目录

一、理论基础

二、案例背景

1.问题描述

2.思路流程

三、部分MATLAB仿真

四、仿真结论分析

五、参考文献

一、理论基础

       The neural network is mainly composed of processing units、网络拓扑结构、Composition of training rules.The processing unit is the basic unit of operation of the neural network,to simulate the function of neurons in the human brain.A processing unit has multiple inputs、输出,The input analog neural dendrites function,to transmit information;Outputs mimic axonal function of cranial nerves,Pass the processed information to the next processing unit,如图1所示.

图1 Neural network basic processing unit

Basic neural processing unit which is equivalent to the human neuron,如图2所示,

图2 Neurons vs. Neural Processing Units

       Processing units with the same function form the processing layer.A commonly used multilayer perceptron consists of an input layer、The output layer and several hidden layers are composed of,The topology of the neural network determines the processing units、The way and way of information transmission between layers.The training rule uses the transformation function to weight and sum the data processing,Training the Network System for Pattern Recognition,and convert it into a potential output value.Basic starting point for neural networks,is through multiple iterations of a simple function,Implements fitting and approximation to complex mappings.Neural network can achieve one-to-one、一对多的映射关系.因此,Many practical problems can be solved with neural network models

二、案例背景

1.问题描述

      Residential prices are at the heart of the housing market,The change of the housing market is related to the vital interests of the consumers,Commodity house price rise is lower,Sales are cold or prosperous,is a hot issue of social concern.因此,从不同角度来看,There are important theoretical and practical significance in the research on the price of commercial housing.Changes in commodity housing prices are affected by market supply and demand、人口、居民收入水平、Economic policy and many other factors,Its process of changing with time has great uncertainty,In order to more comprehensively describe the impact of various aspects on housing prices,To grasp the future trend of housing prices,The prediction method that will be passed through the neural network theory,Extended application to the research on the price of commercial housing,Make scientific predictions on housing prices.

2.思路流程

        The factors that affect the price changes of commercial housing are complex、多变的,It is difficult to all the factors into the analysis and research.But it can be considered that in a period of economic、politically stable period,The change in the price of commercial housing is determined by some basic factors.According to the introduction in Chapter 2 of this paper,Taking into account the realities of the Auckland region,将选取13a major factor as the main factor affecting the price of a house：

·Average crime rate per town;

·住宅用地超过500In proportion to the square;

·Proportion of non-commercial land in each town;

·The distance from the ocean is1公里内,则为1,否则为0;

·Oxide concentration;

·Every house on the number of average room;

·1940Proportion of former self-built houses;

·Weighted distance to shopping center;

·The label of high-speed km;

·每1万美元的管理费;

·教师比例;

·20Proportion of population under the age of;

·Retirement population ratio.

The above factors are expressed as：X1~X13.

三、部分MATLAB仿真

clc;
close all;
clear all;
warning off;

%% Parameters initialization 
%load data
load data\housing_data.mat
%Display the original data 
figure;
subplot(4,4,1);plot(x(1,:));title('Per capita crime rate per town');
subplot(4,4,2);plot(x(2,:));title('Proportion of residential land zoned for lots over 500m2');
subplot(4,4,3);plot(x(3,:));title('Proportion of non-retail business acres per town');
subplot(4,4,4);plot(x(4,:));title('1 within 1km from the sea, 0 otherwise');
subplot(4,4,5);plot(x(5,:));title('Nitric oxides concentration (parts per 10 million)');
subplot(4,4,6);plot(x(6,:));title('Average number of rooms per dwelling');
subplot(4,4,7);plot(x(7,:));title('Proportion of owner-occupied units built prior to 1940');
subplot(4,4,8);plot(x(8,:));title('Weighted distances to a main shopping center');
subplot(4,4,9);plot(x(9,:));title('Index of accessibility to motorways');
subplot(4,4,10);plot(x(10,:));title('Full-value of council rate per $10,000');
subplot(4,4,11);plot(x(11,:));title('Pupil-teacher ratio by town');
subplot(4,4,12);plot(x(12,:));title('Population below the age of 20');
subplot(4,4,13);plot(x(13,:));title('Percentage of retirees');
figure;
plot(10000*t,'r');title('PRICE');grid on

%% Select multiple data,train neural network 
%step1：parameter
net                   = fitnet(10);
net.trainParam.epcohs = 1000;%train times
net.trainParam.goal   = 0.0001;%aim error
%step2：train
net                   = train(net,x,t);

%% By using the neural network to predict the price of houses
view(net);
y1 = net(x);%predict
%% Shows the result 
figure;
subplot(221);plot(t);
title('Original price');axis([0,length(t),0,max(t)]);
subplot(222);plot(y1);
title('Predict prices ');axis([0,length(y1),0,max(y1)]);
subplot(223);plot(y1);hold on;plot(t,'r');hold off;
legend('Predict prices','Original price');
title('Predict prices');axis([0,length(y1),0,max(y1)]);
subplot(224);plot(y1 - t,'k');
title('Prediction error ');


figure
plot(y1);hold on;plot(t,'r');hold off;
legend('Predict prices','Original price');
title('Predict prices');axis([0,length(y1),0,max(y1)]);

figure
plot(y1 - t,'k');grid on;
title('Prediction error ');axis([0,length(y1),-50,50]);
%save networks
save net.mat net

四、仿真结论分析

 首先通过“load data\housing_data.mat”语句,You can call the function that needs to be trained toMATLAB的workspace中,Convenient data call.

图1 数据调用

    First execute the followingMATLAB指令：

net                = fitnet(10);

net.trainParam.epcohs = 1000;

net.trainParam.goal   = 0.0001;

The main meaning here is to usefitnetfunction to generate a random neural network,Then set the number of training to1000,The error target for training is set as0.0001.随机产生的netIts information is as follows：

Neural Network

…………………………….

dimensions:

…………………………….

connections:

…………………………….

subobjects:

…………………………….

functions:

…………………………….

weight and bias values:

…………………………….

methods:

…………………………….

    evaluate: outputs = net(inputs)

然后开始训练,执行如下的指令：

net= train(net,x,t);

训练完成后,The system will appear the following neural network interface：

图2 Neural Network Interface

     通过查看相关的信息,We can see the performance of the whole training process as shown below：

图3 Neural network training curve

Its training error distribution is as follows：

图4 training error distribution

    从图4.4可知,After training the neural network,Most data can be distributed around small errors,Individual data will produce large errors.

图5 数据分布

执行view,You can see the designed neural network model：

图4.6Neural network data model

Finally using the designednetFunction for data prediction.

Here, the original sample data is compared with the data predicted by the neural network,其结果如下：

图7 Comparison of original sample data and predicted data

    从图7可以看到,The data predicted by the neural network is basically similar to the original data,The error information obtained by subtraction is as follows：

图8 误差曲线

从图8可知,After passing through the neural network,The error between the predicted output value and the sample value is0附近,but for partial values,such as areas with several jumps in house prices,误差较大,This is due to the weak ability to predict emergencies..

五、参考文献

[01]White, H. Economic prediction using neural networks: the case of IBM Gaily stock returns, Neural Networks, IEEE International Conference on,1988,2(6): 451-458.

[02]Kamijo K &Tanigawa T,Stock Price Pattern Recognition: A Recurrent Network Approach. Proceeding of the International Joint Conference on Neural Networks,1990, 215-222.

[03]Youngohc Yoon&George Swales, Predicting Stock Price Per-Formance: A Neural Network Approach, System Sciences, International Conference on,1991. Proceedings of the Twenty-Fourth Annual Hawaii1991,4:156-162.A05-03