3E-LDA

2021 ◽  
Vol 15 (4) ◽  
pp. 1-20
Author(s):  
Yanni Li ◽  
Bing Liu ◽  
Yongbo Yu ◽  
Hui Li ◽  
Jiacan Sun ◽  
...  
Keyword(s):  
Null Space ◽  
Small Sample Size ◽  
Small Sample ◽  
Geometric Information ◽  
Linear Discriminant ◽  
The Matrix ◽  
Benchmark Datasets ◽  
Weighted Median ◽  
The Mean ◽  
Reduction Machine

Linear discriminant analysis (LDA) is one of the important techniques for dimensionality reduction, machine learning, and pattern recognition. However, in many applications, applying the classical LDA often faces the following problems: (1) sensitivity to outliers, (2) absence of local geometric information, and (3) small sample size or matrix singularity that can result in weak robustness and efficiency. Although several researchers have attempted to address one or more of the problems, little work has been done to address all of them together to produce a more effective and efficient LDA algorithm. This article proposes 3E-LDA, an enhanced LDA algorithm, that deals with all three problems as an attempt to further improve LDA. It proposes to learn a weighted median rather than the mean of the samples to deal with (1), to embed both between-class and within-class local geometric information to deal with (2), and to calculate the projection vectors in the null space of the matrix to deal with (3). Experiments on six benchmark datasets show that these three enhancements enable 3E-LDA to markedly outperform state-of-the-art LDA baselines in both accuracy and efficiency.

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.

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.

Stillbirth Rate and Weight at Birth of Quintuplets in Japan

1989 ◽  
Vol 38 (1-2) ◽  
pp. 65-69 ◽  
Author(s):  
Yoko Imaizumi
Keyword(s):  
Sample Size ◽  
Birth Order ◽  
Gestational Age ◽  
Size Effects ◽  
Maternal Age ◽  
Small Sample Size ◽  
Small Sample ◽  
Stillbirth Rate ◽  
The Mean

AbstractNation-wide data in Japan on births and prenatal deaths of 16 sets of quintuplets during 1974-1985 were analysed. Among the 16 sets, 3 sets were liveborn, 8 were stillborn, and 5 were mixed, with a stillbirth rate of 0.64 (51/80). Effects of sex, maternal age and birth order on the stillbirth rate were not considered because of the small sample size. Effects of gestational age and birthweight on stillbirth rate were also examined. The mean weight of the 40 quintuplet individuals was 1,048 g.

The use of frequency distributions in an attempt to detect host mortality induced by infections of diplostomatid metacercariae

Parasitology ◽  
1984 ◽  
Vol 89 (2) ◽  
pp. 209-220 ◽  
Author(s):  
C. R. Kennedy
Keyword(s):  
Small Sample Size ◽  
Parasite Burden ◽  
Fish Host ◽  
Small Sample ◽  
Host Age ◽  
Parasite Abundance ◽  
Frequency Distributions ◽  
Host Mortality ◽  
The Mean ◽  
Over Dispersion

SummaryFollowing recent suggestions that a peaked host age–parasite abundance curve, concomitant with a decline in the degree of dispersion of parasites in the older age classes of hosts, can provide evidence of parasite-induced host mortality, the changes in mean abundance and over-dispersion of metacercarial stages of Diplostomum spathaceum, D. gasterostei, Tylodelphys clavata and T. podicipina in relation to fish age were studied in a field locality. The mean parasite burden of D. spathaceum, D. gasterostei and T. clavata increased with host age and the maximum mean burden was found in the oldest hosts. The variance to mean ratio also increased in D. gasterostei, but decreased in the oldest hosts in D. spathaceum and T. clavata. It is concluded that this decrease could be due to parasite-induced host mortality but could equally be due to death of parasites within the host or to changes in infection rate or could be a reflection of the small sample size of the oldest fish. The mean burden of T. podicipina declined gradually with host age, but the variance to mean ratio remained constant and it is concluded that this could be explained by death of the parasites within the host. None of these data or data from other localities provided clear and unambiguous evidence of host mortality induced by heavy infections of any of the four species, although they are consistent with such mortality and do not refute such a possibility. It is concluded that it may be just as difficult to detect and unequivocally demonstrate parasite-induced host mortality in metacercarial digenean–fish host systems as in any other parasite–host systems.

A Multi-Linear Statistical Method for Discriminant Analysis of 2D Frontal Face Images

2012 ◽  
pp. 18-33 ◽  
Author(s):  
Carlos Eduardo Thomaz ◽  
Vagner do Amaral ◽  
Gilson Antonio Giraldi ◽  
Edson Caoru Kitani ◽  
João Ricardo Sato ◽  
...  
Keyword(s):  
Small Sample Size ◽  
Face Image ◽  
Small Sample ◽  
High Dimensional ◽  
Data Set ◽  
Linear Discriminant ◽  
Face Images ◽  
Linear Framework ◽  
Facial Changes ◽  
2D Data

This chapter describes a multi-linear discriminant method of constructing and quantifying statistically significant changes on human identity photographs. The approach is based on a general multivariate two-stage linear framework that addresses the small sample size problem in high-dimensional spaces. Starting with a 2D data set of frontal face images, the authors determine a most characteristic direction of change by organizing the data according to the patterns of interest. These experiments on publicly available face image sets show that the multi-linear approach does produce visually plausible results for gender, facial expression and aging facial changes in a simple and efficient way. The authors believe that such approach could be widely applied for modeling and reconstruction in face recognition and possibly in identifying subjects after a lapse of time.

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.

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