A Simple and Effective Generalization of Exponential Matrix Discriminant Analysis and Its Application to Face Recognition

Ran, Ruisheng; Fang, Bin; Wu, Xuegang

doi:10.1587/transinf.2017edl8198

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…Furthermore, Ran et al [22] presented an efficient Generalization of Exponential Discriminant Analysis (GEDA), which replaced the Euler matrix exponential function with a general exponential function. Due to the property difference between these two functions, samples from distinct classes are separated at a greater distance by using GEDA.…”

Section: 𝑍 = 𝑌𝑊 𝑇mentioning

confidence: 99%

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Dimensionality reduction techniques for high dimensional data: State of the art

Jiang

2023

ACE

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In the past decades, tons of data have been generated every single day as people increasingly rely on electronic products and networks in their lives. The developments in techniques and storage capabilities provide a fundamental condition for analyzing those huge-volumed data. Each captured feature represents a dimension of the data. So far, high dimensional data analysis has become a challenging task in various study fields. Redundant and irrelevant features can be removed by using different dimensionality reduction techniques. Effective information extraction can be achieved by using the proper method. This paper reviews the most widely used dimensionality reduction techniques and their application fields. It can be found that though DRTs have been successfully applied to many areas (i.e., image, audio/video data, biomedical), DRTs still need to be improved and developed to achieve better classification and prediction accuracy. Inter-method combinations will remain the focus of research in the future. Computation time and cost may not be a limitation anymore as the computation power of the computer is still developing. So, the development of the algorithm is becoming particularly important. This study provides a brief introduction to widely used DRTs and their variants, it will be helpful for understanding HDD analysis, and more DRTs will be researched in future work.

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Section: 𝑍 = 𝑌𝑊 𝑇mentioning

confidence: 99%

“…Multi-variate MFPCA [12] Outliers ER-PCA, JSPCA [8], [15] Response Time 2D-PCA [10] Singularity 2DLDA, G2DLDA [20], [21] Small sample size GEDA [22] Sparsity SPCA, JSPCA [14], [15] Unknown subspace GPCA [9]…”

Section: Hdd Issues Solution Drts Referencesmentioning

confidence: 99%

Dimensionality reduction techniques for high dimensional data: State of the art

Jiang

2023

ACE

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“…Different extension of LDA has been proposed to solve the SSS problem. This includes the regularized LDA (RLDA) [145], Direct LDA (DLDA) [146], PCA + LDA [147], Null LDA [148], Generalized EDA (GEDA) [149], kernel DLDA (KDLDA) [150] and PCA + LDA [147]. A semi supervised variant of LDA was proposed by [151] with its main objective of combining both labeled and unlabeled data for training LDA and to allow for the situation where the labeled data are few.…”

Section: Linear Discriminant Analysis (Lda)mentioning

confidence: 99%

Review of Dimension Reduction Methods

Nanga¹,

Bawah²,

Acquaye³

et al. 2021

JDAIP

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Purpose: This study sought to review the characteristics, strengths, weaknesses variants, applications areas and data types applied on the various Dimension Reduction techniques. Methodology: The most commonly used databases employed to search for the papers were ScienceDirect, Scopus, Google Scholar, IEEE Xplore and Mendeley. An integrative review was used for the study where 341 papers were reviewed. Results: The linear techniques considered were Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Singular Value Decomposition (SVD), Latent Semantic Analysis (LSA), Locality Preserving Projections (LPP), Independent Component Analysis (ICA) and Project Pursuit (PP). The non-linear techniques which were developed to work with applications that have complex non-linear structures considered were Kernel Principal Component Analysis (KPCA), Multi-dimensional Scaling (MDS), Isomap, Locally Linear Embedding (LLE), Self-Organizing Map (SOM), Latent Vector Quantization (LVQ), t-Stochastic neighbor embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP). DR techniques can further be categorized into supervised, unsupervised and more recently semi-supervised learning methods. The supervised versions are the LDA and LVQ. All the other techniques are unsupervised. Supervised variants of PCA, LPP, KPCA and MDS have been developed. Supervised and semi-supervised variants of PP and t-SNE have also been developed and a semi supervised version of the LDA has been developed. Conclusion: The various application areas, strengths, weaknesses and variants of the DR tech

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“…Matrix based exponential method is also used to solve such small sample sized problem (SSS problems). ELDE [24] is based on local discriminant embedding (LDE) [25], which was put forward to overcome the limits that global linear discriminant analysis method meets. Matrix based exponential method also helps to improve the flaw of LPP's sensitivity to neighborhood sized k [26] and fix singularity problems.…”

Section: Introductionmentioning

confidence: 99%

2D-MELPP: A two dimensional matrix exponential based extension of locality preserving projections for dimensional reduction

2022

KSII TIIS

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Two dimensional locality preserving projections (2D-LPP) is an improved algorithm of 2D image to solve the small sample size (SSS) problems which locality preserving projections (LPP) meets. It's able to find the low dimension manifold mapping that not only preserves local information but also detects manifold embedded in original data spaces. However, 2D-LPP is simple and elegant. So, inspired by the comparison experiments between two dimensional linear discriminant analysis (2D-LDA) and linear discriminant analysis (LDA) which indicated that matrix based methods don't always perform better even when training samples are limited, we surmise 2D-LPP may meet the same limitation as 2D-LDA and propose a novel matrix exponential method to enhance the performance of 2D-LPP. 2D-MELPP is equivalent to employing distance diffusion mapping to transform original images into a new space, and margins between labels are broadened, which is beneficial for solving classification problems. Nonetheless, the computational time complexity of 2D-MELPP is extremely high. In this paper, we replace some of matrix multiplications with multiple multiplications to save the memory cost and provide an efficient way for solving 2D-MELPP. We test it on public databases: random 3D data set, ORL, AR face database and Polyu Palmprint database and compare it with other 2D methods like 2D-LDA, 2D-LPP and 1D methods like LPP and exponential locality preserving projections (ELPP), finding it outperforms than others in recognition accuracy. We also compare different dimensions of projection vector and record the cost time on the ORL, AR face database and Polyu Palmprint database. The experiment results above proves that our advanced algorithm has a better performance on 3 independent public databases.

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A Simple and Effective Generalization of Exponential Matrix Discriminant Analysis and Its Application to Face Recognition

Cited by 7 publications

References 11 publications

Dimensionality reduction techniques for high dimensional data: State of the art

Dimensionality reduction techniques for high dimensional data: State of the art

Review of Dimension Reduction Methods

2D-MELPP: A two dimensional matrix exponential based extension of locality preserving projections for dimensional reduction

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