线性回归

一、数据准备：文件 lpsa.data 数据如下：

-0.4307829,-1.63735562648104 -2.00621178480549 -1.86242597251066 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
-0.1625189,-1.98898046126935 -0.722008756122123 -0.787896192088153 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
-0.1625189,-1.57881887548545 -2.1887840293994 1.36116336875686 -1.02470580167082 -0.522940888712441 -0.863171185425945 0.342627053981254 -0.155348103855541
-0.1625189,-2.16691708463163 -0.807993896938655 -0.787896192088153 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
0.3715636,-0.507874475300631 -0.458834049396776 -0.250631301876899 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
0.7654678,-2.03612849966376 -0.933954647105133 -1.86242597251066 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
0.8544153,-0.557312518810673 -0.208756571683607 -0.787896192088153 0.990146852537193 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
1.2669476,-0.929360463147704 -0.0578991819441687 0.152317365781542 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
1.2669476,-2.28833047634983 -0.0706369432557794 -0.116315079324086 0.80409888772376 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
1.2669476,0.223498042876113 -1.41471935455355 -0.116315079324086 -1.02470580167082 -0.522940888712441 -0.29928234305568 0.342627053981254 0.199211097885341
1.3480731,0.107785900236813 -1.47221551299731 0.420949810887169 -1.02470580167082 -0.522940888712441 -0.863171185425945 0.342627053981254 -0.687186906466865
1.446919,0.162180092313795 -1.32557369901905 0.286633588334355 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
1.4701758,-1.49795329918548 -0.263601072284232 0.823898478545609 0.788388310173035 -0.522940888712441 -0.29928234305568 0.342627053981254 0.199211097885341
1.4929041,0.796247055396743 0.0476559407005752 0.286633588334355 -1.02470580167082 -0.522940888712441 0.394013435896129 -1.04215728919298 -0.864466507337306
1.5581446,-1.62233848461465 -0.843294091975396 -3.07127197548598 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
1.5993876,-0.990720665490831 0.458513517212311 0.823898478545609 1.07379746308195 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
1.6389967,-0.171901281967138 -0.489197399065355 -0.65357996953534 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
1.6956156,-1.60758252338831 -0.590700340358265 -0.65357996953534 -0.619561070667254 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
1.7137979,0.366273918511144 -0.414014962912583 -0.116315079324086 0.232904453212813 -0.522940888712441 0.971228997418125 0.342627053981254 1.26288870310799
1.8000583,-0.710307384579833 0.211731938156277 0.152317365781542 -1.02470580167082 -0.522940888712441 -0.442797990776478 0.342627053981254 1.61744790484887
1.8484548,-0.262791728113881 -1.16708345615721 0.420949810887169 0.0846342590816532 -0.522940888712441 0.163172393491611 0.342627053981254 1.97200710658975
1.8946169,0.899043117369237 -0.590700340358265 0.152317365781542 -1.02470580167082 -0.522940888712441 1.28643254437683 -1.04215728919298 -0.864466507337306
1.9242487,-0.903451690500615 1.07659722048274 0.152317365781542 1.28380453408541 -0.522940888712441 -0.442797990776478 -1.04215728919298 -0.864466507337306
2.008214,-0.0633337899773081 -1.38088970920094 0.958214701098423 0.80409888772376 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
2.0476928,-1.15393789990757 -0.961853075398404 -0.116315079324086 -1.02470580167082 -0.522940888712441 -0.442797990776478 -1.04215728919298 -0.864466507337306
2.1575593,0.0620203721138446 0.0657973885499142 1.22684714620405 -0.468824786336838 -0.522940888712441 1.31421001659859 1.72741139715549 -0.332627704725983
2.1916535,-0.75731027755674 -2.92717970468456 0.018001143228728 -1.02470580167082 -0.522940888712441 -0.863171185425945 0.342627053981254 -0.332627704725983
2.2137539,1.11226993252773 1.06484916245061 0.555266033439982 0.877691038550889 1.89254797819741 1.43890404648442 0.342627053981254 0.376490698755783
2.2772673,-0.468768642850639 -1.43754788774533 -1.05652863719378 0.576050411655607 -0.522940888712441 0.0120483832567209 0.342627053981254 -0.687186906466865
2.2975726,-0.618884859896728 -1.1366360750781 -0.519263746982526 -1.02470580167082 -0.522940888712441 -0.863171185425945 3.11219574032972 1.97200710658975
2.3272777,-0.651431999123483 0.55329161145762 -0.250631301876899 1.11210019001038 -0.522940888712441 -0.179808625688859 -1.04215728919298 -0.864466507337306
2.5217206,0.115499102435224 -0.512233676577595 0.286633588334355 1.13650173283446 -0.522940888712441 -0.179808625688859 0.342627053981254 -0.155348103855541
2.5533438,0.266341329949937 -0.551137885443386 -0.384947524429713 0.354857790686005 -0.522940888712441 -0.863171185425945 0.342627053981254 -0.332627704725983
2.5687881,1.16902610257751 0.855491905752846 2.03274448152093 1.22628985326088 1.89254797819741 2.02833774827712 3.11219574032972 2.68112551007152
2.6567569,-0.218972367124187 0.851192298581141 0.555266033439982 -1.02470580167082 -0.522940888712441 -0.863171185425945 0.342627053981254 0.908329501367106
2.677591,0.263121415733908 1.4142681068416 0.018001143228728 1.35980653053822 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
2.7180005,-0.0704736333296423 1.52000996595417 0.286633588334355 1.39364261119802 -0.522940888712441 -0.863171185425945 0.342627053981254 -0.332627704725983
2.7942279,-0.751957286017338 0.316843561689933 -1.99674219506348 0.911736065044475 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
2.8063861,-0.685277652430997 1.28214038482516 0.823898478545609 0.232904453212813 -0.522940888712441 -0.863171185425945 0.342627053981254 -0.155348103855541
2.8124102,-0.244991501432929 0.51882005949686 -0.384947524429713 0.823246560137838 -0.522940888712441 -0.863171185425945 0.342627053981254 0.553770299626224
2.8419982,-0.75731027755674 2.09041984898851 1.22684714620405 1.53428167116843 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
2.8535925,1.20962937075363 -0.242882661178889 1.09253092365124 -1.02470580167082 -0.522940888712441 1.24263233939889 3.11219574032972 2.50384590920108
2.9204698,0.570886990493502 0.58243883987948 0.555266033439982 1.16006887775962 -0.522940888712441 1.07357183940747 0.342627053981254 1.61744790484887
2.9626924,0.719758684343624 0.984970304132004 1.09253092365124 1.52137230773457 -0.522940888712441 -0.179808625688859 0.342627053981254 -0.509907305596424
2.9626924,-1.52406140158064 1.81975700990333 0.689582255992796 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
2.9729753,-0.132431544081234 2.68769877553723 1.09253092365124 1.53428167116843 -0.522940888712441 -0.442797990776478 0.342627053981254 -0.687186906466865
3.0130809,0.436161292804989 -0.0834447307428255 -0.519263746982526 -1.02470580167082 1.89254797819741 1.07357183940747 0.342627053981254 1.26288870310799
3.0373539,-0.161195191984091 -0.671900359186746 1.7641120364153 1.13650173283446 -0.522940888712441 -0.863171185425945 0.342627053981254 0.0219314970149
3.2752562,1.39927182372944 0.513852869452676 0.689582255992796 -1.02470580167082 1.89254797819741 1.49394503405693 0.342627053981254 -0.155348103855541
3.3375474,1.51967002306341 -0.852203755696565 0.555266033439982 -0.104527297798983 1.89254797819741 1.85927724828569 0.342627053981254 0.908329501367106
3.3928291,0.560725834706224 1.87867703391426 1.09253092365124 1.39364261119802 -0.522940888712441 0.486423065822545 0.342627053981254 1.26288870310799
3.4355988,1.00765532502814 1.69426310090641 1.89842825896812 1.53428167116843 -0.522940888712441 -0.863171185425945 0.342627053981254 -0.509907305596424
3.4578927,1.10152996153577 -0.10927271844907 0.689582255992796 -1.02470580167082 1.89254797819741 1.97630171771485 0.342627053981254 1.61744790484887
3.5160131,0.100001934217311 -1.30380956369388 0.286633588334355 0.316555063757567 -0.522940888712441 0.28786643052924 0.342627053981254 0.553770299626224
3.5307626,0.987291634724086 -0.36279314978779 -0.922212414640967 0.232904453212813 -0.522940888712441 1.79270085261407 0.342627053981254 1.26288870310799
3.5652984,1.07158528137575 0.606453149641961 1.7641120364153 -0.432854616994416 1.89254797819741 0.528504607720369 0.342627053981254 0.199211097885341
3.5876769,0.180156323255198 0.188987436375017 -0.519263746982526 1.09956763075594 -0.522940888712441 0.708239632330506 0.342627053981254 0.199211097885341
3.6309855,1.65687973755377 -0.256675483533719 0.018001143228728 -1.02470580167082 1.89254797819741 1.79270085261407 0.342627053981254 1.26288870310799
3.6800909,0.5720085322365 0.239854450210939 -0.787896192088153 1.0605418233138 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
3.7123518,0.323806133438225 -0.606717660886078 -0.250631301876899 -1.02470580167082 1.89254797819741 0.342907418101747 0.342627053981254 0.199211097885341
3.9843437,1.23668206715898 2.54220539083611 0.152317365781542 -1.02470580167082 1.89254797819741 1.89037692416194 0.342627053981254 1.26288870310799
3.993603,0.180156323255198 0.154448192444669 1.62979581386249 0.576050411655607 1.89254797819741 0.708239632330506 0.342627053981254 1.79472750571931
4.029806,1.60906277046565 1.10378605019827 0.555266033439982 -1.02470580167082 -0.522940888712441 -0.863171185425945 -1.04215728919298 -0.864466507337306
4.1295508,1.0036214996026 0.113496885050331 -0.384947524429713 0.860016436332751 1.89254797819741 -0.863171185425945 0.342627053981254 -0.332627704725983
4.3851468,1.25591974271076 0.577607033774471 0.555266033439982 -1.02470580167082 1.89254797819741 1.07357183940747 0.342627053981254 1.26288870310799
4.6844434,2.09650591351268 0.625488598331018 -2.66832330782754 -1.02470580167082 1.89254797819741 1.67954222367555 0.342627053981254 0.553770299626224
5.477509,1.30028987435881 0.338383613253713 0.555266033439982 1.00481276295349 1.89254797819741 1.24263233939889 0.342627053981254 1.97200710658975

二、scala代码实现：

package com.bjsxt.lr

import org.apache.log4j.{Level, Logger}
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.regression.{LabeledPoint, LinearRegressionWithSGD}
import org.apache.spark.rdd.RDD
import org.apache.spark.{SparkConf, SparkContext}

object LinearRegression {

  def main(args: Array[String]) {
    // 构建Spark对象
    val conf = new SparkConf().setAppName("LinearRegressionWithSGD").setMaster("local")
    val sc = new SparkContext(conf)
    Logger.getRootLogger.setLevel(Level.WARN)

    //读取样本数据
    val data = sc.textFile("lpsa.data")
    val examples :RDD[LabeledPoint]= data.map { line =>
      val parts = line.split(',')
      val y = parts(0)
      val xs = parts(1)
      LabeledPoint(parts(0).toDouble, Vectors.dense(parts(1).split(' ').map(_.toDouble)))//训练时需要LabeledPoint这样格式的数据
    }

    val train2TestData: Array[RDD[LabeledPoint]] = examples.randomSplit(Array(0.8, 0.2), 1L)  //将数据切成80%和20%两份，seed表示每次抽样时，数据不变

    /*
     *  迭代次数
     *  训练一个多元线性回归模型收敛（停止迭代）条件：
     *      1、error值小于用户指定的error值
     *      2、达到一定的迭代次数
     */
    val numIterations = 100

    //在每次迭代的过程中 梯度下降算法的下降步长大小    0.1 0.2 0.3 0.4
    val stepSize = 0.003  //调节步长的经验：以0.001的3倍往上调节，即先设置0.001，再设置0.003、0.006、0.009、0.01、0.03、0.09、0.1、0.3、0.9...步长一般不超过1

    val miniBatchFraction = 1

    val lrs = new LinearRegressionWithSGD()
    //让训练出来的模型有w0参数，就是有截距
    lrs.setIntercept(true)  //true代表有截距，false代表无截距
    //设置步长
    lrs.optimizer.setStepSize(stepSize)
    //设置迭代次数
    lrs.optimizer.setNumIterations(numIterations)
    //每一次下山后，是否计算所有样本的误差值,1代表所有样本,默认就是1.0
    lrs.optimizer.setMiniBatchFraction(miniBatchFraction)

    val model = lrs.run(train2TestData(0))
    println("weights = "+  model.weights)
    println("intercept = "+ model.intercept)

    // 对样本进行测试
    val prediction = model.predict(train2TestData(1).map(_.features))//拿到测试数据集的特征，特征就是对应的那一堆x值
    val predictionAndLabel: RDD[(Double, Double)] = prediction.zip(train2TestData(1).map(_.label))//拿到测试数据集的y值，y值就是label

    val print_predict = predictionAndLabel.take(20)
    println("prediction" + "\t" + "label")
    for (i <- 0 to print_predict.length - 1) {
      println(print_predict(i)._1 + "\t" + print_predict(i)._2)
    }
    
    // 计算测试集平均误差
    val loss = predictionAndLabel.map {
      case (p, v) =>   //p代表预测值，v代表真实值
        val err = p - v
        Math.abs(err)  //对err取绝对值
    }.reduce(_ + _)  //reduce得到总的误差
    val error = loss / train2TestData(1).count  //平均误差
    println("Test RMSE = " + error)
    // 模型保存
//    val ModelPath = "model"
//    model.save(sc, ModelPath)
//    val sameModel = LinearRegressionModel.load(sc, ModelPath)
    sc.stop()
  }

}

三、运行结果如下：

weights = [0.03341745068017534,0.019786000202187768,0.013434622349497674,0.006071911495676415,0.02922095129033674,0.021361470054533056,0.012104441528065182,0.026489189942420874]
intercept = 1.0497152698605494
prediction    label
0.9448426640617988    0.3715636
0.975846171211713    1.3480731
1.0966812931717833    1.7137979
1.0685996721312716    1.8484548
0.9240844140181999    2.0476928
1.0063107793129846    2.5533438
1.0513648618159988    2.7180005
1.0309792358064582    2.8063861
1.0223340040240285    2.8419982
1.0886902420617615    2.9626924
1.196931992352681    3.2752562
1.0684477645709864    3.5876769
Test RMSE = 1.3955317777986609