Dimensionality Reduction by Integrating Sparse Representation and Fisher Criterion and its Applications

Gao, Quanxue; Wang, Qianqian; Huang, Yunfang; Gao, Xinbo; Hong, Xin; Zhang, Hailin

doi:10.1109/tip.2015.2479559

Cited by 34 publications

(3 citation statements)

References 47 publications

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“…The OSNS algorithm not only extracted the null space and its orthogonal complement space of the between-class scatter matrix, but also obtained the null space and its orthogonal complement of the withinclass scatter matrix. A dimensionality reduction method by integrating sparse representation and fisher criterion was proposed in [8] and this method had very good computational efficiency. In order to fully utilize different features, a feature fusion strategy (FFS) was proposed in [25].…”

Section: Where Non-singular Matrix Smentioning

confidence: 99%

Range space super spherical cap discriminant analysis

Pei

Fan

2017

Neurocomputing

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To overcome the separability problem caused by sample fusion in the process of sample vectors normalization, this paper presents a unit super spherical cap discriminant analysis in the range space of the total scatter matrix. It is proved that the unit super spherical cap model can maintain the topological invariability of the structural characteristics of sample vectors. Furthermore, a sufficient condition is derived for improving the separability of sample data under the proposed model. The proposed algorithm projects sample data to the range space of the total scatter matrix, and then adds one dimension to each sample of the range space and nonlinearly maps it on the surface of the unit super spherical cap. We put forth a new classifier called the "spherical inner product nearest neighbor classifier" for the transformed data. It is designed for the deviation problem of the discriminant vector and the separability problem caused by sample vectors normalization when different sub-classes are located in different low-dimensional subspaces or manifolds. Experimental results on different databases show that our method outperforms other methods in terms of recognition accuracy and numerical stability.

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Section: Where Non-singular Matrix Smentioning

confidence: 99%

Range space super spherical cap discriminant analysis

Pei

Fan

2017

Neurocomputing

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“…Data with high dimensions exist in many real-world applications, such as content-based image retrieval, visual recognition, feature clustering, and multi view data handling, 1–4 which raises great challenges for human society. Therefore, it is important to perform dimensionality reduction on the data by effectively exploiting the underlying structure information and the discriminative information.…”

Section: Introductionmentioning

confidence: 99%

Jointly Linear Embedding via L_2,1-Norm for Dimensionality Reduction

Cui

Wen

et al. 2021

AATCC Journal of Research

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In this study, we present a novel dimensionality reduction method called Jointly Linear Embedding (JLE). Unlike previous methods such as Neighborhood Preserving Embedding (NPE), in which local neighborhood information is preserved during the dimensionality reduction procedure, JLE aims to preserve the sparse reconstructive relationship of the original data by taking the merits of jointly sparse learning based on L2,1-norm. In the framework of JLE, the sparse weight matrix can reflect the intrinsic geometric structures of the original data and inherit the ability of discriminant analysis. By solving the L2,1-norm regularized objective function, the optimal projections, which are invariant to rotations and robust to outliers, can be obtained by JLE. Extensive experiments on visual recognition and fabric defect classification datasets demonstrate the superiority of the proposed L2,1-norm regularized learning method compared with the state-of-the-art methods.

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“…Image classification and clustering problems are topics fundamental to various areas of machine learning [1][2][3] including image recognition and image clustering. Principal component analysis (PCA) has been widely used to perform dimensionality reduction and extract useful information for these problems [4][5][6][7][8][9][10][11]. One of the common objectives of dimensionality reduction is to retain the most important information that is beneficial to data processing tasks and meanwhile filter out corrupted and noisy information from the dataset.…”

Section: Introductionmentioning

confidence: 99%

A Trimmed Clustering-Based l1-Principal Component Analysis Model for Image Classification and Clustering Problems with Outliers

Lam

Choy

2019

Applied Sciences

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Different versions of principal component analysis (PCA) have been widely used to extract important information for image recognition and image clustering problems. However, owing to the presence of outliers, this remains challenging. This paper proposes a new PCA methodology based on a novel discovery that the widely used l1-PCA is equivalent to a two-groups k-means clustering model. The projection vector of the l1-PCA is the vector difference between the two cluster centers estimated by the clustering model. In theory, this vector difference provides inter-cluster information, which is beneficial for distinguishing data objects from different classes. However, the performance of l1-PCA is not comparable with the state-of-the-art methods. This is because the l1-PCA can be sensitive to outliers, as the equivalent clustering model is not robust to outliers. To overcome this limitation, we introduce a trimming function to the clustering model and propose a trimmed-clustering based l1-PCA (TC-PCA). With this trimming set formulation, the TC-PCA is not sensitive to outliers. Besides, we mathematically prove the convergence of the proposed algorithm. Experimental results on image classification and clustering indicate that our proposed method outperforms the current state-of-the-art methods.

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Dimensionality Reduction by Integrating Sparse Representation and Fisher Criterion and its Applications

Cited by 34 publications

References 47 publications

Range space super spherical cap discriminant analysis

Range space super spherical cap discriminant analysis

Jointly Linear Embedding via L_2,1-Norm for Dimensionality Reduction

A Trimmed Clustering-Based l1-Principal Component Analysis Model for Image Classification and Clustering Problems with Outliers

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Dimensionality Reduction by Integrating Sparse Representation and Fisher Criterion and its Applications

Cited by 34 publications

References 47 publications

Range space super spherical cap discriminant analysis

Range space super spherical cap discriminant analysis

Jointly Linear Embedding via L2,1-Norm for Dimensionality Reduction

A Trimmed Clustering-Based l1-Principal Component Analysis Model for Image Classification and Clustering Problems with Outliers

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Jointly Linear Embedding via L_2,1-Norm for Dimensionality Reduction