Question

这是我第一次从头开始编写感知器学习算法。我之前使用过开箱即用的ML解决方案，但想要真正理解并自己编写。出于某种原因，我的错误率不断增加而不是减少。所以看来我的算法是分歧而不是收敛。我写了一个公差范围，因为它有时会接近，但从来没有达到过标记。

我有三个重量; 1表示偏差，2表示X和Y.

我发现我的判别力： D = (weight0 + weight1 * Xi) + (weight2 * Yi)

如果判别式与预期输出不匹配，那么我用以下内容更新权重：注意：假设c和k是预定义常量，d =预期输出 w0 = w0 + cdk，w1 = w1 + cdXi，w2 = w2 + cdYi

以下是我在Python中的实现：

def weightsUpdate(weights, constantC, constantK, classificationd, x, y):
     weights[0] = weights[0] + constantC * classificationd * constantK # w0 = w0 + cdk
     weights[1] = weights[1] + constantC * classificationd * x #w1 = w1 + cdx
     weights[2] = weights[2] + constantC * classificationd * y #w2 = w2 + cdy

     return weights

def trainModel(df, weights, constantC, constantK, maxIter, threshHold):
     #grab the values in a list
     x = df['X'].values
     y = df['Y'].values
     d = df['Class'].values

     #define some variables to keep track
     numTurns = 0

     while numTurns < maxIter:
          errorRate = 0
          falsePosNeg = 0
          truePosNeg = 0

          '''assign som threshhold values. must accomodate for slight variance.'''
          posThreshHoldCeiling = 1 + threshHold
          posThreshHoldFloor = 1 - threshHold
          negThreshHoldFloor = -1 - threshHold
          negThreshHoldCeiling = -1 + threshHold

          for i in range(len(x)):
              ''' calculate the discriminant D = w0 + w1*xi + w2*yi '''
              discriminant = weights[0] + (weights[1] * x[i]) + (weights[2] * y[i])

              '''if the discriminant is not correct when compared to the correct output'''
              if ((discriminant >= posThreshHoldFloor and discriminant <= posThreshHoldCeiling) or
                (discriminant >= negThreshHoldFloor and discriminant <= negThreshHoldCeiling)):
                  truePosNeg += 1
                 #weights = weightsUpdate(weights, constantC, constantK, d[i], x[i], y[i])
        else:
                 '''update the weights'''
                 weights = weightsUpdate(weights, constantC, constantK, d[i], x[i], y[i])
                 falsePosNeg += 1


          numTurns += 1 #increase number of turns by 1 iteration
          print("Number of False Positive/Negative: " + str(falsePosNeg))
          print("Number of True Positive/Negative: " + str(truePosNeg))
          errorRate = falsePosNeg / len(x) * 100
          print("Error rate: " + str(errorRate) + "%")


         '''add stop conditions'''
         if (errorRate < 25):
             break
         else:
             continue

感谢您的帮助。

Answer 1

感知器学习算法（PLA）不需要阈值。 PLA也要求只有判别和预期输出的符号才能匹配，即sign(Discriminant) == d，因此不需要收敛于实际输出。以下是trainModel()的修改版本。

def trainModel(df, weights, constantC, constantK, maxIter):
#grab the values in a list
x = df['X'].values
y = df['Y'].values
d = df['Class'].values
globalErrorRate = 0

#define some variables to keep track
numTurns = 0

while numTurns < maxIter:
    localErrorRate = 0
    successRate = 0
    falsePosNeg = 0
    truePosNeg = 0

    for i in range(len(x)):
        #calculate the discriminant
        discriminant = weights[0] + (weights[1] * x[i]) + (weights[2] * y[i])

        if(isPos(discriminant) and d[i] == 1):
            truePosNeg += 1

        elif(isPos(discriminant) == False and d[i] == -1):
            truePosNeg += 1

        else:
            falsePosNeg += 1
            weights = weightsUpdate(weights, constantC, constantK, d[i], x[i], y[i])

    numTurns += 1 #increase number of turns by 1 iteration
    print("Number of False Positive/Negative: " + str(falsePosNeg))
    print("Number of True Positive/Negative: " + str(truePosNeg))
    localErrorRate = falsePosNeg / len(x) * 100
    successRate = truePosNeg / len(x) * 100
    print("Error rate: " + str(localErrorRate) + "%")
    print("Success rate: " + str(successRate) + "%")

    if successRate == 100:
        print("Trained Weight Values: " + str(weights))
        break
    else:
        continue

感知器学习算法发散

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