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perceptron:
激活函数 感知机模型：f(x)=sign(w*x+b) import numpy as np class Perceptron: """ This class models an artificial neuron with step activation function. """ def __init__(self, weights = np.array([1]), threshold = 0): self.weights = weights.astype(float) self.threshold = threshold def activate(self, values): strength = np.dot(values,self.weights) return int(strength > self.threshold) def update(self, values, train, eta=.1): for data_point in xrange(len(values)): prediction = self.activate(values[data_point]) error = train[data_point] - prediction weight_update = values[data_point]*error*eta# TODO self.weights += weight_update def test(): def sum_almost_equal(array1, array2, tol = 1e-6): return sum(abs(array1 - array2)) < tol p1 = Perceptron(np.array([1,1,1]),0) p1.update(np.array([[2,0,-3]]), np.array([1])) assert sum_almost_equal(p1.weights, np.array([1.2, 1, 0.7])) p2 = Perceptron(np.array([1,2,3]),0) p2.update(np.array([[3,2,1],[4,0,-1]]),np.array([0,0])) assert sum_almost_equal(p2.weights, np.array([0.7, 1.8, 2.9])) p3 = Perceptron(np.array([3,0,2]),0) p3.update(np.array([[2,-2,4],[-1,-3,2],[0,2,1]]),np.array([0,1,0])) assert sum_almost_equal(p3.weights, np.array([2.7, -0.3, 1.7])) if __name__ == "__main__": test()
sigmoid:
激活函数：sigmoid:1/(1+exp(x))
感知机与logistic regression的差别就是感知机激活函数是sign，logistic regression的激活函数是sigmoid 逻辑回归模型：f（x）= sigmoid(w*x+b) import numpy as np class Sigmoid: def __init__(self, weights = np.array([1])): self.weights = weights self.last_input = 0 # strength of last input self.delta = 0 # error signal def activate(self, values): strength = np.dot(values, self.weights) self.last_input = strength result = 1/(1+np.exp(-self.last_input)) return result def update(self, values, train, eta=.1): for X, y_true in zip(values, train): y_pred = self.activate(X) error = y_true - y_pred dx = 1/(1+np.exp(-self.last_input))*(1-1/(1+np.exp(-self.last_input))) dw = eta*error*dx*X self.weights += dw def test(): def sum_almost_equal(array1, array2, tol = 1e-5): return sum(abs(array1 - array2)) < tol u1 = Sigmoid(weights=[3,-2,1]) assert abs(u1.activate(np.array([1,2,3])) - 0.880797) < 1e-5 u1.update(np.array([[1,2,3]]),np.array([0])) assert sum_almost_equal(u1.weights, np.array([2.990752, -2.018496, 0.972257])) u2 = Sigmoid(weights=[0,3,-1]) u2.update(np.array([[-3,-1,2],[2,1,2]]),np.array([1,0])) assert sum_almost_equal(u2.weights, np.array([-0.030739, 2.984961, -1.027437])) if __name__ == "__main__": test()