Low rank approximation with sparse integration of multiple manifolds for data representation

Tao, Liang; Ip, Horace H. S.; Wang, Yinglin; Shu, Xin

doi:10.1007/s10489-014-0600-7

Cited by 18 publications

(17 citation statements)

References 28 publications

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“…In fact such types of experiments have become a standard practice in the PCA community [5], [14], [4], [6], [15]. We perform our clustering experiments on 3 benchmark databases: CMU PIE, ORL and COIL20 using two opensource toolboxes: the UNLocBoX [16] for the optimization part and the GSPBox [17] for the graph creation.…”

Section: Resultsmentioning

confidence: 99%

PCA using graph total variation

Shahid

Perraudin

Kalofolias

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Mining useful clusters from high dimensional data has received significant attention of the signal processing and machine learning community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with problems such as high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) or susceptibility to gross corruptions in the data. In this paper we propose a convex, robust, scalable and efficient Principal Component Analysis (PCA) based method to approximate the low-rank representation of high dimensional datasets via a two-way graph regularization scheme. Compared to the exact recovery methods, our method is approximate, in that it enforces a piecewise constant assumption on the samples using a graph total variation and a piecewise smoothness assumption on the features using a graph Tikhonov regularization. Futhermore, it retrieves the low-rank representation in a time that is linear in the number of data samples. Clustering experiments on 3 benchmark datasets with different types of corruptions show that our proposed model outperforms 7 state-ofthe-art dimensionality reduction models.

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Section: Resultsmentioning

confidence: 99%

PCA using graph total variation

Shahid

Perraudin

Kalofolias

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…Furthermore, additional structures from low-dimensional data can be utilized as prior knowledge to enhance the representability of the models [62,63,64]. Discrete graphs are also utilized to incorporate data manifold information into the dimensionality reduction framework [65,66,67,68,69,70,71,72,73].…”

Section: Geometric Methods For Generic Objectsmentioning

confidence: 99%

A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis

Gong

Zhang

Wang

et al. 2019

Sensors

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Geometric features, such as the topological and manifold properties, are utilized to extract geometric properties. Geometric methods that exploit the applications of geometrics, e.g., geometric features, are widely used in computer graphics and computer vision problems. This review presents a literature review on geometric concepts, geometric methods, and their applications in human-related analysis, e.g., human shape analysis, human pose analysis, and human action analysis. This review proposes to categorize geometric methods based on the scope of the geometric properties that are extracted: object-oriented geometric methods, feature-oriented geometric methods, and routine-based geometric methods. Considering the broad applications of deep learning methods, this review also studies geometric deep learning, which has recently become a popular topic of research. Validation datasets are collected, and method performances are collected and compared. Finally, research trends and possible research topics are discussed.

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“…Note that only RPCA and our proposed model leverage convexity and enjoy a unique global optimum with guaranteed convergence. IV. COMPARISON WITH RELATED WORKS The main differences between our model (1) and the various state-of-the-art factorized PCA models [7], [19], [12], [8], [15] are, as summarized in Table I, the following. Non-factorized model: Instead of explicitly learning the principal directions U and principal components Q, it learns their product, i.e. the low-rank matrix L. Hence, (1) is a non-factorized PCA model.…”

Section: Related Work: Factorized Pca Modelsmentioning

confidence: 96%

Robust Principal Component Analysis on Graphs

Shahid

Kalofolias

Bresson

et al. 2015

2015 IEEE International Conference on Computer Vision (ICCV)

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Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called 'Robust PCA on Graphs' which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks.

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Low rank approximation with sparse integration of multiple manifolds for data representation

Cited by 18 publications

References 28 publications

PCA using graph total variation

PCA using graph total variation

A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis

Robust Principal Component Analysis on Graphs

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