python实现实现BP神经网络回归预测模型神经网络回归预测模型
主要介绍了python实现BP神经网络回归预测模型，文中通过示例代码介绍的非常详细，对大家的学习或者工作
具有一定的参考学习价值，需要的朋友们下面随着小编来一起学习学习吧
神经网络模型一般用来做分类，回归预测模型不常见，本文基于一个用来分类的BP神经网络，对它进行修改，实现了一个回
归模型，用来做室内定位。模型主要变化是去掉了第三层的非线性转换，或者说把非线性激活函数Sigmoid换成f(x)=x函数。
这样做的主要原因是Sigmoid函数的输出范围太小，在0-1之间，而回归模型的输出范围较大。模型修改如下：
代码如下：
#coding: utf8
''''
author: Huangyuliang
'''
import json
import random
import sys
import numpy as np
#### Define the quadratic and cross-entropy cost functions
class CrossEntropyCost(object):
@staticmethod
def fn(a, y):
return np.sum(np.nan_to_num(-y*np.log(a)-(1-y)*np.log(1-a)))
@staticmethod
def delta(z, a, y):
return (a-y)
#### Main Network class
class Network(object):
def __init__(self, sizes, cost=CrossEntropyCost):
self.num_layers = len(sizes)
self.sizes = sizes
self.default_weight_initializer()
self.cost=cost
def default_weight_initializer(self):
self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]]
self.weights = [np.random.randn(y, x)/np.sqrt(x)
for x, y in zip(self.sizes[:-1], self.sizes[1:])]
def large_weight_initializer(self):
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):
"""Return the output of the network if ``a`` is input."""
for b, w in zip(self.biases[:-1], self.weights[:-1]): # 前n-1层
a = sigmoid(np.dot(w, a)+b)
b = self.biases[-1] # 最后一层
w = self.weights[-1]
a = 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_accuracy=False): # 用随机梯度下降算法进行训练
n = len(training_data)
for j in xrange(epochs):
random.shuffle(training_data)
mini_batches = [training_data[k:k+mini_batch_size] for k in xrange(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_evaluation_accuracy:
print ("Accuracy on evaluation data: {} / {}".format(self.accuracy(evaluation_data), j))
def update_mini_batch(self, mini_batch, eta, lmbda, n):
"""Update the network's weights and biases by applying gradient
descent using backpropagation to a single mini batch. The
``mini_batch`` is a list of tuples ``(x, y)``, ``eta`` is the
learning rate, ``lmbda`` is the regularization parameter, and
``n`` is the total size of the training data set.
"""
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):
"""Return a tuple ``(nabla_b, nabla_w)`` representing the
gradient for the cost function C_x. ``nabla_b`` and
``nabla_w`` are layer-by-layer lists of numpy arrays, similar
to ``self.biases`` and ``self.weights``."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
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