WAVELET-FACE BASED SUBSPACE LDA METHOD TO SOLVE SMALL SAMPLE SIZE PROBLEM IN FACE RECOGNITION

2009 ◽  
Vol 07 (02) ◽  
pp. 199-214 ◽  
Author(s):  
WEN-SHENG CHEN ◽  
JIAN HUANG ◽  
JIN ZOU ◽  
BIN FANG
Keyword(s):  
Feature Extraction ◽  
Face Recognition ◽  
Dimensionality Reduction ◽  
Sample Size ◽  
Null Space ◽  
Small Sample Size ◽  
Small Sample ◽  
Projection Matrix ◽  
Scatter Matrix ◽  
Linear Discriminant

Linear Discriminant Analysis (LDA) is a popular statistical method for both feature extraction and dimensionality reduction in face recognition. The major drawback of LDA is the so-called small sample size (3S) problem. This problem always occurs when the total number of training samples is smaller than the dimension of feature space. Under this situation, the within-class scatter matrix Sw becomes singular and LDA approach cannot be implemented directly. To overcome the 3S problem, this paper proposes a novel wavelet-face based subspace LDA algorithm. Wavelet-face feature extraction and dimensionality reduction are based on two-level D4-filter wavelet transform and discarding the null space of total class scatter matrix St. It is shown that our obtained projection matrix satisfies the uncorrelated constraint conditions. Hence in the sense of statistical uncorrelation, this projection matrix is optimal. The proposed method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. Comparing with existing LDA-based methods to solve the 3S problem, our method gives the best performance.

Kernel Null Space Marginal Fisher Analysis for Face Recognition

2014 ◽  
Vol 889-890 ◽  
pp. 1065-1068
Author(s):  
Yu’e Lin ◽  
Xing Zhu Liang ◽  
Hua Ping Zhou
Keyword(s):  
Feature Extraction ◽  
Face Recognition ◽  
Sample Size ◽  
High Performance ◽  
Null Space ◽  
Small Sample Size ◽  
Recognition Rate ◽  
Original Data ◽  
Small Sample ◽  
Neighborhood Structure

In the recent years, the feature extraction algorithms based on manifold learning, which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure, have drawn much attention. Among them, the Marginal Fisher Analysis (MFA) achieved high performance for face recognition. However, MFA suffers from the small sample size problems and is still a linear technique. This paper develops a new nonlinear feature extraction algorithm, called Kernel Null Space Marginal Fisher Analysis (KNSMFA). KNSMFA based on a new optimization criterion is presented, which means that all the discriminant vectors can be calculated in the null space of the within-class scatter. KNSMFA not only exploits the nonlinear features but also overcomes the small sample size problems. Experimental results on ORL database indicate that the proposed method achieves higher recognition rate than the MFA method and some existing kernel feature extraction algorithms.

A NEW REGULARIZED LINEAR DISCRIMINANT ANALYSIS METHOD TO SOLVE SMALL SAMPLE SIZE PROBLEMS

2005 ◽  
Vol 19 (07) ◽  
pp. 917-935 ◽  
Author(s):  
WEN-SHENG CHEN ◽  
PONG C. YUEN ◽  
JIAN HUANG
Keyword(s):  
Face Recognition ◽  
Discriminant Analysis ◽  
Sample Size ◽  
Linear Discriminant Analysis ◽  
Small Sample Size ◽  
Small Sample ◽  
Scatter Matrix ◽  
Linear Discriminant ◽  
Matrix Formula ◽  
Parameter Regularization

This paper presents a new regularization technique to deal with the small sample size (S3) problem in linear discriminant analysis (LDA) based face recognition. Regularization on the within-class scatter matrix Sw has been shown to be a good direction for solving the S3 problem because the solution is found in full space instead of a subspace. The main limitation in regularization is that a very high computation is required to determine the optimal parameters. In view of this limitation, this paper re-defines the three-parameter regularization on the within-class scatter matrix [Formula: see text], which is suitable for parameter reduction. Based on the new definition of [Formula: see text], we derive a single parameter (t) explicit expression formula for determining the three parameters and develop a one-parameter regularization on the within-class scatter matrix. A simple and efficient method is developed to determine the value of t. It is also proven that the new regularized within-class scatter matrix [Formula: see text] approaches the original within-class scatter matrix Sw as the single parameter tends to zero. A novel one-parameter regularization linear discriminant analysis (1PRLDA) algorithm is then developed. The proposed 1PRLDA method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. The average recognition accuracies of 50 runs for ORL and FERET databases are 96.65% and 94.00%, respectively. Comparing with existing LDA-based methods in solving the S3 problem, the proposed 1PRLDA method gives the best performance.

Discriminant Analysis for Biometric Recognition

2011 ◽  
pp. 25-29
Author(s):  
David Zhang ◽  
Fengxi Song ◽  
Yong Xu ◽  
Zhizhen Liang
Keyword(s):  
Pattern Recognition ◽  
Feature Extraction ◽  
Discriminant Analysis ◽  
Sample Size ◽  
Linear Discriminant Analysis ◽  
Small Sample Size ◽  
Small Sample ◽  
Biometric Recognition ◽  
Linear Discriminant

This chapter is a brief introduction to biometric discriminant analysis technologies — Section I of the book. Section 2.1 describes two kinds of linear discriminant analysis (LDA) approaches: classification-oriented LDA and feature extraction-oriented LDA. Section 2.2 discusses LDA for solving the small sample size (SSS) pattern recognition problems. Section 2.3 shows the organization of Section I.

scholarly journals A Complete Subspace Analysis of Linear Discriminant Analysis and Its Robust Implementation

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Zhicheng Lu ◽  
Zhizheng Liang
Keyword(s):  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Null Space ◽  
Small Sample Size ◽  
Classification Performance ◽  
Optimization Criterion ◽  
Small Sample ◽  
Scatter Matrix ◽  
Linear Discriminant ◽  
Maximum Margin Criterion

Linear discriminant analysis has been widely studied in data mining and pattern recognition. However, when performing the eigen-decomposition on the matrix pair (within-class scatter matrix and between-class scatter matrix) in some cases, one can find that there exist some degenerated eigenvalues, thereby resulting in indistinguishability of information from the eigen-subspace corresponding to some degenerated eigenvalue. In order to address this problem, we revisit linear discriminant analysis in this paper and propose a stable and effective algorithm for linear discriminant analysis in terms of an optimization criterion. By discussing the properties of the optimization criterion, we find that the eigenvectors in some eigen-subspaces may be indistinguishable if the degenerated eigenvalue occurs. Inspired from the idea of the maximum margin criterion (MMC), we embed MMC into the eigen-subspace corresponding to the degenerated eigenvalue to exploit discriminability of the eigenvectors in the eigen-subspace. Since the proposed algorithm can deal with the degenerated case of eigenvalues, it not only handles the small-sample-size problem but also enables us to select projection vectors from the null space of the between-class scatter matrix. Extensive experiments on several face images and microarray data sets are conducted to evaluate the proposed algorithm in terms of the classification performance, and experimental results show that our method has smaller standard deviations than other methods in most cases.

NEAREST NEIGHBOR DISCRIMINANT ANALYSIS

2006 ◽  
Vol 20 (08) ◽  
pp. 1245-1259 ◽  
Author(s):  
XIPENG QIU ◽  
LIDE WU
Keyword(s):  
Feature Extraction ◽  
Discriminant Analysis ◽  
Nearest Neighbor ◽  
Small Sample Size ◽  
Small Sample ◽  
Real World Data ◽  
Scatter Matrix ◽  
Linear Discriminant ◽  
Feature Extraction Method ◽  
Gaussian Density

Linear Discriminant Analysis (LDA) is a popular feature extraction technique in statistical pattern recognition. However, it often suffers from the small sample size problem when dealing with high-dimensional data. Moreover, while LDA is guaranteed to find the best directions when each class has a Gaussian density with a common covariance matrix, it can fail if the class densities are more general. In this paper, a novel nonparametric linear feature extraction method, nearest neighbor discriminant analysis (NNDA), is proposed from the view of the nearest neighbor classification. NNDA finds the important discriminant directions without assuming the class densities belong to any particular parametric family. It does not depend on the nonsingularity of the within-class scatter matrix either. Then we give an approximate approach to optimize NNDA and an extension to k-NN. We apply NNDA to the simulated data and real world data, the results demonstrate that NNDA outperforms the existing variant LDA methods.

scholarly journals Simulasi Ektraksi Citra Wajah dengan Deskriptor Global Direct Fractional-Step Linear Discriminant Analysis (DF-LDA) untuk Pengenalan Wajah

2015 ◽  
Vol 14 (01) ◽  
pp. 59-66
Author(s):  
Ikuthen Gabriel Barus ◽  
Riko Arlando Saragih
Keyword(s):  
Face Recognition ◽  
Discriminant Analysis ◽  
Sample Size ◽  
Linear Discriminant Analysis ◽  
Weighting Function ◽  
Small Sample Size ◽  
Small Sample ◽  
Fractional Step ◽  
Linear Discriminant

Tulisan ini memaparkan simulasi ekstraksi citra wajah secara global dengan menggunakan salah satu teknik Linear Discriminant Analysis (LDA), yaitu Direct Fractional-Step LDA (DF-LDA) untuk pengenalan wajah. Tujuan tulisan ini adalah untuk mengevaluasi unjuk kerja teknik ini terhadap masalah small sample size (SSS) yang sering muncul di dalam pengenalan wajah. Pada dasarnya teknik berbasis LDA ini (DF-LDA) merupakan kombinasi dari teknik D-LDA dan F-LDA, dimana untuk merepresentasikan citra wajah secara global secara efisien dapat ditambahkan sebuah fungsi pembobot (weighting function) dengan bertahap secara langsung dan fraksional pada proses LDA. Proses pencocokan dilakukan dengan mencari jarak Euclidean minimum antara ciri citra wajah uji terhadap ciri citra wajah latih yang terdapat di dalam database. Dari hasil simulasi untuk Database Face Recognition Data dan Database Mahasiswa Maranatha diperoleh akurasi pengenalan wajah yang lebih baik untuk kondisi jumlah citra wajah satu per orang di dalam proses pelatihan jika database wajah diproses secara terpisah.

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