神經網路（Neural Network）

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#!/usr/bin/env python# -*- coding: utf-8 -*-import numpy as np#矩陣運算def tanh(x):    return np.tanh(x)def tanh_deriv(x):#對tanh求導    return 1.0 - np.tanh(x)*np.tanh(x)def logistic(x):#s函數    return 1/(1 + np.exp(-x))def logistic_derivative(x):#對s函數求導    return logistic(x)*(1-logistic(x))class NeuralNetwork:#物件導向定義一個神經網路類    def __init__(self, layers, activation=‘tanh‘):#底線建構函式self 相當於本身這個類的指標 layer就是一個list 數字代表神經元個數        """        :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#之前定義的s函數            self.activation_deriv = logistic_derivative#求導函數        elif activation == ‘tanh‘:            self.activation = tanh#雙曲線函數            self.activation_deriv = tanh_deriv#求導雙曲線函數        self.weights = []#初始化一個list作為   權重        #初始化權重兩個值之間隨機初始化        for i in range(1, len(layers) - 1):#有幾層神經網路 除去輸出層            #i-1層 和i層之間的權重 隨機產生layers[i - 1] + 1 *  layers[i] + 1 的矩陣 -0.25-0.25            self.weights.append((2*np.random.random((layers[i - 1] + 1, layers[i] + 1))-1)*0.25)            #i層和i+1層之間的權重            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):#訓練神經網路        #learning rate        X = np.atleast_2d(X)#x至少2維        temp = np.ones([X.shape[0], X.shape[1]+1])#初始化一個全為1的矩陣        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])#隨機選行            a = [X[i]]            for l in range(len(self.weights)):  #going forward network, for each layer                #選擇一條執行個體與權重點乘 並且將值傳給啟用函數，經過a的append 使得所有神經元都有了值（正向）                a.append(self.activation(np.dot(a[l], self.weights[l])))  #Computer the node value for each layer (O_i) using activation function            error = y[i] - a[-1]  #Computer the error at the top layer 真實值與計算值的差（向量）            #通過求導 得到權重應當調整的誤差            deltas = [error * self.activation_deriv(a[-1])] #For output layer, Err calculation (delta is updated error)            #Staring backprobagation 更新weight            for l in range(len(a) - 2, 0, -1): # we need to begin at the second to last layer 每次減一                #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

　異或運算　

from NeuralNetwork import NeuralNetworkimport numpy as npnn = 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))

　

([0, 0], array([-0.00475208]))([0, 1], array([ 0.99828477]))([1, 0], array([ 0.99827186]))([1, 1], array([-0.00776711]))　　

　手寫體識別

#!/usr/bin/python# -*- coding:utf-8 -*-# 每個圖片8x8  識別數字：0,1,2,3,4,5,6,7,8,9import numpy as npfrom sklearn.datasets import load_digitsfrom sklearn.metrics import confusion_matrix, classification_reportfrom sklearn.preprocessing import LabelBinarizerfrom NeuralNetwork import NeuralNetworkfrom sklearn.model_selection import train_test_splitdigits = load_digits()X = digits.datay = digits.targetX -= X.min()  # normalize the values to bring them into the range 0-1X /= 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)

　

confusion_matrix

precision    recall  f1-score   support          0       1.00      0.97      0.99        34          1       0.75      0.91      0.82        46          2       1.00      0.92      0.96        50          3       1.00      0.92      0.96        51          4       0.94      0.91      0.92        53          5       0.95      0.96      0.96        57          6       0.97      0.95      0.96        38          7       0.88      1.00      0.93        35          8       0.88      0.83      0.85        42          9       0.86      0.82      0.84        44avg / total       0.92      0.92      0.92       450

　　

神經網路（Neural Network）