SVM高斯核函式-RBF優化
重要了解數學的部分：
協方差矩陣，高斯核函式公式。
個人建議具體的求法還是看下面的核心程式碼吧，更好理解，反正就我個人而言，煩躁的公式，還不如一段程式碼來的實際。本來想用java的一個叫jblas的矩陣包，但是想了想，還是自己動手寫一下吧。加深一下自己理解。實現的語言用的是java孿生兄弟scala。我想應該不難懂。矩陣變換用二位陣列將就。
以下程式碼建議用scala命令列除錯

核心程式碼

def TransposedMatrix(a:Array[Array[Double]]):Array[Array[Double]]={//返回轉置矩陣
    val length=a.length
    val width=a(0
 
).length
    var TransposedM =Array.ofDim[Double](width,length)
    for(i <- 0 to length-1)
      for(j <- 0 to width-1) {
        TransposedM(j)(i) = a(i)(j)
      }
    TransposedM
  }


  def R1(i:Int,j:Int,M:Array[Array[Double]]):Double={//R(i,j)=(第i列-第j列)*[（第i列-第j列）轉置]
    var sum:Double=0
    for
 
(x <- 0 to M.length-1)
      sum+=Math.pow((M(x)(i)-M(x)(j)),2)
    sum

  }



  def RowAverage(a:Array[Array[Double]]):Array[Double]={//返回列的均值，返回一個列矩陣
    val length=a.length
    val width=a(0).length
    var b=new Array[Double](width)
    for(i <- 0 to width-1)
        for(j <- 0 to length-1)
          b(i) += a(j)(i)

    for
 
(i <- 0 to width-1)
      b(i)=b(i)/length
    b
  }

  def sumOfRow(a:Array[Array[Double]]):Array[Double]={//返回矩陣列的和，返回一個列矩陣
  val length=a.length
    val width=a(0).length
    var b=new Array[Double](width)
    for(i <- 0 to width-1)
      for(j <- 0 to length-1)
        b(i) += a(j)(i)

    for(i <- 0 to width-1)
      b(i)=b(i)
    b
  }

  def sum(i:Int,j:Int,a:Array[Array[Double]]):Double={//i列乘j列的轉置
    var result:Double=0
    for(x<- 0 to a.length-1)
      result +=(a(x)(i)*a(x)(j))
    result
  }


  def cov(a:Array[Array[Double]]):Array[Array[Double]]={//將特徵矩陣作為引數，返回協方差矩陣
    val m1=TransposedMatrix(a)
    val m2=RowAverage(m1)
    val m3=datasort(m1,m2)//將矩陣中心化
    val width=m3(0).length
    var b =Array.ofDim[Double](width,width)
    for(i <- 0 to width-1)
      for(j <- 0 to width-1)
        b(i)(j)=sum(i,j,m3)
    b
  }



  def datasort(a:Array[Array[Double]],b:Array[Double]):Array[Array[Double]]={//矩陣中心化，將每列減去列的均值
          for(i <- 0 to a(0).length-1)
            for(j <- 0 to a.length-1)
              a(j)(i) -= b(i)
    a
  }

  def gaussMatrix(a:Array[Array[Double]],delta:Array[Double]):Array[Array[Double]]={//a為特徵矩陣，delta為協方差矩陣列之和，返回高斯核函式矩陣
    val b=TransposedMatrix(a)
    val length=b(0).length
    var R =Array.ofDim[Double](length,length)
    for(i <- 0 to length-1)
      for(j <- 0 to length-1)
        R(i)(j)=Math.exp(-R1(i,j,b)/delta(j))
    R
  }

val test=Array(Array(2.0, 8.0), Array(3.0, 6.0), Array(9.0, 2.0))
val test2=cov(test)
val rowOfsum=sumOfRow(res65)
gaussMatrix(test,rowOfsum)

歡迎各位看官大爺批評指教。