这是我第一次从头开始编写感知器学习算法。我之前使用过现成的机器学习解决方案，但这次我想真正理解它并自己编写。不知为何，我的错误率一直在增加而不是减少。因此，看来我的算法在发散而不是收敛。我设置了一个容忍范围，因为它有时会接近目标，但从未完全达到要求。

我有三个权重；一个用于偏置，另外两个分别用于X和Y。

我通过以下方式找到判别函数：D = (weight0 + weight1 * Xi) + (weight2 * Yi)

如果判别函数与预期输出不匹配，那么我会使用以下方式更新权重：注意：假设c和k是预定义的常数，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

感谢所有帮助。

回答：

感知器学习算法（PLA）不应该需要阈值。此外，PLA要求判别函数和预期输出的符号应该匹配，即，sign(Discriminant) == d，因此不需要实际输出的收敛。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