例子中對K元邏輯迴歸沒有詳細推導，我自己推導了一下，過程也比較簡單。（太長時間不寫字，感覺已經不會拿筆了。。。）

過程如圖：

然後運行了一下spark自帶的LogisticRegressionWithLBFGSExample例子。

原始碼如下：

import org.apache.spark.{SparkConf, SparkContext}
// $example on$
import org.apache.spark.mllib.classification.{LogisticRegressionModel, LogisticRegressionWithLBFGS}
import org.apache.spark.mllib.evaluation.MulticlassMetrics
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.util.MLUtils
// $example off$

object LogisticRegressionWithLBFGSExample {

  def main(args: Array[String]): Unit = {
    val conf = new SparkConf().setAppName("LogisticRegressionWithLBFGSExample")
    val sc = new SparkContext(conf)

    // $example on$
    // Load training data in LIBSVM format.
    val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")

    // Split data into training (60%) and test (40%).
    val splits = data.randomSplit(Array(0.6, 0.4), seed = 11L)
    val training = splits(0).cache()
    val test = splits(1)

    // Run training algorithm to build the model
    val model = new LogisticRegressionWithLBFGS()
      .setNumClasses(10)
      .run(training)

    // Compute raw scores on the test set.
    val predictionAndLabels = test.map { case LabeledPoint(label, features) =>
      val prediction = model.predict(features)
      (prediction, label)
    }

    // Get evaluation metrics.
    val metrics = new MulticlassMetrics(predictionAndLabels)
    val accuracy = metrics.accuracy

    println(s"Accuracy = $accuracy")

    // Save and load model
    model.save(sc, "target/tmp/scalaLogisticRegressionWithLBFGSModel")
    val sameModel = LogisticRegressionModel.load(sc,
      "target/tmp/scalaLogisticRegressionWithLBFGSModel")
    // $example off$
  
    sc.stop()
  }
}
// scalastyle:on println