Regularized generalized eigen-decomposition with applications to sparse supervised feature extraction and sparse discriminant analysis

Han, Xixuan; Clemmensen, Line Katrine Harder

doi:10.1016/j.patcog.2015.07.008

Cited by 22 publications

(7 citation statements)

References 34 publications

(58 reference statements)

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“…The generalized Hermitian eigenvalue problem (GHEP) [1] is of great interest in signal processing, machine learning and data analysis applications. The GHEP algorithms provide powerful tools to treat problems in blind source separation [2,3], feature extraction [4,5], noise filtering [6], fault detection [7], antenna array processing [8], classification [9], and speech enhancement [10]. Traditional methods for solving the GHEP include power and inverse iteration based methods, Lanczos method and Jacobi-Davidson method [1,11].…”

Section: Introductionmentioning

confidence: 99%

“…The generalized eigenvalues and eigenvectors are extracted from a matrix pencil (A, B). In online applications [2,4,[6][7][8][9][10], however, this pair is unknown, and the rank-1 update strategy [14-16, 18, 19] uses the observed streaming stochastic signals to estimate it. Also, in many cases, the signal subspace spanned by the dominant generalized eigenvectors, lies in a low-dimensional space [10].…”

Section: Introductionmentioning

confidence: 99%

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Online Dominant Generalized Eigenvectors Extraction Via A Randomized Method

Cai

Kaloorazi

Chen

et al. 2021

2020 28th European Signal Processing Conference (EUSIPCO)

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The generalized Hermitian eigendecomposition problem is ubiquitous in signal and machine learning applications. Considering the need of processing streaming data in practice and restrictions of existing methods, this paper is concerned with fast and efficient generalized eigenvectors tracking. We first present a computationally efficient algorithm based on randomization termed alternate-projections randomized eigenvalue decomposition (APR-EVD) to solve a standard eigenvalue problem. By exploiting rank-1 strategy, two online algorithms based on APR-EVD are developed for the dominant generalized eigenvectors extraction. Numerical examples show the practical applicability and efficacy of the proposed online algorithms.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Online Dominant Generalized Eigenvectors Extraction Via A Randomized Method

Cai

Kaloorazi

Chen

et al. 2021

2020 28th European Signal Processing Conference (EUSIPCO)

View full text Add to dashboard Cite

show abstract

“…Therefore, tensor-based methods have been proposed because they can preserve the overall spatial structure, and they have been applied in several areas, including biological [21] and medical research [22], facial recognition [23], [24], natural image processing [25], hyperspectral image analysis [26]- [28], [42] and PolSAR image processing [29], [30]. Lower rank tensor approximation (LTRA) [26] is an extension of PCA to higher-order data sets that assumes strong global correlations in the spatial and feature domains.…”

Section: Introductionmentioning

confidence: 99%

Cluster-Based Tensorial Semisupervised Discriminant Analysis for Feature Extraction of SAR Images

Wen

Yuan

et al. 2019

IEEE Access

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Several features have been developed to characterize the land cover in synthetic aperture radar (SAR) data with speckle noise. Feature extraction has become an essential task for SAR image processing. However, how to preserve the original intrinsic structural information and enhance the discriminant ability to reduce the impact of noise is still a challenge in this area. In this paper, using a clustering method to maintain the nonlocal information in images and tensors with the ability to preserve spatial neighborhood structure information, a new cluster-based tensorial semisupervised discriminant analysis (CTSDA) method is proposed for feature extraction of SAR images. In the CTSDA, the block clustering algorithm is employed to generate several high-order clustering tensors of multifeature SAR images, which preserves the intrinsic nonlocal spatial information and neighborhood structure. In the multiple manifold structures of the cluster tensors, the improved discriminant analysis enhances the feature discrimination by considering the local structure and labeled and unlabeled information through the Laplace matrix, and the fusion of tensor algebraic analysis and improved discriminant analysis produces multiple new projection directions of the cluster tensors. Finally, feature extraction is achieved by rearranging the projected cluster tensors. The experimental results on the simulated SAR data and four real SAR images demonstrate the superiority of the proposed method over several state-of-the-art approaches.

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“…() consider a regularized GEP with

ℓ_{0}

‐norm penalty and used a majorization–minimization (MM) algorithm to solve the non‐convex problem. Han and Clemmensen () transformed GEP to an eigen‐decomposition and use alternating direction method of multipliers (ADMM) to obtain sparse eigenvectors, which is a solution to an optimization problem with an

ℓ_{1}

penalty.…”

Section: Introductionmentioning

confidence: 99%

Sparse Generalized Eigenvalue Problem with Application to Canonical Correlation Analysis for Integrative Analysis of Methylation and Gene Expression Data

Safo

Ahn²,

Jeon

et al. 2018

Biometrics

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We present a method for individual and integrative analysis of high dimension, low sample size data that capitalizes on the recurring theme in multivariate analysis of projecting higher dimensional data onto a few meaningful directions that are solutions to a generalized eigenvalue problem. We propose a general framework, called SELP (Sparse Estimation with Linear Programming), with which one can obtain a sparse estimate for a solution vector of a generalized eigenvalue problem. We demonstrate the utility of SELP on canonical correlation analysis for an integrative analysis of methylation and gene expression profiles from a breast cancer study, and we identify some genes known to be associated with breast carcinogenesis, which indicates that the proposed method is capable of generating biologically meaningful insights. Simulation studies suggest that the proposed method performs competitive in comparison with some existing methods in identifying true signals in various underlying covariance structures.

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Regularized generalized eigen-decomposition with applications to sparse supervised feature extraction and sparse discriminant analysis

Cited by 22 publications

References 34 publications

Online Dominant Generalized Eigenvectors Extraction Via A Randomized Method

Online Dominant Generalized Eigenvectors Extraction Via A Randomized Method

Cluster-Based Tensorial Semisupervised Discriminant Analysis for Feature Extraction of SAR Images

Sparse Generalized Eigenvalue Problem with Application to Canonical Correlation Analysis for Integrative Analysis of Methylation and Gene Expression Data

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