CN108536730B - Text classification method for hybrid Fourier kernel function support vector machine - Google Patents

Text classification method for hybrid Fourier kernel function support vector machine Download PDF

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CN108536730B
CN108536730B CN201810160983.3A CN201810160983A CN108536730B CN 108536730 B CN108536730 B CN 108536730B CN 201810160983 A CN201810160983 A CN 201810160983A CN 108536730 B CN108536730 B CN 108536730B
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于舒娟
张昀
朱文峰
何伟
董茜茜
金海红
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Nanjing University Of Posts And Telecommunications Institute At Nantong Co ltd
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Abstract

The invention provides a text classification method of a hybrid Fourier kernel function support vector machine. The method comprises the steps of forming a new mixed Fourier kernel function through a linear weighted mixed polynomial and a Fourier kernel function according to different learning and generalization capabilities of various kernel functions in a support vector machine; since the learning ability and generalization ability of the kernel function greatly influence the classification effect of the support vector machine, the polynomial kernel function is combined with the fourier kernel function. The method inherits the high learning capability of the Fourier kernel function and the generalization capability of the polynomial kernel function, and improves the performance of the support vector machine classifier; compared with a polynomial kernel function, a Gaussian kernel function, a Fourier kernel function in a single kernel and a polynomial and Gaussian kernel combined kernel function in a mixed kernel function, the mixed Fourier kernel function has better generalization and learning capabilities and the best text classification effect.

Description

Text classification method for hybrid Fourier kernel function support vector machine
Technical Field
The invention is mainly applied to the aspect of natural language processing in machine learning, and particularly relates to a text classification method for a hybrid Fourier kernel function support vector machine.
Background
With the advent of the big data age, the data processing aspects such as natural language processing and image processing have been rapidly developed. Due to the high-dimensional characteristics of the text information, how to find a specific rule in the complex high-dimensional characteristics so as to provide better service for people in the future is an important research direction of the statistical learning theory. Support Vector Machines (SVMs) are a statistical learning theory-based machine learning method proposed by Vapnik et al in 1995. SVMs solve the non-linearity problem by relying on a variety of kernel functions.
At present, SVM has also been widely studied on the problem of nonlinear text classification. Article [ liu gaohui, yang star a support vector machine of mixed kernel [ J ] microcomputer and application, 2017, 36 (11): 19-22 ] the excellent generalization capability of the polynomial kernel is well suited to the text classification problem. The addition of a polynomial kernel function to a kernel function with stronger learning ability can often improve the classification effect. A text classification method of an improved mixed kernel function support vector machine [ J ]. an industrial control computer [ 2016,29(6): 113-. The article [ j.a.k.suykens, j.vandewalle, Least square supported vector machines, Neural Processing Letters 9(3),293(1999) ], proposes a Least squares support vector machine to solve the non-linearity problem, but the accuracy is not very high. The document [ Zbraong. Performance analysis of Fourier kernel in support vector machine [ D ]. university of east China.2008 ] researches an N-dimensional Fourier kernel on the basis of a one-dimensional Fourier kernel, but experimental analysis shows that the classification effect of the N-dimensional Fourier kernel function is similar to that of the one-dimensional Fourier kernel function on the aspect of text classification. The basic theory of the support vector machine is firstly explained, and the advantages and the disadvantages of the traditional kernel function and the Fourier kernel in text classification are analyzed and compared. Through comparing and analyzing different classification effects, learning ability, generalization ability and the like shown by the kernel function, the text classification method of the mixed Fourier kernel function support vector machine model is provided.
Disclosure of Invention
The invention aims to solve the technical problem of providing a text classification method of a hybrid Fourier kernel function support vector machine in order to improve the effect of the support vector machine in text classification. The method mainly comprises the step of adding a polynomial kernel function to a one-dimensional Fourier kernel function to form a new mixed Fourier kernel function, wherein the mixed Fourier kernel function inherits the learning capability of the Fourier kernel function and the generalization capability of the polynomial kernel function, so that a new support vector machine model is formed, and the text classification effect is improved.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a text classification method for a hybrid Fourier kernel function support vector machine comprises the following steps:
step A, training a support vector machine to obtain αiAnd b, according to the Lagrange multiplication and the KKT condition which are commonly used in the optimization problem, combining the solving expression with an equality constraint condition and an inequality constraint condition respectively, simplifying the solving process of the support vector machine, and converting the solving into the following steps:
Figure BDA0001582924570000021
constraint conditions are as follows:
Figure BDA0001582924570000022
wherein C represents a relaxation variable;
in the formula (I), the compound is shown in the specification,
Figure BDA0001582924570000023
representing the maximum interval equivalent conversion result of the support vector;
Figure BDA0001582924570000024
expressing the minimum value of the expression;
Figure BDA0001582924570000025
display tableThe maximum value of the expression;
Figure BDA0001582924570000026
represents summing the expressions;
xi,xj∈{x1,x2,...,xnexpressing the i, j training set document vectorization value, wherein n expresses the number of training set documents, i is more than or equal to 1, and j is less than or equal to n;
yi,yj∈{y1,y2,...,ynrepresenting the category of the ith and j training set documents, and taking the value of 1 or-1;
αi,αj∈α＝{α1,α2,...,αndenotes xi,xjA corresponding lagrange multiplier;
Figure BDA0001582924570000027
representing a normal vector;
wTrepresents w transpose;
||w||2represents the square of the w euclidean norm;
b represents the intercept of the hyperplane on the coordinate axis;
K(xi,xj) Representing a kernel function;
step B, constructing a mixed Fourier kernel function to be introduced into the support vector machine, wherein the mixed Fourier kernel function is as follows:
Figure BDA0001582924570000031
in the formula, u is more than or equal to 0 and less than or equal to 1;
Kpoly＝(xi×xj+c)drepresenting a polynomial kernel, wherein c takes the value 1 and d takes the value 2 or 3;
Figure BDA0001582924570000032
representing a Fourier kernel in which cos (x)i-xj) Watch (A)Show xi-xjThe cosine value of (q is more than 0 and less than 1);
step C, introducing a mixed Fourier kernel function into a support vector machine:
Figure BDA0001582924570000033
step D, vectorizing the document:
Figure BDA0001582924570000034
in the formula, λkjRepresenting a document deMiddle characteristic word tkAs a result of vectorization
tk∈{t1,t2,...,tmMeans a feature word tkWherein m represents the total number of the feature words in the total document, and i is more than or equal to 1 and less than or equal to m;
de∈{d1,d2,...,dNrepresenting the e document in the total documents, wherein e is more than or equal to 1 and less than or equal to N;
tf(tk,de) Representation feature word tkIn document deThe number of occurrences in (a);
Nkmeaning containing a characteristic word tkThe number of documents;
n represents the total document number;
β is an empirical value, taken at 0.1;
e, selecting a training set and a testing set from the total document by a cross validation method, and finally deciding a function:
Figure BDA0001582924570000041
wherein f (x's) Representing a classification result of the support vector machine model;
xs'∈{x1',x'2,...,x'zrepresenting the s test set document after vectorization, wherein z represents that the number of the test set documents is more than or equal to 1 and less than or equal to z;
K(x's,xi) Representing the proposed hybrid fourier kernel;
αib represents parameters obtained by training the support vector machine;
sgn (·) denotes a sign function;
the invention has the beneficial effects that: the invention uses a new mixed Fourier kernel function to support the vector machine model, thereby improving the text classification effect. The method comprises the following steps: and according to different learning and generalization capabilities of various kernel functions in the support vector machine, forming a new mixed Fourier kernel function by linear weighted mixed polynomial and Fourier kernel functions. Because the learning capability and the generalization capability of the kernel function influence the classification effect of the support vector machine to a great extent, the polynomial kernel function is combined with the Fourier kernel function, the high learning capability of the Fourier kernel function and the generalization capability of the polynomial kernel function are inherited by the method, and the performance of the support vector machine classifier is improved; compared with a polynomial kernel function, a Gaussian kernel function, a Fourier kernel function in a single kernel and a polynomial and Gaussian kernel combined kernel function in a mixed kernel function, the mixed Fourier kernel function has better generalization and learning capabilities and the best text classification effect.
Description of the drawings:
fig. 1 is a diagram of a two-dimensional sample of a linear weighted combination kernel of a conventional polynomial kernel and a gaussian kernel.
FIG. 2 is a two-dimensional spatial sample diagram of the hybrid Fourier hybrid kernel of the present invention.
Detailed Description
The following describes in detail a text classification method of a hybrid fourier kernel function support vector machine proposed by the present invention with reference to the accompanying drawings and simulation results:
a text classification method for a hybrid Fourier kernel function support vector machine is implemented as follows:
training the support vector machine to obtain αiAnd b, respectively combining the solving expression with an equality constraint condition and an inequality constraint condition according to the Lagrange multiplication and the KKT condition which are commonly used in the optimization problem, simplifying the solving process of the support vector machine, and solvingThe solution is converted into:
Figure BDA0001582924570000051
constraint conditions are as follows:
Figure BDA0001582924570000052
wherein C represents a relaxation variable;
in the formula (I), the compound is shown in the specification,
Figure BDA0001582924570000053
representing the maximum interval equivalent conversion result of the support vector;
Figure BDA0001582924570000054
expressing the minimum value of the expression;
Figure BDA0001582924570000055
expressing the maximum value of the expression;
Figure BDA0001582924570000056
represents summing the expressions;
xi,xj∈{x1,x2,...,xnexpressing the i, j training set document vectorization value, wherein n expresses the number of training set documents, i is more than or equal to 1, and j is less than or equal to n;
yi,yj∈{y1,y2,...,ynrepresenting the category of the ith and j training set documents, and taking the value of 1 or-1;
αi,αj∈α＝{α1,α2,...,αndenotes xi,xjA corresponding lagrange multiplier;
Figure BDA0001582924570000057
representing a normal vector;
wTrepresents w transpose;
||w||2represents the square of the w euclidean norm;
b represents the intercept of the hyperplane on the coordinate axis;
K(xi,xj) Representing a kernel function;
constructing a hybrid Fourier kernel function to be introduced into a support vector machine, wherein the hybrid Fourier kernel function is as follows:
Figure BDA0001582924570000061
in the formula, u is more than or equal to 0 and less than or equal to 1;
Kpoly＝(xi×xj+c)drepresenting a polynomial kernel, wherein c takes the value 1 and d takes the value 2 or 3;
Figure BDA0001582924570000062
representing a Fourier kernel in which cos (x)i-xj) Denotes xi-xjThe cosine value of (q is more than 0 and less than 1);
introducing a hybrid fourier kernel function into a support vector machine:
Figure BDA0001582924570000063
vectorizing the document:
Figure BDA0001582924570000064
in the formula, λkjRepresenting a document deMiddle characteristic word tkAs a result of vectorization
tk∈{t1,t2,...,tmMeans a feature word tkWherein m represents the total number of the feature words in the total document, and i is more than or equal to 1 and less than or equal to m;
de∈{d1,d2,...,dNrepresenting the e document in the total documents, wherein e is more than or equal to 1 and less than or equal to N;
tf(tk,de) Representation feature word tkIn document deThe number of occurrences in (a);
Nkmeaning containing a characteristic word tkThe number of documents;
n represents the total document number;
β is an empirical value, taken at 0.1;
selecting a training set and a testing set from the total documents by a cross validation method, and finally deciding a function:
Figure BDA0001582924570000065
wherein f (x's) Representing a classification result of the support vector machine model;
xs'∈{x1',x'2,...,x'zrepresenting the s test set document after vectorization, wherein z represents that the number of the test set documents is more than or equal to 1 and less than or equal to z;
K(x's,xi) Representing the proposed hybrid fourier kernel;
αib represents parameters obtained by training the support vector machine;
sgn (·) represents a sign function.
The value of the polynomial and the Gaussian kernel function mixed kernel function shown in FIG. 1 is consistent with the Gaussian kernel function at the test point, which shows that the mixed kernel function has no great change in learning ability, but the values at the points far away from the test point are increased, which shows that the generalization ability of the polynomial and the Gaussian kernel function mixed kernel function is improved. In the figure, d, gamma represents the exponential parameter and the gaussian kernel function parameter in the polynomial kernel function, respectively.
The parameter u in fig. 2 represents the linear weighting coefficient u in equation 3. The value of the Fourier kernel function parameter q is 0.5, and compared with the one-dimensional Fourier kernel function, the value of the mixed Fourier kernel function at the test point is approximate to the one-dimensional Fourier kernel function, so that the mixed Fourier kernel function inherits the learning capability of the one-dimensional Fourier kernel function; the value far away from the test point is higher than the one-dimensional Fourier kernel function, which shows that the generalization capability of the mixed Fourier kernel function is higher than that of the traditional one-dimensional Fourier kernel function. Comparing the mixed kernel functions of the polynomial and the Gaussian kernel function, the values of the mixed Fourier kernel function at the test points and other points are higher than the mixed kernel functions of the polynomial and the Gaussian kernel function, which shows that the mixed Fourier kernel function is higher than the mixed kernel functions of the polynomial and the Gaussian kernel function in both learning ability and generalization ability.
The document selects characteristic dimensions through a word frequency method, and the characteristic quantity selects 500 to 3000, 5000, 7000 and 9000 dimensions. And transmitting the features into support vector machine models composed of different kernel functions, and comparing precision ratio, recall ratio and F1 value of different kernel function support vector machine model results. The comparison result shows that along with the increase of dimensionality, the three indexes of each kernel function are increased by about 2% -4%, compared with other single kernel functions, the three indexes of the one-dimensional Fourier kernel function are all increased by 2% -3%, compared with the one-dimensional Fourier kernel function, the mixed Fourier function is improved by 2% -3%, compared with the polynomial and the Gaussian kernel function, the mixed Fourier function is improved by 1.5% -2%.
In summary, the hybrid fourier kernel function support vector machine model provided by the invention is superior to other kernel functions in learning ability and generalization ability, and is superior to the conventional kernel function in classification performance under the condition that parameters such as data sets and feature quantity are equal.

Claims (1)

1. A text classification method for a hybrid Fourier kernel Support Vector Machine (SVM), the method comprising the steps of:
step A, training a support vector machine to obtain αiAnd b, simplifying the solving process of the support vector machine according to Lagrange multiplication and KKT conditions, and converting the solving into:
Figure FDA0002269589610000011
constraint conditions are as follows:
Figure FDA0002269589610000012
wherein C represents a relaxation variable;
in the formula (I), the compound is shown in the specification,
Figure FDA0002269589610000013
representing the maximum interval equivalent conversion result of the support vector;
Figure FDA0002269589610000014
expressing the minimum value of the expression;
Figure FDA0002269589610000015
expressing the maximum value of the expression;
Figure FDA0002269589610000016
represents summing the expressions;
xi,xj∈{x1,x2,...,xnexpressing the i, j training set document vectorization value, wherein n expresses the number of training set documents, i is more than or equal to 1, and j is less than or equal to n;
yi,yj∈{y1,y2,...,ynrepresenting the category of the ith and j training set documents, and taking the value of 1 or-1;
αi,αj∈α＝{α1,α2,...,αndenotes xi,xjA corresponding lagrange multiplier;
Figure FDA0002269589610000017
representing a normal vector;
wTrepresents w transpose;
||w||2represents the square of the w euclidean norm;
b represents the intercept of the hyperplane on the coordinate axis;
K(xi,xj) Representing a kernel function;
step B, constructing a mixed Fourier kernel function to be introduced into the support vector machine, wherein the mixed Fourier kernel function is as follows:
Figure FDA0002269589610000021
wherein, 0 is not less than η is not more than 1;
Kpoly＝(xi×xj+c)drepresenting a polynomial kernel, wherein c takes the value 1 and d takes the value 2 or 3;
Figure FDA0002269589610000022
representing a Fourier kernel in which cos (x)i-xj) Denotes xi-xjThe parameter q represents the amplitude change and the attenuation degree of the Fourier kernel function, and q is more than 0 and less than 1;
step C, introducing a mixed Fourier kernel function into a support vector machine:
Figure FDA0002269589610000023
step D, vectorizing the document:
Figure FDA0002269589610000024
in the formula, λkjRepresenting a document deMiddle characteristic word tkAs a vectorization result;
tk∈{t1,t2,...,tmmeans a feature word tkWherein m represents the total number of the feature words in the total document, and k is more than or equal to 1 and less than or equal to m;
de∈{d1,d2,...,dNrepresenting the e document in the total documents, wherein e is more than or equal to 1 and less than or equal to N;
tf(tk,de) Representation feature word tkIn document deThe number of occurrences in (a);
Nkmeaning containing a characteristic word tkThe number of documents;
n represents the total document number;
β is an empirical value, taken at 0.1;
e, selecting a training set and a testing set from the total document by a cross validation method, and finally deciding a function:
Figure FDA0002269589610000025
wherein f (x's) Representing a classification result of the support vector machine model;
x′s∈{x′1,x′2,...,x′zrepresenting the s test set document after vectorization, wherein z represents that the number of the test set documents is more than or equal to 1 and less than or equal to z;
K(x′s,xi) Representing the proposed hybrid fourier kernel;
αib represents parameters obtained by training the support vector machine;
sgn (·) represents a sign function.
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