CN102609693A - Human face recognition method based on fuzzy two-dimensional kernel principal component analysis - Google Patents

Human face recognition method based on fuzzy two-dimensional kernel principal component analysis Download PDF

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CN102609693A
CN102609693A CN2012100321304A CN201210032130A CN102609693A CN 102609693 A CN102609693 A CN 102609693A CN 2012100321304 A CN2012100321304 A CN 2012100321304A CN 201210032130 A CN201210032130 A CN 201210032130A CN 102609693 A CN102609693 A CN 102609693A
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sample
fuzzy
class
matrix
face
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曾接贤
田金权
符祥
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Nanchang Hangkong University
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Abstract

The invention discloses a kind of face identification methods based on fuzzy two-dimensional core principle component analysis, comprising: introduces fuzzy concept in two-dimentional core principle component analysis (K2DPCA) first, calculates sample in high-dimensional feature space (abbreviation using fuzzy k nearest neighbor algorithm
Figure 2012100321304100004DEST_PATH_IMAGE001
) in degree of membership relative to each class of class center and each sample, defined according to degree of membership information
Figure 629106DEST_PATH_IMAGE001
In Fuzzy Divergence matrix, the classification of sample and distributed intelligence are fully immersed into the feature extraction of face in this way, solve the problems, such as face vulnerable to the factors such as illumination, expression influence and generate edge class and existing Hard clustering problem; By establishing sort separability criterion of the face sample in higher dimensional space, choosing the class scatter after meeting projection to be greater than the feature vector of divergence in class is optimal projection axis direction, improves accuracy that optimal axis of projection is chosen and fuzzy two-dimensional core principle component analysis method to the expression ability of face characteristic.

Description

Face identification method based on fuzzy two-dimensional nucleus principal component analysis (PCA)
Technical field
The present invention relates to a kind of face identification method; Relate in particular to a kind of face identification method based on fuzzy two-dimensional nucleus principal component analysis (PCA) and belong to pattern-recognition and computer vision research category, the major technique field relates to extracts effective people's face diagnostic characteristics and sorter reasonable in design.
Background technology
Recognition of face has become important research direction in the living things feature recognition, mainly carries out through the sorter that extracts effective people's face diagnostic characteristics and complex design.Principal component analysis (PCA) (PCA) and two-dimentional principal component analysis (PCA) (2DPCA) all are a kind of linear characteristic extracting methods on the least squares error meaning, and they can not extract the nonlinear organization characteristic of people's face effectively and classify.To this problem; People such as Hui Kong have proposed two-dimensional nucleus principal component analysis (PCA) (K2DPCA) method [Hui Kong; Lei Wang; Eam K T; Et al. Generalized 2D Principal Component Analysis for face image representation and recognition [J]. Neural Networks; 2005; 18 (5-6): 585-594.]; It utilizes the nuclear learning method not only can extract the nonlinear organization characteristic of people's face effectively; And can also in
Figure 993119DEST_PATH_IMAGE001
, set up optimum lineoid with having in non-linear inseparable facial image data map to a high-dimensional feature space
Figure 492868DEST_PATH_IMAGE001
, realize linear separability.But PCA, 2DPCA, the K2DPCA method does not all make full use of classification information [the Chen Songcan of training sample; Sun Tingkai. Class Information-Incorporated principal Component Analysis [J]. Neurocomputing, 2005,69 (1-3): 216-223.]; Therefore people such as Li Yongzhi proposed a kind of core principle component analysis of combination sort information method [Li Yongzhi, Yang Jingyu, Wu Songsong. a kind of method of core principle component analysis of combination sort information [J]. pattern-recognition and artificial intelligence; 2008,21 (3): 410-416.], utilize the known category information of training sample to carry out feature extraction; Part has solved the classification information problem of utilizing training sample, but also has the problem of two aspects, is on the one hand influenced by illumination, expression and jewelry etc. and during away from the average (i.e. class center) of sample when sample; Meeting generation edge class problem [Zhuan Zhemin opens Ah girl, Li Fenlan. based on the LDA algorithm recognition of face research of optimizing [J]. and electronics and information journal; 2007; 29 (9): 2047-2049.], put sample under certain type way simply this moment is unscientific, can produce hard classification problem [poplar ten thousand buttons; Wang Jianguo; Ren Mingwu etc. fuzzy contrary Fisher discriminatory analysis and the application in recognition of face [J] thereof. Chinese image graphics journal, 2009,14 (1): 88-93.]; Be only to select relatively large eigenwert characteristic of correspondence vector on the other hand as optimum axis of projection; [jade pendant is taken root to have abandoned the slight change information of people's face; Zhou Jiliu, imperial court is refined etc. based on the recognition of face [J] of statistical nature fusion. and Sichuan University's journal (natural science edition), 2009; 46 (3): 618-621.], such optimum axis of projection is chosen and is inaccurate.
Summary of the invention
Do not make full use of the classification information of people's face to two-dimensional nucleus principal component analytical method (K2DPCA), in recognition of face, have edge class and hard classification problem, the present invention provides the face identification method based on fuzzy two-dimensional nucleus principal component analysis (PCA) (FK2DPCA).At first in K2DPCA, introduce fuzzy concept; Secondly utilize the nuclear learning method that classification separability criterion is generalized in the high-dimensional feature space; Choosing the between class scatter that meets after the projection then is optimum axis of projection greater than the proper vector of divergence in the class; Adopt nearest neighbor classifier to carry out Classification and Identification at last.Specifically comprise:
1, with
Figure 39835DEST_PATH_IMAGE002
class Personal face training sample collection
Figure 750488DEST_PATH_IMAGE004
, and
Figure 675718DEST_PATH_IMAGE005
, where
Figure 962343DEST_PATH_IMAGE006
for the first , class
Figure 584692DEST_PATH_IMAGE008
sample image;
Figure 931360DEST_PATH_IMAGE009
for the first
Figure 406204DEST_PATH_IMAGE007
class training samples and
Figure 496519DEST_PATH_IMAGE010
is the total number of training samples;
Figure 678102DEST_PATH_IMAGE011
is the sample After a nonlinear transformation function mapped into a high dimensional feature space
Figure 84441DEST_PATH_IMAGE001
The core sample matrix;
2, obtain corresponding membership function and do according to fuzzy
Figure 946961DEST_PATH_IMAGE013
neighbour's criterion
Figure 369852DEST_PATH_IMAGE014
(1)
Wherein
Figure 819288DEST_PATH_IMAGE015
;
Figure 815188DEST_PATH_IMAGE016
and
Figure 830418DEST_PATH_IMAGE017
; The degree of dependence of
Figure 689789DEST_PATH_IMAGE018
be type
Figure 181041DEST_PATH_IMAGE008
individual sample for type, the number of samples that belongs to
Figure 532311DEST_PATH_IMAGE007
in
Figure 331137DEST_PATH_IMAGE013
individual nearest neighbor point of type the individual sample that is
Figure 629711DEST_PATH_IMAGE019
Lei;
3, to obtain the training samples in
Figure 679521DEST_PATH_IMAGE001
membership matrix corresponding to
Figure 991554DEST_PATH_IMAGE022
;
4, the use of fuzzy - formula to calculate the mean first
Figure 348903DEST_PATH_IMAGE007
class samples in a high dimensional feature space
Figure 481944DEST_PATH_IMAGE001
The sample mean
Figure 96203DEST_PATH_IMAGE024
(2)
Wherein:
Figure 935983DEST_PATH_IMAGE025
;
5, defined samples
Figure 478959DEST_PATH_IMAGE026
(
Figure 771401DEST_PATH_IMAGE027
) in the fuzzy within-class scatter matrix
Figure 753132DEST_PATH_IMAGE028
(3)
6, defined samples
Figure 447418DEST_PATH_IMAGE026
(
Figure 662761DEST_PATH_IMAGE029
) in the fuzzy between-class scatter matrix
Figure 708078DEST_PATH_IMAGE030
(4)
Wherein
Figure 165604DEST_PATH_IMAGE031
is the population sample average;
7, defined samples
Figure 776714DEST_PATH_IMAGE026
(
Figure 864756DEST_PATH_IMAGE029
) in the fuzzy overall scatter degree matrix for the
(5)
8, inference: the fuzzy total volume divergence matrix
Figure 678417DEST_PATH_IMAGE033
in (
Figure 357157DEST_PATH_IMAGE029
) is that sample blurs between class scatter matrix
Figure 232075DEST_PATH_IMAGE034
and blurs divergence matrix
Figure 817778DEST_PATH_IMAGE035
sum in the class in
Figure 432747DEST_PATH_IMAGE001
to sample at
Figure 393006DEST_PATH_IMAGE026
, promptly
Figure 247622DEST_PATH_IMAGE036
(6)
9, with
Figure 787450DEST_PATH_IMAGE002
class
Figure 390470DEST_PATH_IMAGE003
Personal face training sample collection , and
Figure 431424DEST_PATH_IMAGE005
, where
Figure 160345DEST_PATH_IMAGE006
for the first , class
Figure 360306DEST_PATH_IMAGE008
sample image;
Figure 866374DEST_PATH_IMAGE009
for the first
Figure 144908DEST_PATH_IMAGE007
class training samples and
Figure 89731DEST_PATH_IMAGE010
is the total number of training samples;
Figure 442215DEST_PATH_IMAGE037
is the sample
Figure 447080DEST_PATH_IMAGE006
After a nonlinear transformation function mapped into a high dimensional feature space The core sample matrix;
10, the mean distance between all kinds of samples of definition does
Figure 404300DEST_PATH_IMAGE038
(7)
Wherein
Figure 314487DEST_PATH_IMAGE039
representes the prior probability of respective classes;
Figure 239718DEST_PATH_IMAGE040
expression
Figure 526342DEST_PATH_IMAGE006
and
Figure 853419DEST_PATH_IMAGE041
is corresponding to the distance between the vector in and
Figure 935885DEST_PATH_IMAGE042
;
Figure 179784DEST_PATH_IMAGE043
then has for Euclidean distance:
Figure 635036DEST_PATH_IMAGE044
(8)
11, the between class scatter matrix of definition sample in high-dimensional feature space
Figure 597176DEST_PATH_IMAGE001
does
(9)
12, the divergence matrix does in the class of definition sample in high-dimensional feature space
Figure 763158DEST_PATH_IMAGE001
Figure 451628DEST_PATH_IMAGE046
(10)
13, the total volume divergence matrix of definition sample in high-dimensional feature space
Figure 901064DEST_PATH_IMAGE001
does
(11)
14, inference: the nuclear sample matrix in the high-dimensional feature space
Figure 846947DEST_PATH_IMAGE001
is the between class scatter matrix
Figure 315154DEST_PATH_IMAGE048
and type interior divergence matrix sum in the high-dimensional feature space , promptly
Figure 561645DEST_PATH_IMAGE050
(12)
15, classification separability criterion
If the sample frequency
Figure 93382DEST_PATH_IMAGE051
with all kinds of samples is represented prior probability
Figure 251831DEST_PATH_IMAGE052
, then can get total volume divergence matrix trace and do
Figure 760173DEST_PATH_IMAGE053
(13)
So can be with the mark
Figure 236394DEST_PATH_IMAGE055
of sample total volume divergence matrix
Figure 92114DEST_PATH_IMAGE054
in high-dimensional feature space
Figure 890940DEST_PATH_IMAGE001
as the classification separability criterion of sample in
Figure 486110DEST_PATH_IMAGE001
; Promptly the value as
Figure 533701DEST_PATH_IMAGE055
is big more, and the expression sample is overstepping the bounds of propriety to loose;
16, projector space structure
According to the classification separability criterion in the high-dimensional feature space ; The projector space
Figure 656006DEST_PATH_IMAGE056
that all the corresponding nonzero eigenvalue characteristics of correspondence vectors that obtain
Figure 38817DEST_PATH_IMAGE033
constitute, wherein
Figure 495786DEST_PATH_IMAGE057
is the number of nonzero eigenvalue;
17, optimum axis of projection is selected
Choose the between class scatter that can make after the projection greater than the proper vector of divergence in the class as optimum axis of projection, that is:
Figure 393520DEST_PATH_IMAGE058
(14)
18, the major component of sample
The major component of sample can be expressed as:
Figure 312935DEST_PATH_IMAGE059
(15)
Wherein
Figure 7221DEST_PATH_IMAGE060
is optimum axis of projection in the optimum projector space ;
Figure 350705DEST_PATH_IMAGE062
is the axis of projection number; And
Figure 745915DEST_PATH_IMAGE063
, the major component that can be obtained
Figure 357025DEST_PATH_IMAGE064
individual sample
Figure 445066DEST_PATH_IMAGE006
correspondence by formula (15) is:
Figure 774417DEST_PATH_IMAGE065
;
19, using the same method (step 18) onto an arbitrary test samples
Figure 271519DEST_PATH_IMAGE066
will get the appropriate space after the main ingredient
Figure 940398DEST_PATH_IMAGE067
;
20, carry out Classification and Identification with nearest neighbor classifier, that is:
(16)
Need only obtain separating of formula (16); During belong to
Figure 815316DEST_PATH_IMAGE007
as type sample, test sample book
Figure 401018DEST_PATH_IMAGE067
type facial image that belongs to
Figure 126135DEST_PATH_IMAGE007
then.
Technique effect of the present invention is: at first, inherited the advantage of K2DPCA method based on the face identification method of fuzzy two-dimensional nucleus principal component analysis (PCA).Then; In the face identification method of K2DPCA, introduce fuzzy concept; Utilize the fuzzy divergence matrix of degree of membership information definition sample in high-dimensional feature space and a type center; The distributed intelligence and the classification information of sample are dissolved in the last feature extraction fully, are subject to factor affecting such as illumination, expression to people's face and the edge class problem that produces and the hard classification problem of existence have been done effective improvement.At last; Set up the classification separability criterion of people's face sample in higher dimensional space; Choosing the between class scatter that meets after the projection is optimum axis of projection direction greater than the proper vector of divergence in the class; Make the less relatively nonzero eigenvalue characteristic of correspondence vector of total volume divergence matrix
Figure 367761DEST_PATH_IMAGE033
of sample participate in selection like this; Can the little pairing proper vector of eigenwert of selected part be optimum axis of projection; Therefore the present invention has not only extracted effectively and has helped knowing others face slight change information; But also solved between class distance after using nearest neighbor algorithm to the test sample book projection less than the mis-classification problem of distance in the class, improved expression ability to face characteristic.
Description of drawings
Fig. 1 is one type of people's face sample image in the ORL face database.
Fig. 2 is one type of sample image in the YALE face database.
Fig. 3 is people's face best identified performance comparison figure on ORL.
Fig. 4 is people's face best identified performance comparison figure on YALE.
Embodiment
Through concrete enforcement technical scheme of the present invention and effect are done further to describe below.
1, in order to verify the validity of this paper algorithm, will be based on the face identification method and the PCA of fuzzy two-dimensional nucleus principal component analysis (PCA) (FK2DPCA), 2DPCA, the face identification method of K2DPCA have carried out the contrast experiment respectively on facial image database ORL and YALE.
2, as shown in Figure 1; (http://www.uk.research.att. com/facedatabase.html) has 40 people to the ORL facial image database; Everyone 10; By resolution be 112
Figure 970780DEST_PATH_IMAGE070
people's face gray level image of 92 forms, comprising: different times (1992-1994), different expression and facial detail (open eyes/close one's eyes, laugh at/do not laugh at, the wear a pair of spectacles of wear a pair of spectacles/not), degree of depth rotation image with plane rotation (can reach 20 degree), dimensional variation (rate of change is 10%).
3, as shown in Figure 2; YALE facial image database (http://cvc.yale.edu/projects/ yalefaces/yalefaces.html) has 15 people; Everyone have 11 resolution be 243
Figure 348672DEST_PATH_IMAGE070
320 image, comprising: different expressions and different facial detail (surprised/sleepiness/nictation/happiness/grief), lighting angle (left/in/right side) and the gray level image of wearing glasses/not wearing glasses.
4, in order to let experiment have comparability; Here from every type of sample storehouse, choose
Figure 11735DEST_PATH_IMAGE071
individual facial image in order as training sample, the residue sample is tested.
5, in order to reduce calculated amount, the picture size in ORL and the YALE facial image database is normalized to 28 * 24 and 61 * 80 respectively.
6, getting kernel function is gaussian kernel function:
Figure 537394DEST_PATH_IMAGE072
; Wherein
Figure 445569DEST_PATH_IMAGE073
adopts nearest neighbor classifier to classify.
7, shown in accompanying drawing 1 and the accompanying drawing 2 be someone image in ORL and the YALE face database respectively.As can be seen from the figure the image in the YALE face database receives factor affecting such as illumination, expression more outstanding than the image in the ORL face database.
8, accompanying drawing 3 is four kinds of methods people's face best identified performance comparison figure on ORL; Accompanying drawing 4 is four kinds of methods people's face best identified performance comparison figure on YALE; Subordinate list 1 is the average recognition rate of four kinds of methods different training number of samples on the ORL face database; Subordinate list 2 is average recognition rate of four kinds of methods different training number of samples on the YALE face database.Can find out that from accompanying drawing 3 and accompanying drawing 4, subordinate list 1 and subordinate list 2 the FK2DPCA method is more stable more and efficient on the overall performance of recognition of face than PCA, 2DPCA and three kinds of classic methods of K2DPCA.This is because the FK2DPCA method at first utilizes fuzzy membership information that the classification information and the distributed intelligence of sample are dissolved in the last feature extraction fully, has done effective improvement to edge class that exists in the recognition of face and hard classification problem; Secondly improved the accuracy that optimum axis of projection is chosen through the classification separability criterion in the definition high-dimensional feature space
Figure 943547DEST_PATH_IMAGE074
; Choose then the between class scatter that meets after the projection greater than the proper vector of divergence in the class as optimum axis of projection, make the pairing proper vector of less eigenwert that possibly contain people's face diagnostic characteristics participate in choosing of optimum axis of projection.
9, the people's face best identified rate graph of a relation shown in accompanying drawing 3 and the accompanying drawing 4 has explained that also influenced by extraneous factor big more when people's face; Recognition performance will reduce; This mainly be because receive extraneous factor influence bigger facial image in space distribution away from the class center of actual sample, produced edge class sample, and classic method simply is divided into not science of a certain type way with sample; Have hard classification problem, their acting in conjunction has caused the reduction of recognition of face performance.
10, the FK2DPCA method concerns the space distribution between each sample and each type; Again define the divergence matrix of sample through the membership function of sample; The classification information of sample and space distribution information are dissolved in the middle of the feature extraction of people's face fully, have been improved the recognition efficiency of people's face.
The average recognition rate of 1 four kinds of methods of subordinate list different training number of samples on the ORL face database
Table?1 The?average?recognition?rate?among?four?methods?on?ORL?face?database
Figure 511931DEST_PATH_IMAGE075
The average recognition rate of 2 four kinds of methods of subordinate list different training number of samples on the YALE face database
Table?2 The?average?recognition?rate?among?four?methods?on?YALE?face?database
Figure 790466DEST_PATH_IMAGE076

Claims (4)

1. based on the face identification method of fuzzy two-dimensional nucleus principal component analysis (PCA), it is characterized in that method step is:
1.1, fuzzy two-dimensional nucleus principal component analytical method;
1.2, the classification separability criterion in the high-dimensional feature space;
1.3, the choosing method of proper vector and the recognition methods of people's face.
2. the face identification method based on fuzzy two-dimensional nucleus principal component analysis (PCA) according to claim 1 is characterized in that described fuzzy two-dimensional nucleus principal component analytical method, comprises the steps:
2.1 features?
Figure 717161DEST_PATH_IMAGE001
class
Figure 131962DEST_PATH_IMAGE002
Personal Facial training sample collection
Figure 808931DEST_PATH_IMAGE003
, and
Figure 810647DEST_PATH_IMAGE004
, where
Figure 559160DEST_PATH_IMAGE005
for the first
Figure 766150DEST_PATH_IMAGE006
, class
Figure 941917DEST_PATH_IMAGE007
sample image;
Figure 929464DEST_PATH_IMAGE008
for the first
Figure 153772DEST_PATH_IMAGE006
class training samples and
Figure 41701DEST_PATH_IMAGE009
is the total number of training samples; is the sample
Figure 535316DEST_PATH_IMAGE005
After a nonlinear transformation function
Figure 625632DEST_PATH_IMAGE011
mapped into a high dimensional feature space
Figure 807214DEST_PATH_IMAGE012
The core sample matrix;
2.2, obtain corresponding membership function and do according to fuzzy neighbour's criterion
Figure 224606DEST_PATH_IMAGE014
(1)
Wherein
Figure 354498DEST_PATH_IMAGE015
;
Figure 452904DEST_PATH_IMAGE016
and ; The degree of dependence of
Figure 262914DEST_PATH_IMAGE018
be
Figure 695033DEST_PATH_IMAGE019
type
Figure 851208DEST_PATH_IMAGE007
individual sample for
Figure 209114DEST_PATH_IMAGE006
type; The number of samples that belongs to
Figure 551365DEST_PATH_IMAGE006
in
Figure 891451DEST_PATH_IMAGE013
individual nearest neighbor point of
Figure 880267DEST_PATH_IMAGE020
be type
Figure 861179DEST_PATH_IMAGE007
individual sample type, training sample is Xiang Yingde in
Figure 262969DEST_PATH_IMAGE012
, and the degree of membership matrix is
Figure 456053DEST_PATH_IMAGE021
;
2.3, using fuzzy
Figure 657227DEST_PATH_IMAGE022
- formula to calculate the mean first
Figure 975076DEST_PATH_IMAGE006
class samples in a high dimensional feature space
Figure 552688DEST_PATH_IMAGE012
The sample mean
(2)
Wherein:
Figure 432010DEST_PATH_IMAGE024
;
2.4, the definition samples (
Figure 415195DEST_PATH_IMAGE026
) in the fuzzy within-class scatter matrix
Figure 254975DEST_PATH_IMAGE027
(3)
2.5, the definition samples
Figure 797952DEST_PATH_IMAGE025
(
Figure 355972DEST_PATH_IMAGE028
) in the fuzzy between-class scatter matrix
Figure 511272DEST_PATH_IMAGE029
(4)
Wherein
Figure 533455DEST_PATH_IMAGE030
is the population sample average;
2.6, the definition samples
Figure 185016DEST_PATH_IMAGE025
(
Figure 27070DEST_PATH_IMAGE028
) in the matrix of fuzzy overall divergence
Figure 484596DEST_PATH_IMAGE031
(5)
2.7, inference: sample at
Figure 298969DEST_PATH_IMAGE025
the fuzzy total volume divergence matrix
Figure 949317DEST_PATH_IMAGE032
in (
Figure 682283DEST_PATH_IMAGE028
) be sample in
Figure 210534DEST_PATH_IMAGE012
fuzzy between class scatter matrix with fuzzy type in divergence matrix
Figure 935093DEST_PATH_IMAGE034
sum, promptly
(6)?。
3. the face identification method based on fuzzy two-dimensional nucleus principal component analysis (PCA) according to claim 1; It is characterized in that the classification separability criterion in the described high-dimensional feature space; Being characterized in deriving can be with the mark
Figure 68079DEST_PATH_IMAGE037
of sample total volume divergence matrix
Figure 841497DEST_PATH_IMAGE036
in high-dimensional feature space
Figure 318112DEST_PATH_IMAGE012
as the classification separability criterion of sample in
Figure 372022DEST_PATH_IMAGE012
, and derivation is following:
3.1, with
Figure 912724DEST_PATH_IMAGE001
class
Figure 352933DEST_PATH_IMAGE002
Personal Facial training sample collection
Figure 514531DEST_PATH_IMAGE003
, and
Figure 977873DEST_PATH_IMAGE004
, where
Figure 384584DEST_PATH_IMAGE005
for the first
Figure 616982DEST_PATH_IMAGE006
, class
Figure 450946DEST_PATH_IMAGE007
sample image;
Figure 463901DEST_PATH_IMAGE008
for the first
Figure 346406DEST_PATH_IMAGE006
class training samples and
Figure 262672DEST_PATH_IMAGE009
is the total number of training samples;
Figure 267537DEST_PATH_IMAGE038
is the sample
Figure 705472DEST_PATH_IMAGE005
After nonlinear transformation function
Figure 453985DEST_PATH_IMAGE011
mapped into a high dimensional feature space
Figure 660975DEST_PATH_IMAGE012
The core sample matrix;
3.2, the mean distance of definition between all kinds of samples do
Figure 836742DEST_PATH_IMAGE039
(7)
Wherein
Figure 322825DEST_PATH_IMAGE040
representes the prior probability of respective classes;
Figure 547132DEST_PATH_IMAGE041
expression
Figure 936526DEST_PATH_IMAGE005
and
Figure 955297DEST_PATH_IMAGE042
is corresponding to the distance between the vector in
Figure 430141DEST_PATH_IMAGE012
Figure 520457DEST_PATH_IMAGE038
and
Figure 702039DEST_PATH_IMAGE043
;
Figure 721073DEST_PATH_IMAGE044
then has for Euclidean distance:
Figure 355317DEST_PATH_IMAGE045
(8)
3.3, the definition between class scatter matrix of sample in high-dimensional feature space
Figure 983744DEST_PATH_IMAGE012
do
Figure 347729DEST_PATH_IMAGE046
(9)
3.4, the definition sample in high-dimensional feature space
Figure 973883DEST_PATH_IMAGE012
the class in the divergence matrix do
Figure 157739DEST_PATH_IMAGE047
(10)
3.5, the definition total volume divergence matrix of sample in high-dimensional feature space
Figure 88393DEST_PATH_IMAGE012
do
Figure 244568DEST_PATH_IMAGE048
(11)
3.6, inference: the nuclear sample matrix in the high-dimensional feature space be in the high-dimensional feature space
Figure 775092DEST_PATH_IMAGE012
between class scatter matrix with type in divergence matrix
Figure 756004DEST_PATH_IMAGE050
sum, promptly
(12)
3.7, classification separability criterion
If the sample frequency
Figure 383873DEST_PATH_IMAGE052
with all kinds of samples is represented prior probability
Figure 157794DEST_PATH_IMAGE053
, then can get total volume divergence matrix trace and do
Figure 85299DEST_PATH_IMAGE054
(13)
So can be with the mark
Figure 946048DEST_PATH_IMAGE037
of sample total volume divergence matrix
Figure 869901DEST_PATH_IMAGE036
in high-dimensional feature space
Figure 224156DEST_PATH_IMAGE012
as the classification separability criterion of sample in
Figure 665743DEST_PATH_IMAGE012
; Promptly the value as
Figure 37818DEST_PATH_IMAGE037
is big more, and the expression sample is overstepping the bounds of propriety to loose.
4. the face identification method based on fuzzy two-dimensional nucleus principal component analysis (PCA) according to claim 1 is characterized in that the recognition methods of choosing method and people's face of proper vector, comprises the steps:
4.1, projector space structure
According to the classification separability criterion in the high-dimensional feature space
Figure 108542DEST_PATH_IMAGE012
; The projector space
Figure 126363DEST_PATH_IMAGE055
that all the corresponding nonzero eigenvalue characteristics of correspondence vectors that obtain
Figure 224266DEST_PATH_IMAGE032
constitute, wherein
Figure 170804DEST_PATH_IMAGE056
is the number of
Figure 728825DEST_PATH_IMAGE032
nonzero eigenvalue;
4.2, optimum axis of projection selects
Choose the between class scatter that can make after the projection greater than the proper vector of divergence in the class as optimum axis of projection, that is:
(14)
Make the less relatively nonzero eigenvalue characteristic of correspondence vector of total volume divergence matrix
Figure 139263DEST_PATH_IMAGE032
of sample participate in selection like this; Can the little pairing proper vector of eigenwert of selected part be optimum axis of projection; Therefore this method has not only been extracted effectively and has been helped knowing others face slight change information, but also has solved between class distance after using nearest neighbor algorithm to the test sample book projection less than the mis-classification problem of distance in the class;
4.3, the major component of sample
The major component of sample can be expressed as:
Figure 56404DEST_PATH_IMAGE058
(15)
Wherein
Figure 459310DEST_PATH_IMAGE059
is optimum axis of projection in the optimum projector space
Figure 854519DEST_PATH_IMAGE060
;
Figure 731208DEST_PATH_IMAGE061
is the axis of projection number; And
Figure 615988DEST_PATH_IMAGE062
, the major component that can be obtained
Figure 883021DEST_PATH_IMAGE063
individual sample correspondence by formula (15) is:
Figure 813117DEST_PATH_IMAGE064
Using the same method will be projected onto any test samples
Figure 370262DEST_PATH_IMAGE065
will get the appropriate space after the main ingredient
Figure 186909DEST_PATH_IMAGE066
?;
4.4, recognition of face
Carry out Classification and Identification with nearest neighbor classifier, that is:
Figure 986237DEST_PATH_IMAGE067
(16)
Need only obtain separating of formula (16) this moment; During belong to as
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type sample, test sample book
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