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))*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] # 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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