神經網路模型一般用來做分類，迴歸預測模型不常見，本文基於一個用來分類的BP神經網路，對它進行修改，實現了一個迴歸模型，用來做室內定位。模型主要變化是去掉了第三層的非線性轉換，或者說把非線性啟用函式Sigmoid換成f(x)=x函式。這樣做的主要原因是Sigmoid函式的輸出範圍太小，在0-1之間，而回歸模型的輸出範圍較大。模型修改如下：

程式碼如下：

#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層
            a = sigmoid(np.dot(w, a)+b)

        b = self.biases[-1]   # 最後一層
        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):  # 用隨機梯度下降演算法進行訓練

        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]):    # 正向傳播 前n-1層

            z = np.dot(w, activation)+b
            zs.append(z)
            activation = sigmoid(z)
            activations.append(activation)
# 最後一層，不用非線性
        b = self.biases[-1]
        w = self.weights[-1]
        z = np.dot(w, activation)+b
        zs.append(z)
        activation = z
        activations.append(activation)
        # backward pass 反向傳播
        delta = (self.cost).delta(zs[-1], activations[-1], y)   # 誤差 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) 隱藏層誤差
            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 Network
def 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))
 

#coding: utf8
import my_datas_loader_1
import network_0

training_data,test_data = my_datas_loader_1.load_data_wrapper()
#### 訓練網路，儲存訓練好的引數
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)
 

#coding: utf8
import my_datas_loader_1
import network_0
import matplotlib.pyplot as plt

test_data = my_datas_loader_1.load_test_data()
#### 呼叫訓練好的網路，用來進行預測
filename=r'D:\Workspase\Nerual_networks\parameters.txt'      ## 檔案儲存訓練好的引數
net = network_0.load(filename)                               ## 呼叫引數，形成網路
fig=plt.figure(1)
ax=fig.add_subplot(1,1,1)
ax.axis("equal") 
# plt.grid(color='b' , linewidth='0.5' ,linestyle='-')        #  新增網格
x=[-0.3,-0.3,-17.1,-17.1,-0.3]                               ## 這是九樓地形的輪廓
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 是預測出的座標        
    bx=pre[0]
    by=pre[1]                    
    ax.scatter(bx,by,s=4,lw=2,marker='.',alpha=1)  #散點圖   
    plt.pause(0.001)
plt.show() 

真實路徑為行人從原點繞環形走廊一圈。