代码：
import numpy as np
from utils.features import prepare_for_training
from utils.hypothesis import sigmoid, sigmoid_gradient
class MultilayerPerceptron:
def __init__(self,data,labels,layers,normalize_data =False):
data_processed = prepare_for_training(data,normalize_data = normalize_data)[0]
self.data= data_processed
self.labels= labels
self.layers= layers #pixexls(784) hiddenLayer(25) output(10)
self.normalize_data= normalize_data
self.thetas = MultilayerPerceptron.thetas_init(layers) # weight
def predict(self,data):
data_processed = prepare_for_training(data,normalize_data = self.normalize_data)[0]
num_examples = data_processed.shape[0]
predictions = MultilayerPerceptron.feedforward_propagation(data_processed,self.thetas,self.layers)
return np.argmax(predictions,axis=1).reshape((num_examples,1))
def train(self,max_iterations=1000,alpha=0.1):
unrolled_theta = MultilayerPerceptron.thetas_unroll(self.thetas)
(optimized_theta,cost_history) = MultilayerPerceptron.gradient_descent(self.data,self.labels,unrolled_theta,self.layers,max_iterations,alpha)
self.thetas = MultilayerPerceptron.thetas_roll(optimized_theta,self.layers)
return self.thetas,cost_history
@staticmethod # 该方法不强制要求传递参数，如下声明一个静态方法
def thetas_init(layers):
num_layers = len(layers) #3
thetas = {}
"""
会执行两次，得到两组参数矩阵：25*(784+1) , 10*26
layers[0] = 784
layers[1] = 25
layers[2] = 10
"""
for layer_index in range(num_layers - 1):
in_count = layers[layer_index]
out_count = layers[layer_index+1]
# 这里需要考虑到偏置项，记住一点偏置的个数跟输出的结果是一致的
thetas[layer_index] = np.random.rand(out_count,in_count+1)*0.05 #随机进行初始化操作，值尽量小一点
#example: rand(2,3)
#[0.12 0.08 0.17]
#[0.53 0.13 0.98]
return thetas
@staticmethod
def thetas_unroll(thetas):
num_theta_layers = len(thetas)# thetas[0],thetas[1]
unrolled_theta = np.array([])
for theta_layer_index in range(num_theta_layers):
unrolled_theta = np.hstack((unrolled_theta,thetas[theta_layer_index].flatten()))
#arr1=np.array([1,2,3]) , arr2=np.array([4,5,6]) np.hstack(arr1,arr2) is [1,2,3,4,5,6]
#a=array([[1,2],[3,4],[5,6]]) , a.flatten() : array([1,2,3,4,5,6])
return unrolled_theta
@staticmethod
def gradient_descent(data,labels,unrolled_theta,layers,max_iterations,alpha):
optimized_theta = unrolled_theta
cost_history = []
for _ in range(max_iterations):
cost = MultilayerPerceptron.cost_function(data,labels,MultilayerPerceptron.thetas_roll(optimized_theta,layers),layers)
cost_history.append(cost)
theta_gradient = MultilayerPerceptron.gradient_step(data,labels,optimized_theta,layers)
optimized_theta = optimized_theta - alpha* theta_gradient
return optimized_theta,cost_history
@staticmethod
def gradient_step(data,labels,optimized_theta,layers):
theta = MultilayerPerceptron.thetas_roll(optimized_theta,layers)
thetas_rolled_gradients = MultilayerPerceptron.back_propagation(data,labels,theta,layers)
thetas_unrolled_gradients = MultilayerPerceptron.thetas_unroll(thetas_rolled_gradients)
return thetas_unrolled_gradients
@staticmethod
def back_propagation(data,labels,thetas,layers): # 反向传播
num_layers = len(layers)
(num_examples,num_features) = data.shape
num_label_types = layers[-1]
deltas = {}
#初始化操作
for layer_index in range(num_layers -1 ):
in_count = layers[layer_index]
out_count = layers[layer_index+1]
deltas[layer_index] = np.zeros((out_count,in_count+1)) #25*785 10*26
for example_index in range(num_examples):
layers_inputs = {}
layers_activations = {}
layers_activation = data[example_index,:].reshape((num_features,1))#785*1 加入偏置项
layers_activations[0] = layers_activation
#逐层计算
for layer_index in range(num_layers - 1):
layer_theta = thetas[layer_index] #得到当前权重参数值 25*785 10*26
layer_input = np.dot(layer_theta,layers_activation) #第一次得到25*1 第二次10*1
layers_activation = np.vstack((np.array([[1]]),sigmoid(layer_input)))
layers_inputs[layer_index + 1] = layer_input #后一层计算结果
layers_activations[layer_index + 1] = layers_activation #后一层经过激活函数后的结果
output_layer_activation = layers_activation[1:,:]
delta = {}
#标签处理
bitwise_label = np.zeros((num_label_types,1))
bitwise_label[labels[example_index][0]] = 1
#计算输出层和真实值之间的差异（当前样本）
delta[num_layers - 1] = output_layer_activation - bitwise_label
#遍历循环 L L-1 L-2 ...2
for layer_index in range(num_layers - 2,0,-1): # (start,stop,step) 计算一次
layer_theta = thetas[layer_index] # 当前theta
next_delta = delta[layer_index+1] # 下一层 变化
layer_input = layers_inputs[layer_index]
layer_input = np.vstack((np.array((1)),layer_input))# 加入偏置项
#按照公式进行计算
delta[layer_index] = np.dot(layer_theta.T,next_delta)*sigmoid_gradient(layer_input)
#过滤掉偏置参数
delta[layer_index] = delta[layer_index][1:,:]
for layer_index in range(num_layers-1): # 计算梯度值
layer_delta = np.dot(delta[layer_index+1],layers_activations[layer_index].T)
deltas[layer_index] = deltas[layer_index] + layer_delta #第一次25*785 第二次10*26
for layer_index in range(num_layers -1):
deltas[layer_index] = deltas[layer_index] * (1/num_examples)
return deltas
@staticmethod
def cost_function(data,labels,thetas,layers):
num_layers = len(layers) # 3
num_examples = data.shape[0] # 第一维度 数值[[1,2,3],[1,2,4]].shape[0] is 2
num_labels = layers[-1] # output
#前向传播走一次
predictions = MultilayerPerceptron.feedforward_propagation(data,thetas,layers)
#制作标签，每一个样本的标签都得是one-hot
bitwise_labels = np.zeros((num_examples,num_labels)) # 1700 * 10 e.g [0 0 0 0 0 0 0 0 1 0] ...
for example_index in range(num_examples):
bitwise_labels[example_index][labels[example_index][0]] = 1
bit_set_cost = np.sum(np.log(predictions[bitwise_labels == 1])) # here 1 is np.ones(bitwise_labels.shape())
bit_not_set_cost = np.sum(np.log(1-predictions[bitwise_labels == 0]))
cost = (-1/num_examples) *(bit_set_cost+bit_not_set_cost)
return cost
@staticmethod
def feedforward_propagation(data,thetas,layers):
num_layers = len(layers)
num_examples = data.shape[0]
in_layer_activation = data # input 1700 x 784+1 ,+1预处理后，偏置项b
# 逐层计算
for layer_index in range(num_layers - 1):
theta = thetas[layer_index]
out_layer_activation = sigmoid(np.dot(in_layer_activation,theta.T)) #矩阵乘法 dot（ 1700x185 ，185x25^） = shape[1700,25]
# 正常计算完之后是num_examples*25,但是要考虑偏置项 变成num_examples*(25 +1) +1 为偏置项
out_layer_activation = np.hstack((np.ones((num_examples,1)),out_layer_activation))
in_layer_activation = out_layer_activation
#返回输出层结果,结果中不要偏置项了 [0 位置]
return in_layer_activation[:,1:]
@staticmethod
def thetas_roll(unrolled_thetas,layers):
num_layers = len(layers)
thetas = {}
unrolled_shift = 0
for layer_index in range(num_layers - 1):
in_count = layers[layer_index]
out_count = layers[layer_index+1]
thetas_width = in_count + 1
thetas_height = out_count
thetas_volume = thetas_width * thetas_height
start_index = unrolled_shift
end_index = unrolled_shift + thetas_volume
layer_theta_unrolled = unrolled_thetas[start_index:end_index]
thetas[layer_index] = layer_theta_unrolled.reshape((thetas_height,thetas_width))
unrolled_shift = unrolled_shift+thetas_volume
return thetas