python实现神经网络

示例1

神经网络算法预测销量高低：

import pandas as pd
from keras.models import Sequential
from keras.layers.core import Dense, Activation

def cm_plot(y, yp):

  from sklearn.metrics import confusion_matrix  # 导入混淆矩阵函数

  cm = confusion_matrix(y, yp)  # 混淆矩阵

  import matplotlib.pyplot as plt  # 导入作图库

  plt.matshow(cm, cmap=plt.cm.Greens)  # 画混淆矩阵图，配色风格使用cm.Greens，更多风格请参考官网。

  plt.colorbar()  # 颜色标签

  for x in range(len(cm)):  # 数据标签

    for y in range(len(cm)):

      plt.annotate(cm[x, y], xy=(x, y), horizontalalignment='center', verticalalignment='center')

  plt.ylabel('True label')  # 坐标轴标签

  plt.xlabel('Predicted label')  # 坐标轴标签

  return plt
# 参数初始化
inputfile = '../Data/sales_data.xls'
data = pd.read_excel(inputfile, index_col=u'序号')  # 导入数据


# 数据是类别标签，要将它转换为数据
# 用1来表示“好” “是” “高” 这 3 个属性，用 0 来表示 “坏” “否” “低”
data[data == u'好'] = 1
data[data == u'是'] = 1
data[data == u'高'] = 1
data[data != 1] = 0
x = data.iloc[:, :3].values.astype(int)
y = data.iloc[:, 3].values.astype(int)


model = Sequential()  # 建立模型
model.add(Dense(input_dim=3, units=10, activation='relu'))  # 用relu函数作为激活函数，能够大幅度提供准确度
model.add(Dense(input_dim=10, units=1, activation='sigmoid'))  # 由于是 0-1 输出，用 sigmoid 函数作为激活函数
model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])  # 求解方法我们指定用 adam,还有sgd、rmsprop等可选
model.fit(x, y, epochs=1000, batch_size=10)  # 训练模型，学习1000次，每次以10个样本为一个batch进行迭代
yp = model.predict_classes(x).reshape(len(y))  # 分类预测
cm_plot(y, yp).show()  # 显示混淆矩阵可视化结果

效果如下：

示例2

推测出每个人的性别：

import numpy as np

def sigmoid(x):
    # our activation function: f(x) = 1 / (1 * e^(-x))
    return 1 / (1 + np.exp(-x))

class Neuron():
    def __init__(self, weights, bias):
        self.weights = weights
        self.bias = bias
        
    def feedforward(self, inputs):
        # weight inputs, add bias, then use the activation function
        total = np.dot(self.weights, inputs) + self.bias
        return sigmoid(total)
    
weights = np.array([0, 1]) # w1 = 0, w2 = 1
bias = 4
n = Neuron(weights, bias)

# inputs
x = np.array([2, 3])   # x1 = 2, x2 = 3
print(n.feedforward(x)) # 0.9990889488055994
class OurNeuralNetworks():
    """
    A neural network with:
      - 2 inputs
      - a hidden layer with 2 neurons (h1, h2)
      - an output layer with 1 neuron (o1)
    Each neural has the same weights and bias:
      - w = [0, 1]
      - b = 0
    """
    def __init__(self):
        weights = np.array([0, 1])
        bias = 0
        
        # The Neuron class here is from the previous section
        self.h1 = Neuron(weights, bias)
        self.h2 = Neuron(weights, bias)
        self.o1 = Neuron(weights, bias)
        
    def feedforward(self, x):
        out_h1 = self.h1.feedforward(x)
        out_h2 = self.h2.feedforward(x)

        # The inputs for o1 are the outputs from h1 and h2
        out_o1 = self.o1.feedforward(np.array([out_h1, out_h2]))
        return out_o1
        
network = OurNeuralNetworks()
x = np.array([2, 3])
print(network.feedforward(x)) # 0.7216325609518421
def mse_loss(y_true, y_pred):
    # y_true and y_pred are numpy arrays of the same length
    return ((y_true - y_pred) ** 2).mean()

y_true = np.array([1, 0, 0, 1])
y_pred = np.array([0, 0, 0, 0])

print(mse_loss(y_true, y_pred)) # 0.5

def sigmoid(x):
    # Sigmoid activation function: f(x) = 1 / (1 + e^(-x))
    return 1 / (1 + np.exp(-x))

def deriv_sigmoid(x):
    # Derivative of sigmoid: f'(x) = f(x) * (1 - f(x))
    fx = sigmoid(x)
    return fx * (1 - fx)

def mse_loss(y_true, y_pred):
    # y_true and y_pred are numpy arrays of the same length
    return ((y_true - y_pred) ** 2).mean()

class OurNeuralNetwork():
    """
    A neural network with:
      - 2 inputs
      - a hidden layer with 2 neurons (h1, h2)
      - an output layer with 1 neuron (o1)
      
    *** DISCLAIMER ***
    The code below is intend to be simple and educational, NOT optimal.
    Real neural net code looks nothing like this. Do NOT use this code.
    Instead, read/run it to understand how this specific network works.
    """
    def __init__(self):
        # weights
        self.w1 = np.random.normal()
        self.w2 = np.random.normal()
        self.w3 = np.random.normal()
        self.w4 = np.random.normal()
        self.w5 = np.random.normal()
        self.w6 = np.random.normal()
        # biases
        self.b1 = np.random.normal()
        self.b2 = np.random.normal()
        self.b3 = np.random.normal()
        
    def feedforward(self, x):
        # x is a numpy array with 2 elements, for example [input1, input2]
        h1 = sigmoid(self.w1 * x[0] + self.w2 * x[1] + self.b1)
        h2 = sigmoid(self.w3 * x[0] + self.w4 * x[1] + self.b2)
        o1 = sigmoid(self.w5 * h1 + self.w6 * h2 + self.b3)
        return o1
    
    def train(self, data, all_y_trues):
        """
        - data is a (n x 2) numpy array, n = # samples in the dataset.
        - all_y_trues is a numpy array with n elements.
        Elements in all_y_trues correspond to those in data.
        """
        learn_rate = 0.1
        epochs = 1000 # number of times to loop through the entire dataset
        
        for epoch in range(epochs):
            for x, y_true in zip(data, all_y_trues):
                
                # - - - Do a feedforward (we'll need these values later)
                sum_h1 = self.w1 * x[0] + self.w2 * x[1] + self.b1
                h1 = sigmoid(sum_h1)
                
                sum_h2 = self.w3 * x[0] + self.w4 * x[1] + self.b2
                h2 = sigmoid(sum_h2)
                
                sum_o1 = self.w5 * x[0] + self.w6 * x[1] + self.b3
                o1 = sigmoid(sum_o1)
                y_pred = o1
                
                # - - - Calculate partial derivatives.
                # - - - Naming: d_L_d_w1 represents "partial L / partial w1"
                d_L_d_ypred = -2 * (y_true - y_pred)
                
                # Neuron o1
                d_ypred_d_w5 = h1 * deriv_sigmoid(sum_o1)
                d_ypred_d_w6 = h2 * deriv_sigmoid(sum_o1)
                d_ypred_d_b3 = deriv_sigmoid(sum_o1)
                
                d_ypred_d_h1 = self.w5 * deriv_sigmoid(sum_o1)
                d_ypred_d_h2 = self.w6 * deriv_sigmoid(sum_o1)
                
                # Neuron h1
                d_h1_d_w1 = x[0] * deriv_sigmoid(sum_h1)
                d_h1_d_w2 = x[1] * deriv_sigmoid(sum_h1)
                d_h1_d_b1 = deriv_sigmoid(sum_h1)
                
                # Neuron h2
                d_h2_d_w3 = x[0] * deriv_sigmoid(sum_h2)
                d_h2_d_w4 = x[0] * deriv_sigmoid(sum_h2)
                d_h2_d_b2 = deriv_sigmoid(sum_h2)
                
                # - - - update weights and biases
                # Neuron o1
                self.w5 -= learn_rate * d_L_d_ypred * d_ypred_d_w5
                self.w6 -= learn_rate * d_L_d_ypred * d_ypred_d_w6
                self.b3 -= learn_rate * d_L_d_ypred * d_ypred_d_b3
                
                # Neuron h1
                self.w1 -= learn_rate * d_L_d_ypred * d_ypred_d_h1 * d_h1_d_w1
                self.w2 -= learn_rate * d_L_d_ypred * d_ypred_d_h1 * d_h1_d_w2
                self.b1 -= learn_rate * d_L_d_ypred * d_ypred_d_h1 * d_h1_d_b1
                
                # Neuron h2
                self.w3 -= learn_rate * d_L_d_ypred * d_ypred_d_h2 * d_h2_d_w3
                self.w4 -= learn_rate * d_L_d_ypred * d_ypred_d_h2 * d_h2_d_w4
                self.b2 -= learn_rate * d_L_d_ypred * d_ypred_d_h2 * d_h2_d_b2
                
            # - - - Calculate total loss at the end of each epoch
            if epoch % 10 == 0:
                y_preds = np.apply_along_axis(self.feedforward, 1, data)
                loss = mse_loss(all_y_trues, y_preds)
                print("Epoch %d loss: %.3f", (epoch, loss))
                
# Define dataset
data = np.array([
    [-2, -1], # Alice
    [25, 6],  # Bob
    [17, 4],  # Charlie
    [-15, -6] # diana
])
all_y_trues = np.array([
    1, # Alice
    0, # Bob
    0, # Charlie
    1 # diana
])

# Train our neural network!
network = OurNeuralNetwork()
network.train(data, all_y_trues)

# Make some predictions
emily = np.array([-7, -3]) # 128 pounds, 63 inches
frank = np.array([20, 2])  # 155 pounds, 68 inches
print("Emily: %.3f" % network.feedforward(emily)) # 0.951 - F
print("Frank: %.3f" % network.feedforward(frank)) # 0.039 - M