重讀李航博士的《統(tǒng)計學(xué)方法》對感知機(jī)做個總結(jié)包括感知機(jī)原始形式和對偶對偶形式的原理和Python實現(xiàn)所坯。

Python 實現(xiàn)

import numpy as np

steps = 1000
learning_rate = 1


X = np.array([[3,3],[4,3],[1,1]])
y = np.array([1,1,-1])

#  "normal" 感知機(jī)原始形式炸渡； "dual"感知機(jī)對偶形式
class Perceptron():
    def __init__(self, learning_rate,steps,model="normal"):
        """
        :param model: "normal" and "dual"
        """
        self.learning_rate = learning_rate
        self.steps = steps
        self.model = model

    def fit(self, X,y):
        """
        :param X: shape is (samples, feature size)
        :param y: shape is (samples,)
        :return: None
        """
        if self.model == "normal":
            W = np.zeros((X.shape[1]))
            b = np.zeros((1))

            for step in range(self.steps):
                for i in range(X.shape[0]):
                    s = 0
                    # 判斷是否是誤分類點
                    ls = y[i] * (np.dot(X[i],W) + b)
                    if  ls <= 0:
                        # print("第 %d 個樣本分類錯誤" % i)
                        W = W + self.learning_rate* X[i] * y[i]
                        b = b + self.learning_rate* y[i]
                        print("W", W, "b", b)
                        s += 1
                if s == 0:
                    self.W = W
                    self.b = b
                    print("全部分類正確")
                    break

        elif self.model == "dual":
            a = np.zeros((X.shape[0]))
            b = np.zeros((1))
            Gram = np.dot(X,X.T)
            W = np.dot(a * y, X)
            for step in range(self.steps):
                for i in range(X.shape[0]):
                    s = 0
                    ls = y[i] * (np.dot(a * y, Gram[i]) + b)
                    if ls <= 0:
                        a[i] = a[i] + learning_rate
                        b = b + learning_rate * y[i]
                        W = np.dot(a * y, X)
                        print("W", W,"b",b)
                        s += 1
                if s==0:
                    self.W = W
                    self.b = b
                    print("全部分類正確")
                    break

        else:
            print('model is "normal" or "dual"')

    def predict(self, X):
        result = np.dot(X,self.W.reshape(-1,1)) + self.b
        return np.where(result >= 0, 1,-1)


    def sampleLoss(self, X, y, W, b):
        return np.sum(y * (np.dot(X, W.T) + b))



if __name__ == "__main__":
    clf = Perceptron(learning_rate, steps,model="normal")
    clf.fit(X,y)
    print("#######  predict  ####### \n",clf.predict(X))

參考：

1. 《統(tǒng)計學(xué)方法》李航
2. 淺析感知機(jī)（二）--學(xué)習(xí)算法及python代碼剖析