CN106204246A - A kind of BP neutral net credit estimation method based on PCA - Google Patents

Abstract

A kind of BP neutral net credit estimation method based on PCA of the present invention, from bank data, combing goes out the government data relating to individual, and combine bank's credit evaluation result for this individual, form sample data, estimated performance is improve to after sample data normalized, utilize PCA that sample data is carried out dimensionality reduction, complicated index can be solved, the data type of multidimensional, more meet the demand that big data process, and using bank for individual credit evaluation result as training BP neural network model reference, thus build a kind of credit evaluation model based on the big data of government, the subjectivity of expert estimation can be overcome, credit inquiry is provided to enterprise or individual, also the credit system of financial institution is supplemented, there is higher classification accuracy rate, practicality, and preferable Evaluated effect.

Description

A kind of BP neutral net credit estimation method based on PCA

Technical field

The present invention relates to a kind of BP neutral net credit estimation method based on PCA.

Background technology

At present, credit evaluation research is mainly carried out in financial institution, and it is logical according to the business datum of mechanism's themselves capture Cross the analysis and evaluation of professional person, obtain the credit report of enterprise and individual.The business datum relied solely in financial institution is entered Row credit evaluation easily causes the one-sidedness of conclusion.When financial institution is in the face of the less client of information material, tend not to Go out valuable credit evaluation.

Along with the arrival of big data, many-sided data fusion analysis becomes main flow, and the especially big data of government are for reference Play very important effect.The Chinese government grasps the data of more than 80%, but because various limitations and departmental benefits affect, data Can not share, mostly be in isolation and resting state, and complete due to its data of the assessment models set up based on government data Property, popularity and privacy, analyze that the result drawn is more convincing and social value.

The data relating to individual in the big data of government specifically include that people society data, educational data, health care data, just , there is the feature that data dimension is big, the increase of computation complexity can be caused in industry data etc..

Summary of the invention

It is an object of the invention to provide a kind of BP neutral net credit estimation method based on PCA, energy gram Take the subjectivity of expert estimation, there is higher classification accuracy rate, practicality, and preferably Evaluated effect, complexity can be solved Index, the data type of multidimensional, more meet big data process demand.

A kind of BP neutral net credit estimation method based on PCA of the present invention, comprises the following specific steps that:

Step 1, from bank data combing go out the government data relating to individual, and combine bank's letter for this individual By assessment result, form sample data, sample data be normalized, it is thus achieved that the sample data matrix X ' processed:

$X^{\′}=\left(\begin{array}{cccc}{x}_{11}^{\′}& x_{12}^{\′}& \mathrm{...}& x_{1p}^{\′}\\ x_{21}^{\′}& x_{22}^{\′}& \mathrm{...}& x_{2p}^{\′}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{n1}^{\′}& x_{n2}^{\′}& \mathrm{...}& x_{np}^{\′}\end{array}\right)$

Wherein, x '_ijRepresent the jth index of i-th sample data；

Step 11, sample data index for numeric type, use following formula to be normalized:

Wherein, i=1,2,3 ..., n, this n are total sample number, j=1,2,3 ..., p, this p are numeric type index sum, x_ij Represent the jth numeric type index of i-th sample data, max{x_ijRepresent the index that in i-th sample data, numerical value is maximum, min{x_ijRepresent the index that in i-th sample data, numerical value is minimum, x '_ijRepresent the i-th sample data after normalized Jth index；

Step 12, sample data index for nonumeric type, use following formula to be normalized:

Wherein, i=1,2,3 ..., n, this n are total sample number, j=1,2,3 ..., q, this q are nonumeric type index sum, x_ijRepresenting the jth nonumeric type index of i-th sample data, the corresponding final classification grade of m, K refers to classification grade number, w_m Represent the weight that each classification grade m is corresponding, N_m(x_ij) represent sample nonumeric type index x_ijSame alike result under corresponding classification grade m Quantity, N (x_ij) represent sample nonumeric type index x_ijThe quantity that same alike result is total；

Step 2, utilize PCA PCA that the sample data matrix after normalization in step 1 is carried out dimension-reduction treatment, Calculate its principal element affecting credit evaluation and the sequence of each factor, specifically include following steps:

The sample data matrix X ' that step 21, step 1 normalized is crossed:

$X^{\′}=\left(\begin{array}{cccc}{x}_{11}^{\′}& x_{12}^{\′}& \mathrm{...}& x_{1p}^{\′}\\ x_{21}^{\′}& x_{22}^{\′}& \mathrm{...}& x_{2p}^{\′}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{n1}^{\′}& x_{n2}^{\′}& \mathrm{...}& x_{np}^{\′}\end{array}\right)$

Set up the covariance matrix R of dependency relation level of intimate between the sample data after reflecting normalization, as follows:

$R=\left(\begin{array}{cccc}\frac{{\Σ}_{i=1}^n(x_{i1}^{\′}-\stackrel{-}{u_1})(x_{i1}^{\′}-\stackrel{-}{u_1})}{n-1}& \frac{{\Σ}_{i=1}^n(x_{i2}^{\′}-\stackrel{-}{u_2})(x_{i1}^{\′}-\stackrel{-}{u_1})}{n-1}& \mathrm{...}& \frac{{\Σ}_{i=1}^n(x_{ip}^{\′}-\stackrel{-}{u_p})(x_{i1}^{\′}-\stackrel{-}{u_1})}{n-1}\\ \frac{{\Σ}_{i=1}^n(x_{i1}^{\′}-\stackrel{-}{u_1})(x_{i2}^{\′}-\stackrel{-}{u_2})}{n-1}& \frac{{\Σ}_{i=1}^n(x_{i2}^{\′}-\stackrel{-}{u_2})(x_{i2}^{\′}-\stackrel{-}{u_2})}{n-1}& \mathrm{...}& \frac{{\Σ}_{i=1}^n(x_{ip}^{\′}-\stackrel{-}{u_p})(x_{i2}^{\′}-\stackrel{-}{u_2})}{n-1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ \frac{{\Σ}_{i=1}^n(x_{i1}^{\′}-\stackrel{-}{u_1})(x_{ip}^{\′}-\stackrel{-}{u_p})}{n-1}& \frac{{\Σ}_{i=1}^n(x_{i2}^{\′}-\stackrel{-}{u_2})(x_{ip}^{\′}-\stackrel{-}{u_p})}{n-1}& \mathrm{...}& \frac{{\Σ}_{i=1}^n(x_{ip}^{\′}-\stackrel{-}{u_p})(x_{ip}^{\′}-\stackrel{-}{u_p})}{n-1}\end{array}\right)$

Wherein,For the average of sample data X ' middle pth row, described covariance matrix R is real symmetric matrix, i.e. R_ij= R_ji；

Step 22, according to covariance matrix R calculate eigen vector:

Solving characteristic equation | λ I-R |=0, wherein I is unit matrix, obtains eigenvalue λ_i, wherein i=1,2 ..., p, and will Its order arrangement by size；

Obtain respectively corresponding to eigenvalue λ_iCharacteristic vector e_i, require here | | e_i| |=1, i.e.Wherein ei_j Represent characteristic vector e_iJth component；

Select m characteristic vector e_iComposition matrix and sample data X_iIt is multiplied, obtains m main constituent F_i, wherein m < p, Formula is as follows:

Wherein F_i1It is referred to as i-th sample x_iFirst principal component；

Step 23, calculating principal component contributor rate and contribution rate of accumulative total:

Owing to eigenvalue and main constituent are one to one, i-th main constituent F_iIt is by ith feature value λ_iCorresponding Characteristic vector e_iObtain, the i-th main constituent F_iContribution rate be through ith feature value λ_iCalculated, then the i-th main one-tenth Divide F_iContribution rate formula as follows:

Contribution rate of accumulative total computing formula is as follows:

Take contribution rate of accumulative total and reach m eigenvalue its m corresponding main constituent, wherein m < p of 85%～95%, thus obtain Training sample F to new:

Wherein the value in F matrix is calculated by formula 1-3 and obtains；

Step 3, the model of utilization BP neural network personal credit file:

Step 31, design BP neural network topology structure:

According to Kolmogorov theorem, set up three layers of BP neutral net, include respectively: input layer, hidden layer and output layer, should Input layer number is main constituent number m of training sample F newly generated in step 2, and output layer nodes is 1, and hidden layer saves Counting and determine according to Lippmann empirical equation, training function is TRAINLM, and adaptive learning function is LEARNGDM, and performance is divided Analysis function is MSE, and hidden layer transmission function is TANSIG function, and output layer transmission function is PURELIN function, according to Delta Practising rule to be adjusted the network connection weights between each node layer and threshold value, the computing formula of network global error E is:

In formula, p represents the number of training sample, E_tIt is the network training error of t training sample, z_tIt is the t training The network real output value of sample, c_tIt it is the credit evaluation result for individual of the bank known to the t training sample；

Step 32, the training of BP neural network model:

Step 2 being trained through sample data F of Data Dimensionality Reduction, a part of sampling notebook data F is as training number According to, remaining as test data, arrange between learning rate, factor of momentum, the connection weights of each layer, output threshold value imparting (-1,1) Random number, described BP neural metwork training use Delta learning rules, preset network global error E accuracy value and training time Number, calculates network global error E, if network global error E reaches setting value less than preset accuracy value or frequency of training, then ties Shu Xunlian, obtains BP neural network model；

Step 33, personal credit model evaluation

It is input in step 32 train in the BP neural network model obtained by test data and carries out model measurement, if classification Precision reaches more than threshold value, then it is assumed that have preferable classifying quality, and this BP neural network model is by assessment, otherwise, returns step Rapid 31, readjust BP neural network topology structure, until trained BP neural network model carries out letter to test data Threshold classification precision is reached during with assessment；

Step 4, the personal credit file that the data input step 3 of pending credit evaluation is set up model in, output Assessment result.

The data relating to individual in this government data specifically include that people society data, educational data, health care data, just Industry data.

Present invention combing from bank data goes out the government data relating to individual, and combines bank's letter for this individual By assessment result, form sample data, improve estimated performance to after sample data normalized, utilize PCA Sample data is carried out dimensionality reduction, the index of complexity, the data type of multidimensional can be solved, more meet the demand that big data process, and Using bank for the credit evaluation result of individual as the reference of training BP neural network model, thus build a kind of based on government The credit evaluation model of big data, can overcome the subjectivity of expert estimation, provides credit inquiry, also to finance to enterprise or individual The credit system of mechanism is supplemented, and has higher classification accuracy rate, practicality, and preferably Evaluated effect.

Detailed description of the invention

A kind of BP neutral net credit estimation method based on PCA of the present invention, specifically comprises the following steps that

Step 1, from bank data combing go out the government data relating to individual, and combine bank's letter for this individual By assessment result, form sample data, this government data relates to the data of individual specifically include that people society data, educational data, Health care data, employment data, such as, individual's essential information data include: sex, age, schooling, marital status Deng；Health status data include: health care costs situation, whether have major disease etc.；Employment status data include: employment unit, Employment unit property, inactive status etc.；Social security status data includes: social security pays situation etc., returns sample data One change processes, it is thus achieved that the sample data matrix X ' processed:

$X^{\&prime;}=\left(\begin{array}{cccc}{x}_{11}^{\&prime;}& x_{12}^{\&prime;}& \mathrm{...}& x_{1p}^{\&prime;}\\ x_{21}^{\&prime;}& x_{22}^{\&prime;}& \mathrm{...}& x_{2p}^{\&prime;}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{n1}^{\&prime;}& x_{n2}^{\&prime;}& \mathrm{...}& x_{np}^{\&prime;}\end{array}\right)$

Wherein, x '_ijRepresent the jth index of i-th sample data；

Step 11, sample data index for numeric type, use following formula to be normalized:

Wherein, i=1,2,3 ..., n, j=1,2,3 ..., p, n are total sample number, and p is numeric type index sum, x_ijRepresent The jth numeric type index of i-th sample data, max{x_ijRepresent the index that in i-th sample data, numerical value is maximum, min {x_ijRepresent the index that in i-th sample data, numerical value is minimum, x '_ijRepresent the jth of pretreated i-th sample data Index；

Step 12, sample data index for nonumeric type, use following formula to be normalized:

Wherein, i=1,2,3 ..., n, j=1,2,3 ..., q, n are total sample number, and q is nonumeric type index sum, x_ijTable Show the jth nonumeric type index of i-th sample data, the corresponding final classification grade of m, K refers to classification grade number, such as: Classification grade be excellent, good, in, poor, then K is 4, w_mRepresent the weight that each classification grade m is corresponding, N_m(x_ij) represent that sample is nonumeric Type index x_ijThe quantity of same alike result, N (x under corresponding classification grade m_ij) represent sample nonumeric type index x_ijSame alike result is total Quantity；

Illustrate, for this index of sex, be divided into man, two attributes of female, it is assumed that in 100 records, man is 60, Female is 40, classification grade be excellent, good, in, poor, give weight by classification grade, be followed successively by 0.4,0.3,0.2,0.1, if property The distributed number of other point of man, female correspondence classification grade respectively is as shown in the table:

	Excellent	Good	In	Difference
					Man	30	10	10	10
Female	10	6	2	2

Then:

Step 2, utilize PCA PCA that the sample data matrix after normalization in step 1 is carried out dimension-reduction treatment, Calculating its principal element affecting credit evaluation and the sequence of each factor, described PCA PCA is a kind of mathematic(al) manipulation Method, by the thinking of dimensionality reduction, multi objective is converted into a few aggregative indicator, it leads to one group of given correlated variables Crossing linear transformation becomes another to organize incoherent variable, the order arrangement that these new variablees successively decrease successively according to variance, specifically wraps Include following steps:

The sample data matrix X ' that step 21, step 1 normalized is crossed:

$X^{\&prime;}=\left(\begin{array}{cccc}{x}_{11}^{\&prime;}& x_{12}^{\&prime;}& \mathrm{...}& x_{1p}^{\&prime;}\\ x_{21}^{\&prime;}& x_{22}^{\&prime;}& \mathrm{...}& x_{2p}^{\&prime;}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{n1}^{\&prime;}& x_{n2}^{\&prime;}& \mathrm{...}& x_{np}^{\&prime;}\end{array}\right)$

Set up the covariance matrix R of dependency relation level of intimate between the sample data after reflecting normalization, as follows:

$R=\left(\begin{array}{cccc}\frac{{\&Sigma;}_{i=1}^n(x_{i1}^{\&prime;}-\stackrel{-}{u_1})(x_{i1}^{\&prime;}-\stackrel{-}{u_1})}{n-1}& \frac{{\&Sigma;}_{i=1}^n(x_{i2}^{\&prime;}-\stackrel{-}{u_2})(x_{i1}^{\&prime;}-\stackrel{-}{u_1})}{n-1}& \mathrm{...}& \frac{{\&Sigma;}_{i=1}^n(x_{ip}^{\&prime;}-\stackrel{-}{u_p})(x_{i1}^{\&prime;}-\stackrel{-}{u_1})}{n-1}\\ \frac{{\&Sigma;}_{i=1}^n(x_{i1}^{\&prime;}-\stackrel{-}{u_1})(x_{i2}^{\&prime;}-\stackrel{-}{u_2})}{n-1}& \frac{{\&Sigma;}_{i=1}^n(x_{i2}^{\&prime;}-\stackrel{-}{u_2})(x_{i2}^{\&prime;}-\stackrel{-}{u_2})}{n-1}& \mathrm{...}& \frac{{\&Sigma;}_{i=1}^n(x_{ip}^{\&prime;}-\stackrel{-}{u_p})(x_{i2}^{\&prime;}-\stackrel{-}{u_2})}{n-1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ \frac{{\&Sigma;}_{i=1}^n(x_{i1}^{\&prime;}-\stackrel{-}{u_1})(x_{ip}^{\&prime;}-\stackrel{-}{u_p})}{n-1}& \frac{{\&Sigma;}_{i=1}^n(x_{i2}^{\&prime;}-\stackrel{-}{u_2})(x_{ip}^{\&prime;}-\stackrel{-}{u_p})}{n-1}& \mathrm{...}& \frac{{\&Sigma;}_{i=1}^n(x_{ip}^{\&prime;}-\stackrel{-}{u_p})(x_{ip}^{\&prime;}-\stackrel{-}{u_p})}{n-1}\end{array}\right)$

Wherein,For the average of sample data X ' middle pth row, described covariance matrix R is real symmetric matrix, i.e. R_ij= R_ji；

Step 22, according to covariance matrix R calculate eigen vector:

Solving characteristic equation | λ I-R |=0, wherein I is unit matrix, obtains eigenvalue λ_i, wherein i=1,2 ..., p, and will It sequentially arranges by size, i.e. λ₁≥λ₂≥…≥λ_p≥0；

Obtain respectively corresponding to eigenvalue λ_iCharacteristic vector e_i, require here | | e_i| |=1, i.e.Wherein e_ijTable Show characteristic vector e_iJth component；

Select m characteristic vector e_iComposition matrix and sample data X_iIt is multiplied, obtains m main constituent F_i, wherein m < p, Formula is as follows:

Wherein F_i1It is referred to as i-th sample x_iFirst principal component；

Step 23, calculating principal component contributor rate and contribution rate of accumulative total:

Owing to eigenvalue and main constituent are one to one, i-th main constituent F_iIt is by ith feature value λ_iCorresponding Characteristic vector e_iObtain, the i-th main constituent F_iContribution rate be through ith feature value λ_iCalculated, then the i-th main one-tenth Divide F_iContribution rate formula as follows:

Contribution rate of accumulative total computing formula is as follows:

Take contribution rate of accumulative total and reach the eigenvalue λ of 85%～95%₁,λ₂,…,λ_mCorresponding the 1st, the 2nd ..., m-th Main constituent, wherein m < p, thus obtain new training sample F:

Wherein the value in F matrix is obtained by formula (1-3)；

Step 3, the model of utilization BP neural network personal credit file:

Step 31, design BP neural network topology structure:

According to Kolmogorov theorem, set up three layers of BP neutral net, include respectively: input layer, hidden layer and output layer, should Input layer number is main constituent number m of training sample F newly generated in step 2, and output layer nodes is 1, and hidden layer saves Counting and determine according to Lippmann empirical equation, training function is TRAINLM, and adaptive learning function is LEARNGDM, and performance is divided Analysis function is MSE, and hidden layer transmission function is TANSIG function, and output layer transmission function is PURELIN function, according to Delta Practising rule to be adjusted the network connection weights between each node layer and threshold value, the computing formula of network global error E is:

In formula, p represents the number of training sample, E_tIt is the network training error of t training sample, z_tIt is the t training The network real output value of sample, c_tIt it is the credit evaluation result for individual of the bank known to the t training sample；

Step 32, the training of BP neutral net:

Step 2 is trained through sample data F of Data Dimensionality Reduction, the 70% of sampling notebook data F as training data, Remaining 30% as test data, and arranging learning rate is 0.6, and factor of momentum takes 0.5, the connection weights of each layer, output threshold value Giving the random number between (-1,1), described BP neural metwork training uses Delta learning rules, preset network global error E essence Angle value is 0.5 or frequency of training is more than 5000, calculates network global error E, if network global error E is less than preset accuracy value Or frequency of training reaches setting value, then terminate training, obtain BP neural network model；

Step 33, personal credit model evaluation

It is input in step 32 train in the BP neural network model obtained by test data and carries out model measurement, if classification Precision reaches more than threshold value (70%), then it is assumed that have preferable classifying quality, and this BP neural network model is by assessment, otherwise, Return step 31, readjust BP neural network topology structure, until trained BP neural network model, to test data When carrying out credit evaluation, reach threshold classification precision；

Step 4, the personal credit file that the data input step 3 of pending credit evaluation is set up model in, output Assessment result.

The present invention focuses on: a kind of BP neutral net credit estimation method based on PCA of the present invention, From bank data, combing goes out the government data relating to individual, and combines bank's credit evaluation result for this individual, shape Become sample data, improve estimated performance to after sample data normalized, utilize PCA that sample data is entered Row dimensionality reduction, can solve the index of complexity, the data type of multidimensional, more meets the demand that big data process, and by bank for individual The credit evaluation result of people is as the reference of training BP neural network model, thus builds a kind of credit based on the big data of government Assessment models, can overcome the subjectivity of expert estimation, provides credit inquiry, also the credit body to financial institution to enterprise or individual System supplements, and has higher classification accuracy rate, practicality, and preferably Evaluated effect.

The above, not impose any restrictions the technical scope of the present invention, therefore every technical spirit according to the present invention Any trickle amendment, equivalent variations and the modification being made above example, all still falls within the range of technical solution of the present invention.

Claims (2)

1. a BP neutral net credit estimation method based on PCA, it is characterised in that include following concrete step Rapid:

Step 1, from bank data combing go out the government data relating to individual, and combine bank the credit of this individual commented Estimate result, form sample data, sample data is normalized, it is thus achieved that the sample data matrix X ' processed:

$X^{\&prime;}=\left(\begin{array}{cccc}{x}_{11}^{\&prime;}& x_{12}^{\&prime;}& \mathrm{...}& x_{1p}^{\&prime;}\\ x_{21}^{\&prime;}& x_{22}^{\&prime;}& \mathrm{...}& x_{2p}^{\&prime;}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{n1}^{\&prime;}& x_{n2}^{\&prime;}& \mathrm{...}& x_{np}^{\&prime;}\end{array}\right)$

Wherein, x '_ijRepresent the jth index of i-th sample data；

Step 11, sample data index for numeric type, use following formula to be normalized:

Wherein, i=1,2,3 ..., n, this n are total sample number, j=1,2,3 ..., p, this p are numeric type index sum, x_ijRepresent The jth numeric type index of i-th sample data, max{x_ijRepresent the index that in i-th sample data, numerical value is maximum, min {x_ijRepresent the index that in i-th sample data, numerical value is minimum, x '_ijRepresent the of the i-th sample data after normalized J index；

Step 12, sample data index for nonumeric type, use following formula to be normalized:

Wherein, i=1,2,3 ..., n, this n are total sample number, j=1,2,3 ..., q, this q are nonumeric type index sum, x_ijTable Showing the jth nonumeric type index of i-th sample data, the corresponding final classification grade of m, K refers to classification grade number, w_mRepresent The weight that each classification grade m is corresponding, N_m(x_ij) represent sample nonumeric type index x_ijThe number of same alike result under corresponding classification grade m Amount, N (x_ij) represent sample nonumeric type index x_ijThe quantity that same alike result is total；

Step 2, utilize PCA PCA that the sample data matrix after normalization in step 1 is carried out dimension-reduction treatment, calculate Go out its principal element affecting credit evaluation and the sequence of each factor, specifically include following steps:

The sample data matrix X ' that step 21, step 1 normalized is crossed:

$X^{\&prime;}=\left(\begin{array}{cccc}{x}_{11}^{\&prime;}& x_{12}^{\&prime;}& \mathrm{...}& x_{1p}^{\&prime;}\\ x_{21}^{\&prime;}& x_{22}^{\&prime;}& \mathrm{...}& x_{2p}^{\&prime;}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{n1}^{\&prime;}& x_{n2}^{\&prime;}& \mathrm{...}& x_{np}^{\&prime;}\end{array}\right)$

Set up the covariance matrix R of dependency relation level of intimate between the sample data after reflecting normalization, as follows:

$R=\left(\begin{array}{cccc}\frac{{\&Sigma;}_{i=1}^n(x_{i1}^{\&prime;}-\stackrel{-}{u_1})(x_{i1}^{\&prime;}-\stackrel{-}{u_1})}{n-1}& \frac{{\&Sigma;}_{i=1}^n(x_{i2}^{\&prime;}-\stackrel{-}{u_2})(x_{i1}^{\&prime;}-\stackrel{-}{u_1})}{n-1}& \mathrm{...}& \frac{{\&Sigma;}_{i=1}^n(x_{ip}^{\&prime;}-\stackrel{-}{u_p})(x_{i1}^{\&prime;}-\stackrel{-}{u_1})}{n-1}\\ \frac{{\&Sigma;}_{i=1}^n(x_{i1}^{\&prime;}-\stackrel{-}{u_1})(x_{i2}^{\&prime;}-\stackrel{-}{u_2})}{n-1}& \frac{{\&Sigma;}_{i=1}^n(x_{i2}^{\&prime;}-\stackrel{-}{u_2})(x_{i2}^{\&prime;}-\stackrel{-}{u_2})}{n-1}& \mathrm{...}& \frac{{\&Sigma;}_{i=1}^n(x_{ip}^{\&prime;}-\stackrel{-}{u_p})(x_{i2}^{\&prime;}-\stackrel{-}{u_2})}{n-1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ \frac{{\&Sigma;}_{i=1}^n(x_{i1}^{\&prime;}-\stackrel{-}{u_1})(x_{ip}^{\&prime;}-\stackrel{-}{u_p})}{n-1}& \frac{{\&Sigma;}_{i=1}^n(x_{i2}^{\&prime;}-\stackrel{-}{u_2})(x_{ip}^{\&prime;}-\stackrel{-}{u_p})}{n-1}& \mathrm{...}& \frac{{\&Sigma;}_{i=1}^n(x_{ip}^{\&prime;}-\stackrel{-}{u_p})(x_{ip}^{\&prime;}-\stackrel{-}{u_p})}{n-1}\end{array}\right)$

Wherein,For the average of sample data X ' middle pth row, described covariance matrix R is real symmetric matrix, i.e. R_ij=R_ji；

Step 22, according to covariance matrix R calculate eigen vector:

Solving characteristic equation | λ I-R |=0, wherein I is unit matrix, obtains eigenvalue λ_i, wherein i=1,2 ..., p, and pressed Size order arranges；

Obtain respectively corresponding to eigenvalue λ_iCharacteristic vector e_i, require here | | e_i| |=1, i.e.Wherein e_ijRepresent Characteristic vector e_iJth component；

Select m characteristic vector e_iComposition matrix and sample data X_iIt is multiplied, obtains m main constituent F_i, wherein m < p, formula As follows:

Wherein F_i1It is referred to as i-th sample x_iFirst principal component；

Step 23, calculating principal component contributor rate and contribution rate of accumulative total:

Owing to eigenvalue and main constituent are one to one, i-th main constituent F_iIt is by ith feature value λ_iCharacteristic of correspondence Vector e_iObtain, the i-th main constituent F_iContribution rate be through ith feature value λ_iCalculated, then the i-th main constituent F_i Contribution rate formula as follows:

Contribution rate of accumulative total computing formula is as follows:

Take contribution rate of accumulative total and reach m eigenvalue its m corresponding main constituent, wherein m < p of 85%～95%, thus obtain new Training sample F:

Wherein the value in F matrix is calculated by formula 1-3 and obtains；

Step 3, the model of utilization BP neural network personal credit file:

Step 31, design BP neural network topology structure:

According to Kolmogorov theorem, set up three layers of BP neutral net, include respectively: input layer, hidden layer and output layer, this input Node layer number is main constituent number m of training sample F newly generated in step 2, and output layer nodes is 1, the number of hidden nodes Determining according to Lippmann empirical equation, training function is TRAINLM, and adaptive learning function is LEARNGDM, performance evaluation letter Number is MSE, and hidden layer transmission function is TANSIG function, and output layer transmission function is PURELIN function, according to Delta study rule Then the network between each node layer being connected weights and threshold value is adjusted, the computing formula of network global error E is:

In formula, p represents the number of training sample, E_tIt is the network training error of t training sample, z_tIt is the t training sample Network real output value, c_tIt it is the credit evaluation result for individual of the bank known to the t training sample；

Step 32, the training of BP neural network model:

Step 2 being trained through sample data F of Data Dimensionality Reduction, a part of sampling notebook data F is as training data, surplus Remaining conduct test data, learning rate is set, factor of momentum, the connection weights of each layer, output threshold value give between (-1,1) with Machine number, described BP neural metwork training uses Delta learning rules, preset network global error E accuracy value and frequency of training, meter Calculate network global error E, if network global error E reaches setting value less than preset accuracy value or frequency of training, then terminate instruction Practice, obtain BP neural network model；

Step 33, personal credit model evaluation

It is input in step 32 train in the BP neural network model obtained by test data and carries out model measurement, if nicety of grading Reaching more than threshold value, then it is assumed that have preferable classifying quality, this BP neural network model is by assessment, otherwise, returns step 31, Readjust BP neural network topology structure, until trained BP neural network model carries out credit evaluation to test data Time reach threshold classification precision；

Step 4, the personal credit file that the data input step 3 of pending credit evaluation is set up model in, output assessment Result.

A kind of BP neutral net credit estimation method based on PCA the most according to claim 1, its feature It is: the data relating to individual in this government data specifically include that people society data, educational data, health care data, employment number According to.