#http://python.jobbole.com/82758/ # import numpy as np # # # # sigmoid function # def nonlin(x, deriv=False): # if (deriv == True): # return x * (1 - x) # return 1 / (1 + np.exp(-x)) # # # # input dataset # X = np.array([[0, 0, 1], # [0, 1, 1], # [1, 0, 1], # [1, 1, 1]]) # # # output dataset # y = np.array([[0, 0, 1, 1]]).T # # # seed random numbers to make calculation # # deterministic (just a good practice) # np.random.seed(1) # # # initialize weights randomly with mean 0 # syn0 = 2 * np.random.random((3, 1)) - 1 # # for iter in range(10000): # # forward propagation # l0 = X # l1 = nonlin(np.dot(l0, syn0)) # # # how much did we miss? # l1_error = y - l1 # # # multiply how much we missed by the # # slope of the sigmoid at the values in l1 # l1_delta = l1_error * nonlin(l1, True) # # # update weights # syn0 += np.dot(l0.T, l1_delta)#反向传播，w = w + f(y) * l1_delta # print("Output After Training:") # print(l1) import numpy as np def nonlin(x, deriv=False): if (deriv == True): return x * (1 - x) return 1 / (1 + np.exp(-x)) X = np.array([[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]]) y = np.array([[0], [1], [1], [0]]) np.random.seed(1) # randomly initialize our weights with mean 0 syn0 = 2 * np.random.random((3, 4)) - 1 syn1 = 2 * np.random.random((4, 1)) - 1 for j in range(60000): # Feed forward through layers 0, 1, and 2 l0 = X l1 = nonlin(np.dot(l0, syn0)) l2 = nonlin(np.dot(l1, syn1)) # how much did we miss the target value? l2_error = y - l2 if (j % 10000) == 0: print("Error:" + str(np.mean(np.abs(l2_error)))) # in what direction is the target value? # were we really sure? if so, don't change too much. l2_delta = l2_error * nonlin(l2, deriv=True) # how much did each l1 value contribute to the l2 error (according to the weights)? l1_error = l2_delta.dot(syn1.T) # in what direction is the target l1? # were we really sure? if so, don't change too much. l1_delta = l1_error * nonlin(l1, deriv=True) syn1 += l1.T.dot(l2_delta) syn0 += l0.T.dot(l1_delta) print("Output After Training:") print(l2)
# 1. # 关于非线性转化方程(non - linear # transformation # function) # # sigmoid函数(S # 曲线)用来作为activation # function: # # 1.1 # 双曲函数(tanh) # # 1.2 # 逻辑函数(logistic # function) # # # 2. # 实现一个简单的神经网络算法 import numpy as np def tanh(x): return np.tanh(x) def tanh_deriv(x): return 1.0 - np.tanh(x) * np.tanh(x) def logistic(x): return 1 / (1 + np.exp(-x)) def logistic_derivative(x): return logistic(x) * (1 - logistic(x)) class NeuralNetwork: def __init__(self, layers, activation='tanh'): """ :param layers: A list containing the number of units in each layer. Should be at least two values :param activation: The activation function to be used. Can be "logistic" or "tanh" """ if activation == 'logistic': self.activation = logistic self.activation_deriv = logistic_derivative elif activation == 'tanh': self.activation = tanh self.activation_deriv = tanh_deriv self.weights = [] for i in range(1, len(layers) - 1): #layers[i - 1]为前一输入层节点数 +1是加上一个偏置点， #layers[i]为当前层的输出节点数 +1是加上一个偏置点， self.weights.append((2 * np.random.random((layers[i - 1] + 1, layers[i] + 1)) - 1) * 0.25) self.weights.append((2 * np.random.random((layers[i] + 1, layers[i + 1])) - 1) * 0.25) def fit(self, X, y, learning_rate=0.2, epochs=10000): X = np.atleast_2d(X) #判断输入训练集是否为二维 temp = np.ones([X.shape[0], X.shape[1] + 1]) temp[:, 0:-1] = X # adding the bias unit to the input layer X = temp y = np.array(y) for k in range(epochs): i = np.random.randint(X.shape[0]) a = [X[i]] #len(self.weights)为输出节点个数，每个输出节点对应了一组权值是weight中的一行self.weights[l] for l in range(len(self.weights)): # going forward network, for each layer # Computer the node value for each layer (O_i) using activation function # a[l] 为输入数据的特征值 print(a[l]) print(self.weights[l]) a.append(self.activation(np.dot(a[l], self.weights[l]))) error = y[i] - a[-1] # Computer the error at the top layer deltas = [error * self.activation_deriv(a[-1])] # For output layer, Err calculation (delta is updated error) # Staring backprobagation for l in range(len(a) - 2, 0, -1): # we need to begin at the second to last layer # Compute the updated error (i,e, deltas) for each node going from top layer to input layer deltas.append(deltas[-1].dot(self.weights[l].T) * self.activation_deriv(a[l])) deltas.reverse() for i in range(len(self.weights)): layer = np.atleast_2d(a[i]) delta = np.atleast_2d(deltas[i]) self.weights[i] += learning_rate * layer.T.dot(delta) def predict(self, x): x = np.array(x) temp = np.ones(x.shape[0] + 1) temp[0:-1] = x a = temp for l in range(0, len(self.weights)): a = self.activation(np.dot(a, self.weights[l])) return a print("简单非线性关系数据集测试(XOR)") # 1. 简单非线性关系数据集测试(XOR): # # X: Y # 0 0 0 # 0 1 1 # 1 0 1 # 1 1 0 #from NeuralNetwork import NeuralNetwork import numpy as np nn = NeuralNetwork([2,2,1], 'tanh') X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]]) y = np.array([0, 1, 1, 0]) nn.fit(X, y) for i in [[0, 0], [0, 1], [1, 0], [1,1]]: print(i, nn.predict(i)) print("\n\n手写数字识别") # 2. 手写数字识别： # # 每个图片8x8 # 识别数字：0,1,2,3,4,5,6,7,8,9 import numpy as np from sklearn.datasets import load_digits from sklearn.metrics import confusion_matrix, classification_report from sklearn.preprocessing import LabelBinarizer #from NeuralNetwork import NeuralNetwork from sklearn.cross_validation import train_test_split digits = load_digits() X = digits.data y = digits.target X -= X.min() # normalize the values to bring them into the range 0-1 X /= X.max() nn = NeuralNetwork([64,100,10],'logistic') X_train, X_test, y_train, y_test = train_test_split(X, y) labels_train = LabelBinarizer().fit_transform(y_train) labels_test = LabelBinarizer().fit_transform(y_test) print("start fitting") nn.fit(X_train,labels_train,epochs=3000) predictions = [] for i in range(X_test.shape[0]): o = nn.predict(X_test[i] ) predictions.append(np.argmax(o)) print (confusion_matrix(y_test,predictions)) print (classification_report(y_test,predictions))
