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
进行训练的话，如果直接用原图进行训练，也是可以的（就如我们最喜欢Mnist手写体），但是大部分图片长和宽不一样，直接resize的话容易出问题。除去resize的问题外，有些时候数据不足该怎么办 ...