatchSGD方法中调用了gradient.compute、updater.compute两个方法，其实现方法如下。
1.2.4 gradient & updater
1）gradient
//计算当前计算对象的类标签与实际类标签值之差
//计算当前平方梯度下降值
//计算权重的更新值
//返回当前训练对象的特征权重向量和误差
class LogisticGradient(numClasses: Int) extends Gradient {

  defthis() = this(2)

  overridedef compute(data: Vector, label: Double, weights: Vector): (Vector, Double) = {
    val gradient = Vectors.zeros(weights.size)
    val loss = compute(data, label, weights, gradient)
    (gradient, loss)
  }

  overridedef compute(
      data: Vector,
      label: Double,
      weights: Vector,
      cumGradient: Vector): Double = {
    val dataSize = data.size

    // (weights.size / dataSize + 1) is number of classes
    require(weights.size % dataSize == 0 && numClasses == weights.size / dataSize + 1)
    numClasses match {
      case2 =>
        /**
         * For Binary Logistic Regression.
         *
         * Although the loss and gradient calculation for multinomial one is more generalized,
         * and multinomial one can also be used in binary case, we still implement a specialized
         * binary version for performance reason.
         */
        val margin = -1.0 * dot(data, weights)
        val multiplier = (1.0 / (1.0 + math.exp(margin))) - label
        axpy(multiplier, data, cumGradient)
        if (label > 0) {
          // The following is equivalent to log(1 + exp(margin)) but more numerically stable.
          MLUtils.log1pExp(margin)
        } else {
          MLUtils.log1pExp(margin) - margin
        }
      case _ =>
        /**
         * For Multinomial Logistic Regression.
         */
        val weightsArray = weights match {
          case dv: DenseVector => dv.values
          case _ =>
            thrownew IllegalArgumentException(
              s"weights only supports dense vector but got type ${weights.getClass}.")
        }
        val cumGradientArray = cumGradient match {
          case dv: DenseVector => dv.values
          case _ =>
            thrownew IllegalArgumentException(
              s"cumGradient only supports dense vector but got type ${cumGradient.getClass}.")
        }

        // marginY is margins(label - 1) in the formula.
        var marginY = 0.0
        var maxMargin = Double.NegativeInfinity
        var maxMarginIndex = 0

        val margins = Array.tabulate(numClasses - 1) { i =>
          var margin = 0.0
          data.foreachActive { (index, value) =>
            if (value != 0.0) margin += value * weightsArray((i * dataSize) + index)
          }
          if (i == label.toInt - 1) marginY = margin
          if (margin > maxMargin) {
            maxMargin = margin
            maxMarginIndex = i
          }
          margin
        }

        /**
         * When maxMargin > 0, the original formula will cause overflow as we discuss
         * in the previous comment.
         * We address this by subtracting maxMargin from all the margins, so it's guaranteed
         * that all of the new margins will be smaller than zero to prevent arithmetic overflow.
         */
        val sum = {
          var temp = 0.0
          if (maxMargin > 0) {
            for (i <- 0 until numClasses - 1) {
              margins(i) -= maxMargin
              if (i == maxMarginIndex) {
                temp += math.exp(-maxMargin)
              } else {
                temp += math.exp(margins(i))
              }
            }
          } else {
            for (i <- 0 until numClasses - 1) {
              temp += math.exp(margins(i))
            }
          }
          temp
        }

        for (i <- 0 until numClasses - 1) {
          val multiplier = math.exp(margins(i)) / (sum + 1.0) - {
            if (label != 0.0 && label == i + 1) 1.0else0.0
          }
          data.foreachActive { (index, value) =>
            if (value != 0.0) cumGradientArray(i * dataSize + index) += multiplier * value
          }
        }

        val loss = if (label > 0.0) math.log1p(sum) - marginY else math.log1p(sum)

        if (maxMargin > 0) {
          loss + maxMargin
        } else {
          loss
        }
    }
  }
}
2）updater
//weihtsOld:上一次迭代计算后的特征权重向量
//gradient:本次迭代计算的特征权重向量
//stepSize:迭代步长
//iter:当前迭代次数
//regParam:正则参数
//以当前迭代次数的平方根的倒数作为本次迭代趋近(下降)的因子
//返回本次剃度下降后更新的特征权重向量
//使用了L2 regularization（R(w) = 1/2 ||w||^2），weights更新规则为：

/**
* :: DeveloperApi ::
* Updater for L2 regularized problems.
*          R(w) = 1/2 ||w||^2
* Uses a step-size decreasing with the square root of the number of iterations.
*/
@DeveloperApi
class SquaredL2Updater extends Updater {
  overridedef compute(
      weightsOld: Vector,
      gradient: Vector,
      stepSize: Double,
      iter: Int,
      regParam: Double): (Vector, Double) = {
    // add up both updates from the gradient of the loss (= step) as well as
    // the gradient of the regularizer (= regParam * weightsOld)
    // w' = w - thisIterStepSize * (gradient + regParam * w)
    // w' = (1 - thisIterStepSize * regParam) * w - thisIterStepSize * gradient
    val thisIterStepSize = stepSize / math.sqrt(iter)
    val brzWeights: BV[Double] = weightsOld.toBreeze.toDenseVector
    brzWeights :*= (1.0 - thisIterStepSize * regParam)
    brzAxpy(-thisIterStepSize, gradient.toBreeze, brzWeights)
    val norm = brzNorm(brzWeights, 2.0)

    (Vectors.fromBreeze(brzWeights), 0.5 * regParam * norm * norm)
  }
}

1.3 Mllib Logistic Regression实例
1、数据
数据格式为：标签, 特征1 特征2 特征3……
0 128:51 129:159 130:253 131:159 132:50 155:48 156:238 157:252 158:252 159:252 160:237 182:54 183:227 184:253 185:252 186:239 187:233 188:252 189:57 190:6 208:10 209:60 210:224 211:252 212:253 213:252 214:202 215:84 216:252 217:253 218:122 236:163 237:252 238:252 239:252 240:253 241:252 242:252 243:96 244:189 245:253 246:167 263:51 264:238 265:253 266:253 267:190 268:114 269:253 270:228 271:47 272:79 273:255 274:168 290:48 291:238 292:252 293:252 294:179 295:12 296:75 297:121 298:21 301:253 302:243 303:50 317:38 318:165 319:253 320:233 321:208 322:84 329:253 330:252 331:165 344:7 345:178 346:252 347:240 348:71 349:19 350:28 357:253 358:252 359:195 372:57 373:252 374:252 375:63 385:253 386:252 387:195 400:198 401:253 402:190 413:255 414:253 415:196 427:76 428:246 429:252 430:112 441:253 442:252 443:148 455:85 456:252 457:230 458:25 467:7 468:135 469:253 470:186 471:12 483:85 484:252 485:223 494:7 495:131 496:252 497:225 498:71 511:85 512:252 513:145 521:48 522:165 523:252 524:173 539:86 540:253 541:225 548:114 549:238 550:253 551:162 567:85 568:252 569:249 570:146 571:48 572:29 573:85 574:178 575:225 576:253 577:223 578:167 579:56 595:85 596:252 597:252 598:252 599:229 600:215 601:252 602:252 603:252 604:196 605:130 623:28 624:199 625:252 626:252 627:253 628:252 629:252 630:233 631:145 652:25 653:128 654:252 655:253 656:252 657:141 658:37
1 159:124 160:253 161:255 162:63 186:96 187:244 188:251 189:253 190:62 214:127 215:251 216:251 217:253 218:62 241:68 242:236 243:251 244:211 245:31 246:8 268:60 269:228 270:251 271:251 272:94 296:155 297:253 298:253 299:189 323:20 324:253 325:251 326:235 327:66 350:32 351:205 352:253 353:251 354:126 378:104 379:251 380:253 381:184 382:15 405:80 406:240 407:251 408:193 409:23 432:32 433:253 434:253 435:253 436:159 460:151 461:251 462:251 463:251 464:39 487:48 488:221 489:251 490:251 491:172 515:234 516:251 517:251 518:196 519:12 543:253 544:251 545:251 546:89 570:159 571:255 572:253 573:253 574:31 597:48 598:228 599:253 600:247 601:140 602:8 625:64 626:251 627:253 628:220 653:64 654:251 655:253 656:220 681:24 682:193 683:253 684:220
……
2、代码
//1 读取样本数据
  valdata_path = "/user/tmp/sample_libsvm_data.txt"
  valexamples = MLUtils.loadLibSVMFile(sc, data_path).cache()

  //2 样本数据划分训练样本与测试样本
  valsplits = examples.randomSplit(Array(0.6, 0.4), seed = 11L)
  valtraining = splits(0).cache()
  valtest = splits(1)
  valnumTraining = training.count()
  valnumTest = test.count()
  println(s"Training: $numTraining, test: $numTest.")

  //3 新建逻辑回归模型，并设置训练参数
  valnumIterations = 1000
  valstepSize = 1
  valminiBatchFraction = 1.0
  valmodel = LogisticRegressionWithSGD.train(training, numIterations, stepSize, miniBatchFraction)
  //4 对测试样本进行测试
  valprediction = model.predict(test.map(_.features))
  valpredictionAndLabel = prediction.zip(test.map(_.label))

  //5 计算测试误差
  valmetrics = new MulticlassMetrics(predictionAndLabel)
  valprecision = metrics.precision
  println("Precision = " + precision)

来自：

http://www.sjsjw.com/107/001018MYM008515/