CN112308288A - Particle swarm optimization LSSVM-based default user probability prediction method - Google Patents

Particle swarm optimization LSSVM-based default user probability prediction method Download PDF

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CN112308288A
CN112308288A CN202011047313.4A CN202011047313A CN112308288A CN 112308288 A CN112308288 A CN 112308288A CN 202011047313 A CN202011047313 A CN 202011047313A CN 112308288 A CN112308288 A CN 112308288A
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江远强
李兰
韩璐
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Abstract

The invention discloses a default user probability prediction method based on a particle swarm optimization LSSVM; s1: acquiring sample data; s2: extracting the collected data features; s3: establishing an LSSVM classification model; s4: optimizing LSSVM prediction model parameter combination (C, sigma) obtained by training in S3 by adopting a particle swarm optimization; s5: inputting a test data set into a default user probability prediction model of the trained LSSVM; s6: deploying the LSSVM prediction model to an application platform; the default probability prediction model of the LSSVM algorithm based on particle swarm optimization has good prediction precision, error evaluation indexes are maintained in a small range, the purpose of predicting risks is reduced, the convergence rate of the algorithm is greatly improved, and the requirements of the online prediction model of Internet financial application behaviors are met.

Description

Particle swarm optimization LSSVM-based default user probability prediction method
Technical Field
The invention belongs to the technical field of probability prediction, and particularly relates to a default user probability prediction method based on a particle swarm optimization LSSVM.
Background
In the current internet financial industry, the method for predicting the default probability of a customer mainly comprises the following steps: machine learning algorithms such as logistic regression, random forest, GBDT and neural network, however, these algorithms have some disadvantages: the neural network model has good nonlinear approximation capability, but various parameters related to network topology in the model need to be specified, large sample data volume is needed for training, and the problem of local optimization is easily caused. The Support Vector Machine (SVM) is based on the modern statistical theory, an algorithm which integrates the structure risk minimization principle and the kernel technology has the characteristics of nonlinearity, high dimensionality, high prediction precision, strong generalization capability, easiness in finding a global optimal solution and the like, but the SVM needs to obtain a Support Vector by means of quadratic programming, the constraint condition is inequality constraint, and when the number of training samples is increased, the problem of quadratic programming faces to 'dimension'. For behavior data of large-scale internet finance, the SVM has the problems of low training speed, long time consumption and the like, and the requirement of online prediction of the default probability of the application user of the mutual-fund platform is difficult to meet.
A Least Square Support Vector Machine (LSSVM) is an expansion and improvement of an SVM, the Least square idea is introduced, a quadratic loss function is used for replacing an insensitive loss function in the SVM, an inequality constraint in the SVM is changed into an equality constraint by adopting a quadratic programming method, the quadratic programming problem solved by a standard SVM is converted into the solution of a group of linear relational expressions, the optimization function only needs to solve a linear equality equation set, the operation process is simplified while the LSSVM inherits the advantages of the SVM, the convergence speed of the algorithm is improved, the training efficiency and accuracy are improved, the practical problems of large data size, over-learning, high dimensionality and the like can be well solved, and the requirement of online prediction of the default probability of an application user on a mutual-fund platform can be realized.
The performance of the LSSVM depends on the selected kernel function parameters to a great extent, the RBF kernel function has extremely high performance, the parameters of the LSSVM based on the RBF kernel function mainly relate to regularization parameters C and kernel width sigma, the fitting performance and generalization capability of the LSSVM are directly influenced, the prediction accuracy and performance of the method are severely restricted, and therefore the parameter selection is very important. The traditional method for selecting parameters based on experience is high in randomness, optimization methods based on grid searching, cross validation and the like have the problems of large calculated amount, long consumed time, low prediction precision and the like, optimization of LSSVM parameters by methods such as a genetic algorithm and an artificial neural network algorithm also has the defects of easiness in falling into local optimization, low convergence speed, long consumed time and the like, and the prior art faces various problems.
Although the method for predicting the probability of the default user based on sparse feature embedding disclosed by the grant publication number CN109919436A effectively improves the processing capability of class coding, and simultaneously effectively reduces the dimension of the feature space in the subsequent machine learning process, which is beneficial to the learning and processing of the machine learning model, the method does not solve the problems of excessive algorithm steps in the existing probability detection, inevitably causes system redundancy, and cannot solve the complicated problems of nonlinearity, incorgrueness and multiple peaks, and therefore the method for predicting the probability of the default user based on the particle swarm optimization LSSVM is proposed.
Disclosure of Invention
The invention aims to provide a default user probability prediction method based on a particle swarm optimization LSSVM, so as to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme: a default user probability prediction method based on particle swarm optimization LSSVM comprises the following steps:
s1: acquiring sample data, selecting the same number of normal repayment and overdue customers as modeling samples according to the post-loan performance from the back end of the Internet financial platform, acquiring personal basic information when the account of the sample customer is registered and applying, and acquiring operation behavior buried point data from monitoring software;
s2: extracting the collected data characteristics, carrying out standardization processing and principal component analysis dimension reduction, and dividing a training set and a verification set according to application time;
s3: establishing an LSSVM classification model, selecting a radial basis function as a kernel function, taking a training sample as an input vector, and training the LSSVM classification model according to KKT optimal conditions and Mercer conditions to obtain a penalty factor C and a kernel function width parameter sigma;
s4: optimizing LSSVM prediction model parameter combination (C, sigma) obtained by training in S3 by adopting a particle swarm algorithm, obtaining an optimal value in a global range, substituting the optimized parameter, and constructing a default user probability prediction model based on the particle swarm optimization LSSVM;
s5: inputting a test data set into a trained default user probability prediction model of the LSSVM, predicting a result and actual data, performing prediction error evaluation analysis, and comparing the prediction error evaluation analysis with the LSSVM model optimized by a gradient descent method, a genetic algorithm and an ant colony algorithm by taking prediction accuracy as an index;
s6: the LSSVM prediction model is deployed to an application platform, real-time data of an application user are collected to carry out standardized input on the prediction model to obtain default probability prediction, real-time approval of the application client is achieved, performance data are input into the model to be trained regularly, and online updating of the model is achieved.
Preferably, the personal basic information in S1 includes: the mobile phone number, the academic calendar, the marital status, the working unit, the address, the contact information, the personal basic information, the credit transaction information, the public information and the special record data which are acquired by the credit investigation report; the data of the buried points comprises equipment behavior data and log data which are collected when the points are buried.
Preferably, the device behavior data comprises the number of times of logging in the platform, the number of clicks, the click frequency, the total input time and the average time consumption, the mobile phone number data, the GPS position, the MAC address, the IP address data, the geographic information application frequency, the IP application frequency, the device electric quantity ratio and the average acceleration of a gyroscope, the log data comprises the login number in 7 days, the time length from the first click to the application and the credit grant, the maximum number of sessions in one day and the behavior statistics of the previous week of the application and the credit grant, and under the requirement of compliance, the log data is not limited to the universe multi-dimensional big data including the mobile internet behavior data, the behavior data in the loan APP, the credit history and the operator data.
Preferably, in the normalization processing in S2, z-score normalization processing is used to unify dimensions of the data, principal component analysis dimension reduction can process isolated points and noise data in the sample, eliminate self-correlation between features, and delete redundancy indexes to achieve dimension reduction.
Preferably, the principal component analysis dimensionality reduction is used as a method for processing high-dimensional data, and the processing mode is as follows:
firstly, standardizing raw data by adopting a z-score method;
secondly, a covariance matrix R of the normalized data vector is established, and m eigenvalues lambda of the covariance matrix R are solved again1＞λ2＞…＞λmAnd a feature vector l1,l2,…,lmSorting according to the descending order of the characteristic values;
finally according to the cumulative variance contribution rate
Figure BDA0002708399490000041
The first M principal components are extracted.
Preferably, in S3, the penalty factor C and the kernel function width parameter σ in the LSSVM are optimized by using a particle swarm algorithm instead of the conventional grid search algorithm, a parameter combination (C, σ) is used as a position coordinate (x, y) of a particle in a search space of the particle swarm algorithm, a total relative error of a prediction result is used as a fitness evaluation function, a particle coordinate vector value [ C, σ ] with the smallest fitness value is selected as an optimal parameter combination of the LSSVM, and an optimal value is obtained in a global range.
Preferably, the specific steps of the particle swarm optimization LSSVM are as follows:
s41: setting a particle search dimension D and a population scale n of a particle swarm optimization algorithm, setting an initial iteration number t to be 0 and a maximum iteration number hmaxLearning factor c1And c2The initial position x and the velocity v of the particle are randomly set, the position x of the particle in the search space is set to be (C, σ) as the parameter combination (C, σ), and C e [1,10000 ] is empirically set]，σ∈[0,1]Velocity v of each particleiIs limited to [ v ]min，vmax]Inner, vmaxUsually taking the width of the search space;
s42: selecting an average Relative Error value (MRE) of the predicted values of the training samples to define a fitness function of the particle swarm algorithm, wherein an optimization objective function is as follows:
Figure BDA0002708399490000042
wherein min fit (C, sigma) is fitness function value, yiAnd
Figure BDA0002708399490000043
respectively representing the ith actual value and the corresponding predicted value, wherein i is 1,2, …, and n represents the number of training samples;
s43: for each particle, comparing its fitness function value with its current best position individual optimum value pBest, the individual extreme value of each particle is updated with the following formula:
Figure BDA0002708399490000051
s44: for each particle, the fitness function value is compared with the current best position global optimum gBest, and the global extreme values for all the particles are selected as follows:
gBest(t+1)＝max(pBesti(t+1))，i＝1,2,…,n；
s45: updating the position and the speed of the particles, and updating the individual optimal value and the global optimal value of the particles, wherein the updating formula is as follows:
vi(t+1)＝wvi(t)+c1r1(t)(pBesti(t)-xi(t))+c2r2(gBest(t)-xi(t))
xi(t+1)＝wxi(t)+vi(t+1)
wherein v isi(t+1)、xi(t +1) denotes the ith particle velocity and position, v, for the t +1 th iteration, respectivelyi(t)、xi(t) denotes the current ith particle velocity and position, pBest, respectivelyi(t) searching the current best position individual optimal value for the ith particle, and gBest (t) searching the current best position for the wholeSet to global optimum, c1、c2For learning factors or acceleration coefficients, the step lengths are used to adjust the current particle to the optimal position of the current particle and the optimal position of the current particle, and the value is usually 2, r1、r2Is a random number on (0,1), w is an inertial weight, and is used for controlling the influence of the previous iteration of the current particle on the current iteration;
s46: repeating S42, and calculating the updated fitness function value;
s47: judging whether the updated fitness function value meets the particle swarm algorithm termination condition or reaches the maximum iteration number hmaxStopping iteration, if not, returning to S43, and if so, ending;
s48: decoding the coordinate vector value [ C, sigma ] of the best position experienced by the whole group to obtain the optimal LSSVM parameter combination, obtaining the optimal value in the global range, carrying out training, precision verification and prediction, stopping operation and substituting the LSSVM prediction classification equation of S3 to obtain the LSSVM prediction model for particle swarm optimization.
Preferably, in S4, the penalty factor and the kernel function width parameter of the LSSVM are optimized by using the particle swarm algorithm to obtain respective optimal optimized values, and finally, the predicted value of the client default probability in the test set is calculated according to the optimal optimized values of the penalty factor and the kernel function width parameter.
Preferably, in S6, the real-time data requested by the customer is collected online, and the collected real-time data is normalized and input into the established LSSVM model to obtain the result of predicting the probability of the default user of the customer.
Preferably, in S3, the LSSVM regression prediction model is built by using training samples, and a set of training samples is given
Figure BDA0002708399490000061
Is an M-dimensional input vector, ykE R is a one-dimensional output vector, k 1, …, N, using a non-linear mapping
Figure BDA0002708399490000062
Mapping the input samples to a high-dimensional feature space in a non-linear mode to construct a high-dimensional space linear regression function:
Figure BDA0002708399490000063
wherein the content of the first and second substances,
Figure BDA0002708399490000064
as a kernel space mapping function, wTIs a weight vector, b is a deviation amount,
according to the principle of minimizing the structural risk, the LSSVM constructs the regression function to form a minimum objective function with equality constraint:
Figure BDA0002708399490000065
Figure BDA0002708399490000066
where J (w, e) is the loss function, C is the regularization parameter, ek(1,2, …, N) is the training error for N training sample points,
in order to solve the optimization problem, a lagrange multiplier is introduced to change the constrained optimization problem into an unconstrained optimization problem:
Figure BDA0002708399490000067
wherein, akLagrange multiplier, k is 1, …, N training sample number,
according to the Karush-Kuhn-Tucker (KKT) optimal condition and Mercer condition theory, L (w, b, e, a) is subjected to w, b, e respectivelyk、akPerforming partial derivative solution and making partial derivativeThe number equals zero, resulting in the following equations and constraints:
Figure BDA0002708399490000071
obtaining an LSSVM classification prediction model:
Figure BDA0002708399490000072
wherein f (x) is the prediction output, akE is the Lagrange multiplier R, b is the deviation, K (x, x)k) As kernel function, x is a fixed sample in the training samples, xkFor the kth sample in the training samples, k is 1,2, …, and N is the number of samples in the training set;
the K (x, x)k) Selecting a Radial Basis Function (RBF) for the kernel Function, the expression:
Figure BDA0002708399490000073
the RBF is used as a kernel function of the LSSVM, and finally the LSSVM classification prediction model formula is obtained as follows:
Figure BDA0002708399490000074
compared with the prior art, the invention has the beneficial effects that:
(1) compared with logistic regression, random forests, neural networks and SVM, the LSSVM algorithm has the advantages of less required determined parameters, strong generalization capability of the model, high prediction precision and difficulty in falling into local minimum values.
(2) The particle swarm optimization is relatively superior to a neural network and a genetic algorithm, many parameters do not need to be adjusted, global optimization is searched for through local optimization through iteration from random solution, and the method is suitable for solving nonlinear, infinitesimal and multi-peak complex problems.
(3) The penalty factor C and the kernel function width parameter sigma of the LSSVM are optimized based on the particle swarm optimization algorithm, so that the defects that the LSSVM has low convergence speed and is easy to fall into local optimization in the training process and the like are avoided in a global optimization mode, and the convergence speed and the prediction accuracy of the LSSVM are improved.
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FIG. 1 is a schematic view of the step structure of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, the present invention provides a technical solution: a default user probability prediction method based on particle swarm optimization LSSVM comprises the following steps:
s1: acquiring sample data, selecting the same number of normal repayment and overdue customers as modeling samples according to the post-loan performance from the back end of the Internet financial platform, acquiring personal basic information when the account of the sample customer is registered and applying, and acquiring operation behavior buried point data from monitoring software;
s2: extracting the collected data characteristics, carrying out standardization processing and principal component analysis dimension reduction, and dividing a training set and a verification set according to application time;
s3: establishing an LSSVM classification model, selecting a radial basis function as a kernel function, taking a training sample as an input vector, and training the LSSVM classification model according to KKT optimal conditions and Mercer conditions to obtain a penalty factor C and a kernel function width parameter sigma;
s4: optimizing LSSVM prediction model parameter combination (C, sigma) obtained by training in S3 by adopting a particle swarm algorithm, obtaining an optimal value in a global range, substituting the optimized parameter, and constructing a default user probability prediction model based on the particle swarm optimization LSSVM;
s5: inputting a test data set into a trained default user probability prediction model of the LSSVM, predicting a result and actual data, performing prediction error evaluation analysis, and comparing the prediction error evaluation analysis with the LSSVM model optimized by a gradient descent method, a genetic algorithm and an ant colony algorithm by taking prediction accuracy as an index;
s6: the LSSVM prediction model is deployed to an application platform, real-time data of an application user are collected to carry out standardized input on the prediction model to obtain default probability prediction, real-time approval of the application client is achieved, performance data are input into the model to be trained regularly, and online updating of the model is achieved.
For effectively implementing data collection, in this embodiment, it is preferable that the personal basic information in S1 includes: the mobile phone number, the academic calendar, the marital status, the working unit, the address, the contact information, the personal basic information, the credit transaction information, the public information and the special record data which are acquired by the credit investigation report; the data of the buried points comprises equipment behavior data and log data which are collected when the points are buried.
In order to realize the integrity of data acquisition, in this embodiment, preferably, the device behavior data includes the number of times of logging in the platform, the number of clicks, the frequency of clicks, total input time and average time consumption, mobile phone number data, GPS location, MAC address, IP address data, frequency of applying geographic information, frequency of applying for IP, device electric quantity ratio, and average acceleration of the gyroscope, the log data includes the number of times of logging in 7 days, the duration from the first click to the time of applying for credit, the maximum number of sessions in one day, and the behavior statistics of one week before applying for credit, and under the compliance requirement, is not limited to global multi-dimensional big data including obtaining mobile internet behavior data, loan APP behavior data, credit history, and operator data.
In order to implement the normalization process, in this embodiment, preferably, the normalization process in S2 utilizes a z-score normalization process to unify dimensions of the data, and the principal component analysis dimension reduction process can process isolated points and noise data in the sample, eliminate self-correlation between features, and remove redundancy indexes to implement the dimension reduction.
In order to implement the dimension reduction operation, in this embodiment, it is preferable that the principal component analysis dimension reduction is used as a method for processing high-dimensional data, and the processing manner is as follows:
firstly, standardizing raw data by adopting a z-score method;
secondly, a covariance matrix R of the normalized data vector is established, and m eigenvalues lambda of the covariance matrix R are solved again1＞λ2＞…＞λmAnd a feature vector l1,l2,…,lmSorting according to the descending order of the characteristic values;
finally according to the cumulative variance contribution rate
Figure BDA0002708399490000091
The first M principal components are extracted.
In order to implement the calculation of the sum of relative errors as the fitness evaluation function, in this embodiment, it is preferable that the penalty factor C and the kernel function width parameter σ in S3 optimize the penalty factor C and the kernel function width parameter σ of the LSSVM by using a particle swarm algorithm instead of a conventional grid search algorithm, use a parameter combination (C, σ) as a position coordinate (x, y) of a particle in a search space of the particle in the particle swarm algorithm, use the sum of relative errors of the prediction result as the fitness evaluation function, select a particle coordinate vector value [ C, σ ] that makes the fitness value minimum as the optimal parameter combination of the LSSVM, and obtain the optimal value in the global range.
In order to implement the ion swarm optimization, in this embodiment, preferably, the specific steps of the particle swarm optimization LSSVM are as follows:
s41: setting a particle search dimension D and a population scale n of a particle swarm optimization algorithm, setting an initial iteration number t to be 0 and a maximum iteration number hmaxLearning factor c1And c2The initial position x and the velocity v of the particle are randomly set, the position x of the particle in the search space is set to be (C, σ) as the parameter combination (C, σ), and C e [1,10000 ] is empirically set]，σ∈[0,1]Velocity v of each particleiIs limited to [ v ]min，vmax]Inner, vmaxIs usually takenThe width of the search space;
s42: selecting an average Relative Error value (MRE) of the predicted values of the training samples to define a fitness function of the particle swarm algorithm, wherein an optimization objective function is as follows:
Figure BDA0002708399490000101
wherein min fit (C, sigma) is fitness function value, yiAnd
Figure BDA0002708399490000103
respectively representing the ith actual value and the corresponding predicted value, wherein i is 1,2, …, and n represents the number of training samples;
s43: for each particle, comparing its fitness function value with its current best position individual optimum value pBest, the individual extreme value of each particle is updated with the following formula:
Figure BDA0002708399490000102
s44: for each particle, the fitness function value is compared with the current best position global optimum gBest, and the global extreme values for all the particles are selected as follows:
gBest(t+1)＝max(pBesti(t+1))，i＝1,2,…,n；
s45: updating the position and the speed of the particles, and updating the individual optimal value and the global optimal value of the particles, wherein the updating formula is as follows:
vi(t+1)＝wvi(t)+c1r1(t)(pBesti(t)-xi(t))+c2r2(gBest(t)-xi(t))
xi(t+1)＝wxi(t)+vi(t+1)
wherein v isi(t+1)、xi(t +1) denotes the ith particle velocity and position, v, for the t +1 th iteration, respectivelyi(t)、xi(t) represents the current ith particle velocity andposition, pBesti(t) the current best position individual optimal value searched for by the ith particle, gBest (t) the current best position global optimal value searched for as a whole, c1、c2For learning factors or acceleration coefficients, the step lengths are used to adjust the current particle to the optimal position of the current particle and the optimal position of the current particle, and the value is usually 2, r1、r2Is a random number on (0,1), w is an inertial weight, and is used for controlling the influence of the previous iteration of the current particle on the current iteration;
researches find that the size of the inertia weight w influences the space searching capability of the particle swarm, larger inertia weight w is beneficial to the global search of particles in a solving space, and smaller inertia weight w is beneficial to the local search in the solving space. Usually w is increased from wmaxLinearly decreasing to w with increasing number of iterationsminTypically linearly decreasing from 0.9 to 0.2, i.e.:
Figure BDA0002708399490000111
wherein: w is amax、wminMaximum and minimum values of the inertial weight, respectively; t, hmaxRespectively the current iteration times and the maximum iteration times;
s46: repeating S42, and calculating the updated fitness function value;
s47: judging whether the updated fitness function value meets the particle swarm algorithm termination condition or reaches the maximum iteration number hmaxStopping iteration, if not, returning to S43, and if so, ending;
s48: decoding the coordinate vector value [ C, sigma ] of the best position experienced by the whole group to obtain the optimal LSSVM parameter combination, obtaining the optimal value in the global range, carrying out training, precision verification and prediction, stopping operation and substituting the LSSVM prediction classification equation of S3 to obtain the LSSVM prediction model for particle swarm optimization.
In order to calculate the penalty factor and the optimized value of the kernel function width parameter and improve the accuracy, in this embodiment, preferably, in S4, the penalty factor and the kernel function width parameter of the LSSVM are optimized by using a particle swarm algorithm to obtain respective optimal optimized values, and finally, the predicted value of the default probability of the customer in the test set is calculated according to the optimal optimized values of the penalty factor and the kernel function width parameter.
In order to realize the prediction of the default user probability, in this embodiment, preferably, in S6, the real-time data applied by the customer is collected online, and the collected real-time data is subjected to standardization processing and input into the established LSSVM model, so as to obtain a default user probability prediction result of the customer.
In order to implement the establishment of the regression prediction model, in this embodiment, preferably, in S3, the LSSVM regression prediction model is established by using training samples, and a set of training samples is given as
Figure BDA0002708399490000121
Is an M-dimensional input vector, ykE R is a one-dimensional output vector, k is 1, …, N, and the input samples are nonlinearly mapped to a high-dimensional feature space by using a nonlinear mapping phi to construct a high-dimensional space linear regression function:
Figure BDA0002708399490000122
wherein the content of the first and second substances,
Figure BDA0002708399490000123
as a kernel space mapping function, wTIs a weight vector, b is a deviation amount,
according to the principle of minimizing the structural risk, the LSSVM constructs the regression function to form a minimum objective function with equality constraint:
Figure BDA0002708399490000124
Figure BDA0002708399490000125
where J (w, e) is the loss function, C is the regularization parameter, ek(1,2, …, N) is the training error for N training sample points,
in order to solve the optimization problem, a lagrange multiplier is introduced to change the constrained optimization problem into an unconstrained optimization problem:
Figure BDA0002708399490000131
wherein, akLagrange multiplier, k is 1, …, N training sample number,
according to the Karush-Kuhn-Tucker (KKT) optimal condition and Mercer condition theory, L (w, b, e, a) is subjected to w, b, e respectivelyk、akPerforming partial derivative solution, and making the partial derivative equal to zero, obtaining the following equation and constraint condition:
Figure BDA0002708399490000132
obtaining an LSSVM classification prediction model:
Figure BDA0002708399490000133
wherein f (x) is the prediction output, akE is the Lagrange multiplier R, b is the deviation, K (x, x)k) As kernel function, x is a fixed sample in the training samples, xkFor the kth sample in the training samples, k is 1,2, …, and N is the number of samples in the training set;
the K (x, x)k) Selecting a Radial Basis Function (RBF) for the kernel Function, the expression:
Figure BDA0002708399490000134
as a kernel function of the LSSVM, the final LSSVM classification prediction model formula is obtained as follows:
Figure BDA0002708399490000135
in a preferred embodiment, referring to fig. 1, in S2, the method for processing high-dimensional data using principal components includes the following steps:
s21: the feature data of the acquired n samples form a spatial feature data set X ═ X1,x2,…,xi,…,xnAnd (4) measuring data of m variables in each sample, wherein the data form a spatial characteristic data set analysis matrix X as follows:
Figure BDA0002708399490000141
can know xijAnd (i is 1,2, …, n, j is 1,2, …, m) is the value of the j characteristic variable of the ith sample.
S22: calculating the mean and standard deviation of each characteristic of each application behavior sample:
Figure BDA0002708399490000142
s23: solving a standardized matrix: normalization by Z-score yields the normalized matrix Z ═ (Z)ij)n×mThe calculation formula is as follows:
Figure BDA0002708399490000143
s24: solving a correlation coefficient matrix, wherein the calculation formula is as follows:
Figure BDA0002708399490000144
s25: solving the eigenvalue and the eigenvector: the eigenvalue of the correlation coefficient matrix R is obtained by a characteristic equation | λ E-R | ═ 0 (wherein E is a unit vector), and λ is ordered from large to small1＞λ2＞…＞λmAnd the corresponding feature vector is l1,l2,…,lm。
S26: and (3) reducing the dimensionality: according to cumulative variance contribution rate
Figure BDA0002708399490000145
K is determined so that the first k principal components can be taken to obtain a principal component matrix (F)ij)n×kThe matrix calculation formula after the dimensionality reduction of the principal components is as follows:
Figure BDA0002708399490000146
reducing dimension from original data X (n × m) to principal component matrix Fij)n×kI.e. from the original m-dimension down to the k-dimension, each column vector F in the matrixv(v-1, 2, …, k) is the v-th principal component value of all application samples.
In a preferred embodiment, as shown in fig. 1, in S3, the method for building the LSSVM regression prediction model with the training samples includes the following steps:
given a training sample set as an M-dimensional input vector, yk ∈ R is a one-dimensional output vector, k ═ 1, …, N. Using non-linear mapping
Figure BDA0002708399490000151
Mapping the input samples to a high-dimensional feature space in a non-linear mode to construct a high-dimensional space linear regression function:
Figure BDA0002708399490000152
wherein the content of the first and second substances,
Figure BDA0002708399490000153
as a kernel space mapping function, wTB is the deviation value.
According to the principle of minimizing the structural risk, the LSSVM constructs the regression function to form a minimum objective function with equality constraint:
Figure BDA0002708399490000154
Figure BDA0002708399490000155
where J (w, e) is the loss function, C is the regularization parameter, ek(1,2, …, N) is the training error for N training sample points.
In order to solve the optimization problem, a lagrange multiplier is introduced to change the constrained optimization problem into an unconstrained optimization problem:
Figure BDA0002708399490000156
wherein, akFor lagrange multiplier, k is 1, …, N training sample number.
According to the Karush-Kuhn-Tucker (KKT) optimal condition and Mercer condition theory, L (w, b, e, a) is subjected to w, b, e respectivelyk、akPerforming partial derivative solution, and making the partial derivative equal to zero, obtaining the following equation and constraint condition:
Figure BDA0002708399490000161
obtaining an LSSVM classification prediction model:
Figure BDA0002708399490000162
wherein f (x) is the prediction output, akE is the Lagrange multiplier R, b is the deviation, K (x, x)k) As kernel function, x is a fixed sample in the training samples, xkFor the kth sample in the training samples, k is 1,2, …, and N is the number of samples in the training set;
the K (x, x)k) Selecting a Radial Basis Function (RBF) for the kernel Function, the expression:
Figure BDA0002708399490000163
the RBF is used as a kernel function of the LSSVM, and finally the LSSVM classification prediction model formula is obtained as follows:
Figure BDA0002708399490000164
known, then selecting a penalty factor C and a kernel function width parameter sigma of the LSSVM as optimization selection parameters; and then taking the interval [0,150] as a value selection range of the penalty factor, and taking the intervals [0.1 and 10] as a value selection range of the kernel function width parameter.
In a preferred embodiment, as shown in fig. 1, in S5, the test data set is input to the trained LSSVM default user probability prediction model, the prediction result and the actual data are subjected to prediction error evaluation analysis, and the prediction accuracy is used as an index to compare with the LSSVM model optimized by the gradient descent law, the genetic algorithm and the ant colony algorithm.
The model accuracy evaluation index can adopt Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) and Mean Absolute Error MAE (MAE), and the calculation formulas are respectively as follows:
Figure BDA0002708399490000171
Figure BDA0002708399490000172
Figure BDA0002708399490000173
wherein, yiIn order to be an actual measurement value,
Figure BDA0002708399490000174
the model is calculated, and n is the number of samples.
Further, in S6, the real-time data of the customer application is collected online, and the collected data is normalized and input into the established LSSVM model, so as to obtain the default user probability prediction result of the customer application.
In another aspect, the present invention further provides a default user probability prediction based on particle swarm optimization LSSVM, including:
a sample acquisition unit: the system comprises a training sample for acquiring personal credit evaluation data and an evaluation result;
a data processing unit: extracting the characteristics of the acquired data samples, and performing data missing completion, abnormal value processing, normalization and the like;
a network training unit: the prediction model is used for training the LSSVM based on particle swarm optimization by using the training samples to obtain a trained prediction model;
a credit detection unit: and the LSSVM prediction model is used for obtaining default probability prediction after the personal credit evaluation data to be detected is acquired and input for training.
The working principle and the using process of the invention are as follows:
the first step is as follows: acquiring sample data, selecting the same number of normal repayment and overdue customers as modeling samples according to the post-loan performance from the back end of the Internet financial platform, acquiring personal basic information when the account of the sample customer is registered and applying, and acquiring operation behavior buried point data from monitoring software;
the second step is that: extracting the collected data characteristics, carrying out standardization processing and principal component analysis dimension reduction, and dividing a training set and a verification set according to application time;
the third step: establishing an LSSVM classification model, selecting a radial basis function as a kernel function, taking a training sample as an input vector, and training the LSSVM classification model according to KKT optimal conditions and Mercer conditions to obtain a penalty factor C and a kernel function width parameter sigma;
the fourth step: optimizing LSSVM prediction model parameter combination (C, sigma) obtained by training in S3 by adopting a particle swarm algorithm, obtaining an optimal value in a global range, substituting the optimized parameter, and constructing a default user probability prediction model based on the particle swarm optimization LSSVM;
the fifth step: inputting a test data set into a trained default user probability prediction model of the LSSVM, predicting a result and actual data, performing prediction error evaluation analysis, and comparing the prediction error evaluation analysis with the LSSVM model optimized by a gradient descent method, a genetic algorithm and an ant colony algorithm by taking prediction accuracy as an index;
and a sixth step: the LSSVM prediction model is deployed to an application platform, real-time data of an application user are collected to carry out standardized input on the prediction model to obtain default probability prediction, real-time approval of the application client is achieved, performance data are input into the model to be trained regularly, and online updating of the model is achieved.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (10)

1. A default user probability prediction method based on particle swarm optimization LSSVM is characterized in that: the method comprises the following steps:
s1: acquiring sample data, selecting the same number of normal repayment and overdue customers as modeling samples according to the post-loan performance from the back end of the Internet financial platform, acquiring personal basic information when the account of the sample customer is registered and applying, and acquiring operation behavior buried point data from monitoring software;
s2: extracting the collected data characteristics, carrying out standardization processing and principal component analysis dimension reduction, and dividing a training set and a verification set according to application time;
s3: establishing an LSSVM classification model, selecting a radial basis function as a kernel function, taking a training sample as an input vector, and training the LSSVM classification model according to KKT optimal conditions and Mercer conditions to obtain a penalty factor C and a kernel function width parameter sigma;
s4: optimizing LSSVM prediction model parameter combination (C, sigma) obtained by training in S3 by adopting a particle swarm algorithm, obtaining an optimal value in a global range, substituting the optimized parameter, and constructing a default user probability prediction model based on the particle swarm optimization LSSVM;
s5: inputting a test data set into a trained default user probability prediction model of the LSSVM, predicting a result and actual data, performing prediction error evaluation analysis, and comparing the prediction error evaluation analysis with the LSSVM model optimized by a gradient descent method, a genetic algorithm and an ant colony algorithm by taking prediction accuracy as an index;
s6: the LSSVM prediction model is deployed to an application platform, real-time data of an application user are collected to carry out standardized input on the prediction model to obtain default probability prediction, real-time approval of the application client is achieved, performance data are input into the model to be trained regularly, and online updating of the model is achieved.
2. The method for predicting the probability of default users based on particle swarm optimization LSSVM of claim 1, wherein: the personal basic information in S1 includes: the mobile phone number, the academic calendar, the marital status, the working unit, the address, the contact information, the personal basic information, the credit transaction information, the public information and the special record data which are acquired by the credit investigation report; the data of the buried points comprises equipment behavior data and log data which are collected when the points are buried.
3. The method for predicting the probability of default users based on particle swarm optimization LSSVM of claim 2, wherein: the device behavior data comprises the number of times of logging in the platform, the number of clicks, the click frequency, the total input time and the average time consumption, the mobile phone number data, the GPS position, the MAC address, the IP address data, the geographic information application frequency, the IP application frequency, the device electric quantity ratio and the average acceleration of a gyroscope, the log data comprises the login number in 7 days, the time length from the first click to the application credit, the maximum number of sessions in one day, the behavior statistics of one week before the application credit, and under the compliance requirement, the log data is not limited to global multi-dimensional big data comprising mobile internet behavior data, loan APP internal behavior data, credit history and operator data.
4. The method for predicting the probability of default users based on particle swarm optimization LSSVM of claim 1, wherein: in the S2, the normalization processing utilizes z-score normalization processing to unify the dimensions of each data, principal component analysis dimensionality reduction can process isolated points and noise data in the sample, self-correlation among features is eliminated, and redundant indexes are deleted to realize dimensionality reduction.
5. The method for predicting the probability of default users based on particle swarm optimization LSSVM of claim 4, wherein: the principal component analysis dimensionality reduction is used as a method for processing high-dimensional data, and the processing mode is as follows:
firstly, standardizing raw data by adopting a z-score method;
secondly, a covariance matrix R of the normalized data vector is established, and m eigenvalues lambda of the covariance matrix R are solved again1＞λ2＞…＞λmAnd a feature vector l1,l2,…,lmSorting according to the descending order of the characteristic values;
finally according to the cumulative variance contribution rate
Figure FDA0002708399480000021
The first M principal components are extracted.
6. The method for predicting the probability of default users based on particle swarm optimization LSSVM of claim 1, wherein: and the penalty factor C and the kernel function width parameter sigma in the S3 are optimized by using a particle swarm algorithm to replace the traditional grid search algorithm, the penalty factor C and the kernel function width parameter sigma of the LSSVM are optimized, a parameter combination (C, sigma) is used as a position coordinate (x, y) of a particle in a search space of the particle swarm algorithm, the relative error sum of a prediction result is used as a fitness evaluation function, the particle coordinate vector value [ C, sigma ] which enables the fitness value to be minimum is selected as the optimal parameter combination of the LSSVM, and the optimal value is obtained in the global range.
7. The method for predicting the probability of default users based on particle swarm optimization LSSVM of claim 6, wherein: the particle swarm optimization LSSVM comprises the following specific steps:
s41: setting a particle search dimension D and a population scale n of a particle swarm optimization algorithm, setting an initial iteration number t to be 0 and a maximum iteration number hmaxLearning factor c1And c2The initial position x and the velocity v of the particle are randomly set, the position x of the particle in the search space is set to be (C, σ) as the parameter combination (C, σ), and C e [1,10000 ] is empirically set]，σ∈[0,1]The value of the velocity vi of each particle is defined as [ v [ ]min，vmax]Inner, vmaxUsually taking the width of the search space;
s42: selecting an average Relative Error value (MRE) of the predicted values of the training samples to define a fitness function of the particle swarm algorithm, wherein an optimization objective function is as follows:
Figure FDA0002708399480000031
wherein min fit (C, sigma) is fitness function value, yiAnd
Figure FDA0002708399480000032
respectively representing the ith actual value and the corresponding predicted value, wherein i is 1,2, …, and n represents the number of training samples;
s43: for each particle, comparing its fitness function value with its current best position individual optimum value pBest, the individual extreme value of each particle is updated with the following formula:
Figure FDA0002708399480000033
s44: for each particle, the fitness function value is compared with the current best position global optimum gBest, and the global extreme values for all the particles are selected as follows:
gBest(t+1)＝max(pBesti(t+1))，i＝1,2,…,n；
s45: updating the position and the speed of the particles, and updating the individual optimal value and the global optimal value of the particles, wherein the updating formula is as follows:
vi(t+1)＝wvi(t)+c1r1(t)(pBesti(t)-xi(t))+c2r2(gBest(t)-xi(t))
xi(t+1)＝wxi(t)+vi(t+1)
wherein v isi(t+1)、xi(t +1) denotes the ith particle velocity and position, v, for the t +1 th iteration, respectivelyi(t)、xi(t) denotes the current ith particle velocity and position, pBest, respectivelyi(t) the current best position individual optimal value searched for by the ith particle, gBest (t) the current best position global optimal value searched for as a whole, c1、c2For learning factors or acceleration coefficients, the step lengths are used to adjust the current particle to the optimal position of the current particle and the optimal position of the current particle, and the value is usually 2, r1、r2Is a random number on (0,1), w is an inertial weight, and is used for controlling the influence of the previous iteration of the current particle on the current iteration;
s46: repeating S42, and calculating the updated fitness function value;
s47: judging whether the updated fitness function value meets the particle swarm algorithm termination condition or reaches the maximum iteration number hmaxStopping iteration, if not, returning to S43, and if so, ending;
s48: decoding the coordinate vector value [ C, sigma ] of the best position experienced by the whole group to obtain the optimal LSSVM parameter combination, obtaining the optimal value in the global range, carrying out training, precision verification and prediction, stopping operation and substituting the LSSVM prediction classification equation of S3 to obtain the LSSVM prediction model for particle swarm optimization.
8. The method for predicting the probability of default users based on particle swarm optimization LSSVM of claim 1, wherein: and in the S4, the penalty factor and the kernel function width parameter of the LSSVM are optimized by using the particle swarm algorithm to obtain respective optimal optimized values, and finally the predicted value of the client default probability in the test set is calculated according to the optimal optimized values of the penalty factor and the kernel function width parameter.
9. The method for predicting the probability of default users based on particle swarm optimization LSSVM of claim 1, wherein: and in the step S6, real-time data applied by the customer is acquired on line, and the acquired real-time data is subjected to standardization and input into the established LSSVM model to obtain a default user probability prediction result of the customer.
10. The method for predicting the probability of default users based on particle swarm optimization LSSVM of claim 1, wherein: in the S3, an LSSVM regression prediction model is established by using training samples, and a training sample set is given
Figure FDA0002708399480000051
Is an M-dimensional input vector, ykE R is a one-dimensional output vector, k 1, …, N, using a non-linear mapping
Figure FDA0002708399480000052
Non-linearly mapping input samples to high-dimensional feature space to constructHigh dimensional spatial linear regression function:
Figure FDA0002708399480000053
wherein the content of the first and second substances,
Figure FDA0002708399480000054
as a kernel space mapping function, wTIs a weight vector, b is a deviation amount,
according to the principle of minimizing the structural risk, the LSSVM constructs the regression function to form a minimum objective function with equality constraint:
Figure FDA0002708399480000055
Figure FDA0002708399480000056
where J (w, e) is the loss function, C is the regularization parameter, ek(1,2, …, N) is the training error for N training sample points,
in order to solve the optimization problem, a lagrange multiplier is introduced to change the constrained optimization problem into an unconstrained optimization problem:
Figure FDA0002708399480000057
wherein, akK is 1, … for lagrange multiplier, N is the number of training samples,
according to the Karush-Kuhn-Tucker (KKT) optimal condition and Mercer condition theory, L (w, b, e, a) is respectively subjected to w, b and ek、akPerforming partial derivative solution, and making the partial derivative equal to zero, obtaining the following equation and constraint condition:
Figure FDA0002708399480000061
finally obtaining an LSSVM classification prediction model:
Figure FDA0002708399480000062
wherein f (x) is the prediction output, akE is the Lagrange multiplier R, b is the deviation, K (x, x)k) As kernel function, x is a fixed sample in the training samples, xkFor the kth sample in the training samples, k is 1,2, …, and N is the number of samples in the training set;
the K (x, x)k) Selecting a Radial Basis Function (RBF) for the kernel Function, the expression:
Figure FDA0002708399480000063
the RBF is used as a kernel function of the LSSVM, and finally the LSSVM classification prediction model formula is obtained as follows:
Figure FDA0002708399480000064
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