#!/usr/bin/env python """ MLP网络 交叉熵损失函数 SGD优化器 """ #### 导入库 import json import random import sys import numpy as np import seaborn #### Miscellaneous functions def vectorized_result(j): """ one-hot函数 """ e = np.zeros((10, 1)) e[j] = 1.0 return e def sigmoid(z): """sigmoid导数""" return 1.0/(1.0 np.exp(-z)) def sigmoid_prime(z): """sigmoid导数""" return sigmoid(z)*(1-sigmoid(z)) #### MSE损失函数 class QuadraticCost(object): @staticmethod def fn(a, y): """计算网络前馈输出``a``和期望输出``y``间的损失 """ return 0.5*np.linalg.norm(a-y)**2 # linear algebra: 0.5* @staticmethod def delta(z, a, y): """返回输出层的误差delta""" return (a-y) * sigmoid_prime(z) #### 交叉熵损失函数 class CrossEntropyCost(object): @staticmethod def fn(a, y): """ 计算网络前馈输出``a``和期望输出``y``间的损失. np.nan_to_num保证数值计算的稳定性. 若``a``和``y``均为1, 则(1-y)*np.log(1-a) = nan np.nan_to_num确保此时输出为正确值0. """ return np.sum(np.nan_to_num(-y*np.log(a)-(1-y)*np.log(1-a))) @staticmethod def delta(z, a, y): """ 返回输出层的误差delta. 参数``z``未使用, 只是为了保证函数界面的一致性. """ return (a-y) #### Network类 class Network(object): def __init__(self, sizes, cost=CrossEntropyCost): """ 列表``sizes``指定网络每层神经元的数量 如列表[2, 3, 1]表示三层网络， 第一层有两个神经元， 第二层三个神经元， 三层一个神经元. """ self.num_layers = len(sizes) self.sizes = sizes self.weight_initializer() self.cost=cost def weight_initializer(self): """ 权值初始化为N(0,1)标准正态分布 偏置初始化为N(0，1)标准正态分布 通常第一层是输入层， 神经元无偏置 """ self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]] self.weights = [np.random.randn(y, x) for x, y in zip(self.sizes[:-1], self.sizes[1:])] def feedforward(self, a): """获取神经网络的输入``a``的输出.""" for b, w in zip(self.biases, self.weights): a = sigmoid(np.dot(w, a) b) return a def SGD(self, training_data, epochs, mini_batch_size, eta, lmbda = 0.0, evaluation_data=None, monitor_evaluation_cost=False, monitor_evaluation_accuracy=False, monitor_training_cost=False, monitor_training_accuracy=False, early_stopping_n = 0): """ 使用mini-batch SGD优化 ``training_data``: tuple list ``(x, y)`` ``evaluation_data``: validation/test数据 返回4 tuple lists: the (per-epoch) costs on the evaluation data the accuracies on the evaluation data the costs on the training data the accuracies on the training data. """ # 早停功能 best_accuracy=1 training_data = list(training_data) n = len(training_data) if evaluation_data: evaluation_data = list(evaluation_data) n_data = len(evaluation_data) # 早停功能 best_accuracy=0 no_accuracy_change=0 evaluation_cost, evaluation_accuracy = [], [] training_cost, training_accuracy = [], [] for j in range(epochs): random.shuffle(training_data) mini_batches = [ training_data[k:k mini_batch_size] for k in range(0, n, mini_batch_size)] for mini_batch in mini_batches: self.update_mini_batch( mini_batch, eta, lmbda, len(training_data)) print("Epoch %s training complete" % j) #if monitor_training_cost: cost = self.total_cost(training_data, lmbda) training_cost.append(cost) print("Cost on training data: {}".format(cost)) if monitor_training_accuracy: accuracy = self.accuracy(training_data, convert=True) training_accuracy.append(accuracy) print("Accuracy on training data: {} / {}".format(accuracy, n)) if monitor_evaluation_cost: cost = self.total_cost(evaluation_data, lmbda, convert=True) evaluation_cost.append(cost) print("Cost on evaluation data: {}".format(cost)) if monitor_evaluation_accuracy: accuracy = self.accuracy(evaluation_data) evaluation_accuracy.append(accuracy) print("Accuracy on evaluation data: {} / {}".format(self.accuracy(evaluation_data), n_data)) # 早停 if early_stopping_n > 0: if accuracy > best_accuracy: best_accuracy = accuracy no_accuracy_change = 0 #print("Early-stopping: Best so far {}".format(best_accuracy)) else: no_accuracy_change = 1 if (no_accuracy_change == early_stoppig_n):
#print("Early-stopping: No accuracy change in last epochs: {}".format(early_stopping_n))
return evaluation_cost, evaluation_accuracy, training_cost, training_accuracy
return evaluation_cost, evaluation_accuracy, \
training_cost, training_accuracy
def update_mini_batch(self, mini_batch, eta, lmbda, n):
"""
使用BP计算每个mini-batch的梯度, 并通过GD更新权值和偏置
``mini_batch``: tuple list ``(x, y)``
``eta``: 学习率
``lmbda``: 正则化参数
``n``: 训练集大小
"""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [(1-eta*(lmbda/n))*w-(eta/len(mini_batch))*nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb
for b, nb in zip(self.biases, nabla_b)]
def backprop(self, x, y):
"""
返回tuple ``(nabla_b, nabla_w)``表示代价函数C_x的梯度
``nabla_b``和``nabla_w``是逐层list
"""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# 前馈
activation = x
activations = [x] # 逐层保存全部激活值
zs = [] # 逐层保存全部z矢量值
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# 后向传播
delta = (self.cost).delta(zs[-1], activations[-1], y)
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
# l = 1表示最后一层神经元
# l = 2表示导数第二层神经元
for l in range(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return (nabla_b, nabla_w)
def accuracy(self, data, convert=False):
"""
返回输入``data``中神经网络输出正确结果的数量
神经网络的输出是最后一层神经元中最大激活值的索引值
``convert``:
False - validation/test data
True - training data
"""
if convert:
results = [(np.argmax(self.feedforward(x)), np.argmax(y))
for (x, y) in data]
else:
results = [(np.argmax(self.feedforward(x)), y)
for (x, y) in data]
result_accuracy = sum(int(x == y) for (x, y) in results)
return result_accuracy
def total_cost(self, data, lmbda, convert=False):
"""
数据集``data``的全部损失
``convert``:
False - training data
True - validation/test data
"""
cost = 0.0
for x, y in data:
a = self.feedforward(x)
if convert: y = vectorized_result(y)
cost += self.cost.fn(a, y)/len(data)
cost += 0.5*(lmbda/len(data))*sum(np.linalg.norm(w)**2 for w in self.weights) # '**' - power函数
return cost
def save(self, filename):
"""保存神经网络结构, 权值, 偏置和代价函数``filename``."""
data = {"sizes": self.sizes,
"weights": [w.tolist() for w in self.weights],
"biases": [b.tolist() for b in self.biases],
"cost": str(self.cost.__name__)}
f = open(filename, "w")
json.dump(data, f)
f.close()
#### 加载网络
def load(filename):
"""从文件filename加载网络，返回网络实例."""
f = open(filename, "r")
data = json.load(f)
f.close()
cost = getattr(sys.modules[__name__], data["cost"])
net = Network(data["sizes"], cost=cost)
net.weights = [np.array(w) for w in data["weights"]]
net.biases = [np.array(b) for b in data["biases"]]
return netnetwork代码，限于测试。