python实现BP神经网络回归预测模型

Python  /  管理员 发布于 7年前   344

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 jsonimport randomimport sysimport numpy as np #### Define the quadratic and cross-entropy cost functionsclass 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 classclass 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))*nwfor w, nw in zip(self.weights, nabla_w)]    self.biases = [b-(eta/len(mini_batch))*nbfor 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]    # feedforward    activation = x    activations = [x] # list to store all the activations, layer by layer    zs = [] # list to store all the z vectors, layer by layer    for b, w in zip(self.biases[:-1], self.weights[:-1]):  # 正向传播 前n-1层       z = np.dot(w, activation)+b      zs.append(z)      activation = sigmoid(z)      activations.append(activation)# 最后一层，不用非线性    b = self.biases[-1]    w = self.weights[-1]    z = np.dot(w, activation)+b    zs.append(z)    activation = z    activations.append(activation)    # backward pass 反向传播    delta = (self.cost).delta(zs[-1], activations[-1], y)  # 误差 Tj - Oj     nabla_b[-1] = delta    nabla_w[-1] = np.dot(delta, activations[-2].transpose()) # (Tj - Oj) * O(j-1)     for l in xrange(2, self.num_layers):      z = zs[-l]  # w*a + b      sp = sigmoid_prime(z) # z * (1-z)      delta = np.dot(self.weights[-l+1].transpose(), delta) * sp # z*(1-z)*(Err*w) 隐藏层误差      nabla_b[-l] = delta      nabla_w[-l] = np.dot(delta, activations[-l-1].transpose()) # Errj * Oi    return (nabla_b, nabla_w)   def accuracy(self, data):     results = [(self.feedforward(x), y) for (x, y) in data]     alist=[np.sqrt((x[0][0]-y[0])**2+(x[1][0]-y[1])**2) for (x,y) in results]     return np.mean(alist)   def save(self, filename):    """Save the neural network to the file ``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() #### Loading a Networkdef load(filename):  """Load a neural network from the file ``filename``. Returns an  instance of Network.  """  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 net def sigmoid(z):  """The sigmoid function."""   return 1.0/(1.0+np.exp(-z)) def sigmoid_prime(z):  """Derivative of the sigmoid function."""  return sigmoid(z)*(1-sigmoid(z))

调用神经网络进行训练并保存参数：

#coding: utf8import my_datas_loader_1import network_0 training_data,test_data = my_datas_loader_1.load_data_wrapper()#### 训练网络，保存训练好的参数net = network_0.Network([14,100,2],cost = network_0.CrossEntropyCost)net.large_weight_initializer()net.SGD(training_data,1000,316,0.005,lmbda =0.1,evaluation_data=test_data,monitor_evaluation_accuracy=True)filename=r'C:\Users\hyl\Desktop\Second_158\Regression_Model\parameters.txt'net.save(filename)

第190-199轮训练结果如下：

调用保存好的参数，进行定位预测：

#coding: utf8import my_datas_loader_1import network_0import matplotlib.pyplot as plt test_data = my_datas_loader_1.load_test_data()#### 调用训练好的网络，用来进行预测filename=r'D:\Workspase\Nerual_networks\parameters.txt'   ## 文件保存训练好的参数net = network_0.load(filename)    ## 调用参数，形成网络fig=plt.figure(1)ax=fig.add_subplot(1,1,1)ax.axis("equal") # plt.grid(color='b' , linewidth='0.5' ,linestyle='-')    # 添加网格x=[-0.3,-0.3,-17.1,-17.1,-0.3]    ## 这是九楼地形的轮廓y=[-0.3,26.4,26.4,-0.3,-0.3]m=[1.5,1.5,-18.9,-18.9,1.5]n=[-2.1,28.2,28.2,-2.1,-2.1]ax.plot(x,y,m,n,c='k') for i in range(len(test_data)):    pre = net.feedforward(test_data[i][0]) # pre 是预测出的坐标      bx=pre[0]  by=pre[1]ax.scatter(bx,by,s=4,lw=2,marker='.',alpha=1) #散点图    plt.pause(0.001)plt.show() 

定位精度达到了1.5米左右。定位效果如下图所示：

真实路径为行人从原点绕环形走廊一圈。

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