TWI474210B - A method of applying a genetic algorithm to automatically group and filter the independent variables to synchronize the regression model parameters - Google Patents

Description

A method for applying genetic algorithm to automatically group and filter independent variables to synchronize regression parameter estimation

The present invention relates to a method for applying genetic algorithms to automatically group and filter independent variables to simultaneously perform regression model parameter estimation.

Regression analysis is a very important tool in the social sciences. In many situations, it is often necessary to group the collected cases to establish a causal pattern. However, the current common software (such as SPSS, Statistica, etc.) does not provide simultaneous grouping and regression model parameters. Estimated function. Therefore, we often have to use some clustering models (such as cluster analysis) to first group cases, then build regression models one by one, and evaluate their parameters. Since the parameter estimation of the clustering and regression models is not simultaneous, the resulting model is not guaranteed to be the most suitable solution. In addition, when trying to establish regression models for each group, it often takes a lot of time to eliminate the inapplicable cases, select suitable independent variables, and judge the rationality of the model parameters.

In addition to cluster analysis in the field of multivariate analysis, in the field of expert systems, case-based reasoning (CBR) technology can also be used for case screening and grouping. For example, Kuncheva and Jain (1999) proposed synchronous optimization cases and feature selection methods. Ahn, Kim and Han (2007) applied CBR technology to customer grouping problems. However, there is no document that applies CBR to automatic clustering and synchronously establishes a regression model and evaluates its parameters, which is the subject of the present invention.

The invention combines gene algorithm, CBR technology and regression model to perform grouping and synchronously establish regression models of each group and evaluate the parameters thereof. The number of clusters and the dependent variable (multiple dependent variables can be set) are set in advance, but the independent variables of each group are not known in advance, so as to find a more accurate grouping criterion to find the key independent variables applicable to each group. .

Accordingly, the main object of the present invention is to provide a method for automatically grouping and screening self-variables to synchronously perform regression model parameter estimation using a genetic algorithm, which can find more accurate grouping criteria to find out that it is applicable to each group. The key to the self-variable.

In order to achieve the foregoing object, a method for automatically grouping and screening independent variables to synchronize regression parameter parameter estimation according to the present invention includes the following steps: A) defining chromosome structure and coding: defining gene calculus The chromosome structure and coding in the method, each chromosome contains the case, the group to which the case belongs, the independent variable, and the group to which the independent variable belongs; wherein the group system to which the case or the independent variable belongs is represented by a predetermined coding format, In addition, the group system to which the case belongs is one of the plural groups or does not belong to any group (ie, the group to which it belongs is zero), the one of the self-variables belongs to more than zero groups; B) the initial group is generated : generating a predetermined number of chromosomes 0 in a random manner and defining them as a previous generation group; C) performing genetic manipulation to generate new progeny: selecting and mating the chromosomes of the previous generation group during gene manipulation And mutations, which in turn produce the next generation of chromosomes, which in turn are defined as a next generation group; D) decoding the chromosomes of the next generation group generated in step C): after decoding, it can be known which group the case is divided into, and which self-variables are used by each group, and these are decoded. The case data is divided into a plurality of data sets according to the group to which they belong; E) the regression model parameters are estimated and the fitness value is calculated (Fitness Value): each data set is introduced into the regression model for parameter estimation, and according to To calculate the fitness value; and F) whether a stop condition is met? If so, the chromosome with the best fitness value and its corresponding ethnic group are extracted, and the clustering result is stored and ended; if not, the next generation group generated in step C) is regarded as the previous generation group, and then Go back to step C).

Preferably, in step A), the group system to which the case belongs is represented by an integer code to the group code to which it belongs; the group system to which the independent variable belongs is corresponding to the number of bits of the binary code. Each of the groups to which they belong.

Preferably, before step C), there is further included a step C0): before selecting, mating and mutating the chromosomes of the previous generation group, first evaluating the fitness value of each chromosome in the previous generation; if the chromosome is non- Infeasible Solution, regenerate the chromosome, or modify the chromosome to make it a feasible solution.

Preferably, generating the next generation group in step C) is called evolution generation; in step F), the stop condition means that the algebra of evolution reaches the algebra set by the user.

Preferably, in step E), the calculation of the fitness value is calculated according to the adjusted determination coefficient of the regression model of each group, and has an overall mode. Two calculation methods can be selected with the weighted average mode.

Preferably, in step E), if the regression model of any group is different from the pre-entered criterion (there are positive, negative, and uncertain), the adjustment of the mode is reset. The post-judgment coefficient is zero.

In order to explain the structure and features of the present invention in detail, the following preferred embodiments,

As shown in the first figure, a method for applying the genetic algorithm to automatically group and filter the self-variables to synchronously perform regression model parameter estimation is provided in a preferred embodiment of the present invention, which mainly includes the following steps:

A) Define chromosome structure and coding: define the chromosome structure and coding in the gene algorithm, each of which contains a case (or may also be called a sample), a group to which the case belongs, an independent variable, and a group to which the independent variable belongs; The case is based on the case of the manufacturer, and the self-variable is taken as an example. The group system to which the case or the independent variable belongs is represented by a predetermined coding format. In addition, the group system to which the case belongs For one of the plural groups or not belonging to any group (ie, the group to which it belongs is zero), the one of the independent variables belongs to more than zero groups. In this embodiment, the group system to which each case belongs is represented by an integer code to the group code to which it belongs; a group system to which the self-variable belongs belongs to each bit of the binary code to correspond to the attribute to which the variable belongs. Each of this group.

B) Generation of an initial population: A predetermined number of Generation 0 chromosomes are generated in a random manner and defined as a previous generation population.

For example, suppose there are 10 cases (I), 5 independent variables (F), divided into 2 groups, and the chromosomes are set to 5, which can be expressed in Table 1.

In Table 1 above, the total number of clusters is 2, and the code value of the case selection is 0, 1, or 2, respectively indicating that the case is classified as not selected, the first group or the second group.

Taking chromosome 5 as an example, the group code to which the case belongs may be 0 to 2, and the gene value of I ₂ is 2, which means that case 2 is classified into group 2. From Table 1 above, it can be seen that Case 1 of chromosome 1 is classified into Group 1, Case 2 is classified into Group 2, and Case 3 is not selected (ie, not classified into any group).

The state in which the argument (F) is selected will be described. In the above Table 1, in the case where the total number of clusters is 2, the code value selected from the variable is set to 0 to 3, and there are four types. Since the decimal value actually exists in the binary mode in the computer, the binary encoding method can use the 1 bit (ie, one digit) inside the computer memory to indicate whether the self-variable is selected by a certain group. And which groups choose the self-variable. Binary code A 1 in the group indicates that the group is selected, and 0 indicates that the group is not selected. The selection state of the self-variable is exemplified by Table 2 below.

Referring to Table 1 and Table 2, the value of the self-variable F ₃ in chromosome 5 is 2, and it is found from Table 2 that the binary value of the integer 2 is 10, indicating that the self-variable F ₃ is selected by the group 2, the group 1 Then the self-variant F ₃ is not used. Look at the argument F ₁ , which has a value of 0, indicating that it is not selected. A value of 1 for F ₂ means that it is selected by group 1. A value of 3 for F ₄ indicates that it is selected by group 1 and group 2.

It can be seen from the above Table 1 that which cases are classified into the first group and which independent variables are used by each group.

C0) The fitness value of each chromosome in the previous generation group is evaluated first. If a chromosome is a non-feasible solution, the chromosome is regenerated or modified to make it a feasible solution. In this embodiment, a regenerated chromosome is taken as an example. (This step is not shown in the first figure)

C) Gene manipulation to generate new progeny: During gene manipulation, the chromosomes of the previous generation are selected, mated, and mutated to produce the next generation of chromosomes, which are defined as a next generation group. This step produces The movement of the next generation of ethnic groups is called the evolutionary generation.

D) decoding the chromosomes of the next generation group generated in step C): after decoding, it can be known which group the case is divided into, and which self-variables are used by each group, and these are decoded. The data is divided into a plurality of data sets according to the group to which they belong.

E) Perform regression model parameter estimation and calculate fitness value (Fitness Value): Import each data set into the regression model for parameter estimation, and calculate the fitness value accordingly. In this embodiment, the calculation of the fitness value is calculated according to the adjusted determination coefficient of the regression model of each group, and there are two calculation modes of the overall mode and the weighted average mode. The calculation method of the fitness value of the overall model is applicable to the case where each case is equivalent (that is, the importance is the same). The calculation method of the weighted average mode fitness value is suitable for the causal mode that each group is expected to have a good explanatory ability. There is no case of being too biased towards a certain group.

If the regression model of any group is different from the pre-entered judgment criterion (there are positive, negative, and uncertain), the adjustment coefficient of this mode is reset to 0.

The adjusted coefficient (adjusted R ² ) of the regression model is expressed by the following formula 1.

The way to calculate the fitness value is as follows:

As can be seen from the above Table 3, the respective cases of the chromosome 5 in Table 1 and the state of the cluster of the self-variables are summarized in Table 3.

The first group (with five cases of I ₁ , I ₅ , I ₆ , I ₈ , I ₁₀ , with F ₂ , F ₄ , F ₅ as independent variables) and the second group (with I ₂ , I ₄ , I ₇ The results of the regression analysis performed in four cases of I ₉ and F ₃ and F ₄ as independent variables are shown in Table 4 below.

The calculation of the overall mode fitness value is to treat all the clusters as a whole, and then use the above formula 1 to calculate, the calculation formula is as follows:

Taking Table 4 above as an example, the overall mode adaptation value is:

The weighted average mode adaptation value is calculated by weighting the number of cases of each group, and weighting the Adj.-R ² of each group as the fitness value.

Taking Table 4 above as an example, the weighted average mode adaptation value is:

F) Does it meet a stop condition? If so, the chromosome with the best fitness value and its corresponding ethnic group are extracted, and the clustering result is stored and ended; if not, the next generation group generated in step C) is regarded as the previous generation group, and then Go back to step C). In the present embodiment, the stopping condition means that the algebra of the evolution reaches the algebra set by the user.

According to the above steps, after the stop condition is satisfied, the optimal fitness value and its corresponding ethnic group are extracted, and the evolution is ended. In this way, a chromosome with the best fitness value in the past generation can be found, and the most accurate clustering criterion can be found from the case of the chromosome decoding and the self-variable. In this embodiment, since the case is corresponding to the manufacturer, and the self-variable is taken as an example corresponding to the performance indicator, the key independent variable (ie, performance) applicable to each cluster manufacturer can be found by the technology of the present invention. index). It can be inferred that when using the technique of the present invention to apply to other problems, the method of grouping and self-variable extraction of the present invention can also be used to simultaneously obtain the optimal parameters of each group of causal models, and save a large amount of Manpower operation and trial and error time.

It can be seen that the present invention combines a gene algorithm, a CBR technique and a regression model to perform grouping and simultaneously establish each group regression model. By setting the number of clusters in advance, but the self-variables of each group are not pre-determined In which group, to find more accurate grouping criteria, and then to find the key independent variables applicable to each group.

The first figure is a flow chart of a preferred embodiment of the present invention.

Claims (6)

A method for applying genetic algorithm to automatically group and filter independent variables to synchronize regression parameter parameter estimation includes the following steps: A) defining chromosome structure and coding: defining chromosome structure and coding in gene algorithm, each of the chromosomes Contains the case, the group to which the case belongs, the independent variable, and the group to which the independent variable belongs; wherein the group system to which the case or the independent variable belongs is represented by a predetermined coding format, and in addition, the group system to which the case belongs is One of the plural groups is not attributable to any group, one of which belongs to more than zero groups; B) the initial group is generated: a predetermined number of chromosomes 0 are generated in a random manner and defined as a previous generation group C) performing genetic manipulation to generate new progeny: in the process of gene manipulation, the chromosomes of the previous generation are selected, mated and mutated, thereby generating the next generation chromosome, which is defined as a next generation group; D) The chromosome of the next generation group generated in step C) is decoded: after decoding, it can be known that each case is divided Which group, and which self-variables are used by each group, and divide the decoded case data into a plurality of data sets according to the group to which they belong; E) perform regression model parameter estimation and calculate fitness value (Fitness Value) : Introduce each data set into the regression model for parameter estimation, and calculate the fitness value accordingly; and F) Does it satisfy a stop condition? If yes, the chromosome with the best fitness value and its corresponding ethnic group are retrieved, and the clustering result is stored and ended; if not, the next generation group generated in step C) is regarded as the previous one. Generation group, go back to step C). The method for automatically grouping and screening the self-variables to synchronously perform regression model parameter estimation according to the applied gene algorithm described in claim 1 of the patent application scope, wherein: in step A), the group system to which the case belongs is encoded by an integer The group code to which it belongs is represented; the group system to which the independent variable belongs is corresponding to each group to which the argument belongs to by the number of bits encoded by the binary. The method for automatically grouping and filtering the self-variables to synchronously perform regression model parameter estimation according to the applied gene algorithm described in claim 1 of the patent application scope, wherein: before step C), there is further included a step C0): on the pair Before selecting, mating, and mutating a chromosome of a generation, first evaluate the fitness of each chromosome in the previous generation; if the chromosome is an Infeasible Solution, regenerate the chromosome, or modify the chromosome to make it feasible. solution. The method for automatically grouping and screening the self-variables to synchronously perform regression model parameter estimation according to the applied gene algorithm described in claim 1 of the patent application scope, wherein: generating a next-generation group in step C) is called an evolution generation; In F), the stopping condition means that the algebra of the evolution reaches the algebra set by the user. The method for automatically grouping and screening the self-variables to synchronously perform regression model parameter estimation according to the applied gene algorithm described in claim 1 of the patent scope, wherein: in step E), the calculation of the fitness value is based on each The adjusted coefficient of the regression model of the group is calculated, and there are two calculation modes: the overall mode and the weighted average mode. According to the applied gene algorithm described in claim 1 of the patent application, the method of automatically grouping and screening the self-variables to synchronously perform regression model parameter estimation, wherein: in step E), if any of the grouped regression models, The variable coefficient symbol is different from the pre-entered judgment criterion (there are positive, negative, and uncertain), and the adjustment coefficient of this mode is reset to 0.