Low-rank matrix factorization with multiple Hypergraph regularizer

Jin, Taisong; Yu, Jun; You, Jane; Zeng, Kun; Li, Cuihua; Yu, Zhengtao

doi:10.1016/j.patcog.2014.09.002

Cited by 56 publications

(41 citation statements)

References 35 publications

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“…This automatically enforces the matrix U to acquire a low-rank structure. This is in contrast to the graph Tikhonov (G-TIK) regularization term ∇G 1 U 2 F = tr(U L1U ) used in [4], [5], [6] which allows the gradients to vary smoothly w.r.t the graph G1.…”

Section: Proposed Model (Pca-gtv)mentioning

confidence: 99%

“…benefit from the graph smoothness assumption of the principal components Q have been proposed recently [4], [5], [6]. These methods, however, are non-convex and susceptible to gross corruptions.…”

Section: Introductionmentioning

confidence: 99%

“…[7]. In contrast to [4], [5], [6] and [7] which use Tikhonov graph regularization tr(x T Lx) = ∇Gx 2 2 ) (G-TIK) w.r.t. the data samples, we propose to use the graph total variation (G-TV) regularization ( ∇Gx 1) w.r.t the data samples which enforces our piecewise constant assumption.…”

Section: Introductionmentioning

confidence: 99%

“…the data samples, we propose to use the graph total variation (G-TV) regularization ( ∇Gx 1) w.r.t the data samples which enforces our piecewise constant assumption. Additionally and unlike [4], [5], [6], we also propose to use a G-TIK w.r.t. the features of the data matrix.…”

Section: Introductionmentioning

confidence: 99%

“…This two-way graph regularization scheme helps in 1) the extraction of a fast low-rank approximation U of the data matrix X without using the expensive nuclear norm operator (as in [8]) and 2) better clustering in the low-dimensional space due to piecewise constant assumption enforced by the G-TV. Furthermore, in contrast to the L2 data fidelity term of [4], [5], [6], we propose to use the L1 fidelity term which makes our model robust to outliers or gross corruptions in the dataset. Finally, our model can be solved efficiently, in time linear in the number of data samples, with a forward-backward based primal dual algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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: Proposed Model (Pca-gtv)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%