1、1The application of the BP neural network in the housing demand modelAbstract. Real estate is the “barometer“ of the national economy, this paper studies the formation of the current domestic real estate prices and the inner mechanism of the influence factors, using the principal component analysis
2、to determine the composition of the real estate market development index model, and the BP neural network model is established, with specific data analysis which verifies the correctness and practicability of the model. Key words: real estate; Principal component analysis; The BP neural network The
3、development of real estate in our country is in the process, which gradually becomes the pillar industry of economic development in China, as a “barometer“ of the national economy. We study the current domestic real estate prices the inner mechanism of the formation and influence factors, using prin
4、cipal component analysis to determine the composition of the real estate market development index model, and established the BP neural network model, using specific data analysis which 2verifies the correctness and practicability of the model. 1. The establishment of the model 1.1 data processing 1.
5、1.1 the data source Data in table 1 provides data from 1997 to 2006, part of the missing data through the calendar issued by the China yearbook statistical analysis. A: gross domestic product per capita (current price), B:Per capita disposable income for urban households, C:Per capita annual income
6、for urban households, D: savings account, E :the natural population growth rate, F: the proportion of population in cities and towns at the end of the year, G: commercial housing sales prices this year, H:real estate enterprises this years national capital (as indicators of national policy control),
7、 I : real estate enterprises operating revenues this year. 1.1.2 data standardization Because the data dimension is different, and in order to eliminate dimension and the limitation of the order of magnitude, first of all before the principal component analysis, 3we make the data standardization. 1.
8、1.3 principal component analysis data Due to numerous factors affecting housing demand, there is a correlation between some factors, we adopt principal component analysis to extract the main factors, standardizing again for new data at the same time, lays the foundation for the establishment of the
9、BP neural network model. Principal component analysis results are shown in table 2 below: Because the former six cumulative contribution rates have reach 99.99%, before taking six principal components. Using EXCEL software according to the weight of each factor we compound six principal components:
10、K is the main component value Y1 in 1998-2006 , L is the main component value Y2 in 1998-2006. And so forth. we take six principal components as the final influence factors of the urban per capita building area.Q is the raw data per capita of building area of urban residents in 1998-2006. Finally, w
11、e normalize the new principal component data. 1.2 The establishment of the housing demand using the BP neural network 1.2.1 BP neural network BP neural network is a kind of according to the error back 4propagation multi-layer feedforward network, in pattern classification, prediction, etc have more
12、extensive application, is now one of the most popular neural network. It can learn and store a lot of input - output model mapping, without needing to know in advance what the mapping relationship between mathematical equations. BP network composed of input layer, hidden layer and output layer, each
13、 layer is composed of many parallel computing simple neuron, the network of neurons with full interconnection between layer and layer, namely a mutual connection between neurons. 1.2.2 housing demand model to determine the input layer Through the related literature, we find that there are many facto
14、rs, which affect the demand for housing, through comparative analysis we identified the influence diagram is as follows: In order to quantify national policy impact on real estate industry, we specially choose the real estate enterprise capital of the country this year as a important influencing fac
15、tors. Using the principal component analysis get six principal component factors affecting housing demand as an input parameter, so the input neurons is 6, corresponding to six factors: X10, X11, X12, X13, X14, X15. 51.2.3 housing demand model for determination of hidden layer The famous Kolmogorov
16、theorem has proved that as long as enough hidden layer nodes, which contains a hidden layer of neural networks we can approximate arbitrary precision of a nonlinear function, so we decide to adopt a hidden layer. The number of hidden layer node determine will largely affect the precision of the mode
17、l, which mainly has the following three formulas available: Where N is input layer node number and L is the output layer node number.A is constant between 1-10. Through the actual calculation contrast we take 15 hidden layer neurons . 1.2.4 housing demand model to determine the output layer This mod
18、el target index is only one per capita urban building area, so there is only one output neurons to Y, forecasting network as shown in figure 1: 2 model solution We use matlab software to solve the model, the key is to how select the transfer functions of hidden layer and output layer, training algor
19、ithm and choose expected error. 2.1 selection of transfer function This model after a large number of practical training 6results, finally selects tanhsig (hyperbolic transfer function) as the hidden layer and output layer transfer function. Its expression is as follows: which ranges from -1 to 1. 2
20、.2 selection of training algorithm function Standard BP algorithm uses the correction weights of the steepest gradient descent method, training process from a starting point for the error function of the slant gradually achieves minimum point which makes the error is zero. For the complex network, e
21、rror curved surface is in a multidimensional space, which therefore in the process of training might fall into a local minimum point, by that point in the direction of more change will make error increases, so that we have nothing to do, in a state of slow convergence speed, easy to fall into local
22、minimum. And by gradient descent method and Newton method combining Levenberg - Marquardt method, its advantage is to escape from the local minimum points. LM neural network optimization algorithm has fewer iteration times, fast convergence speed and high precision than the traditional BP and other
23、improved algorithm (such as the conjugate gradient method, additional momentum method and adaptive adjustment method and quasi-newton method, etc). Therefore, we select LM (trainlm) functions as a training algorithm. 72.3 selection of expected error Expected error control is through the network trai
24、ning parameter set. Considering the specific training networks when the training precision and time, we ensure the system which can be better predicted at the same time, ensure the accuracy of the predicting actual. We in the network make the training frequency extremum net. TrainParam. Epochs equal
25、s 200, network training error of the value net. TrainParam. Goal equals 0.0001. 2.4 results and analysis of BP neural network training We set up the training of the network parameters and use “train“ function for network training, then we consider whether BP neural network meet the accuracy requirem
26、ents, namely the network error output and actual output whether meet the accuracy requirement. If it conforms to specified requirements, the training of BP neural network (expressed ), is that we want to establish neural network model; Otherwise, we just reset the network related parameters, until m
27、eet the accuracy requirement. Demand for housing the training of neural network is shown in figure 2: During the training process, we take the data as the training data from 1997 to 2006, 2005 and 2006 data as test 8data, the results of the normalized forecasts for 2005 and 2006 new town residential
28、 area are 26.3562 and 26.3562. Respectively, compared with the original data 26.1 and 27.1, the predicted results are very satisfactory. Thus we can conclude that under the condition of the hypothesis, our model can more accurately predict the demand for housing in our country. References 1 Xie Zhonghua. MATLAB statistical analysis and application of 40 case analysis M. Beijing university of aeronautics and astronautics press, 2010. 2 MeiJunZhi. Structure optimization and the application of BP neural network D. Zhongshan university ,2010.
