Unsupervised Feature Selection via Graph Regularized Nonnegative CP Decomposition

Chen, Bilian; Guan, Jiewen; Li, Zhening

doi:10.1109/tpami.2022.3160205

Cited by 10 publications

(10 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now we have proved that Ω can decrease the value of the object function in Problem (14) in each iteration. Since all the terms in the objective function obviously have a lower bound 0, the convergence is guaranteed.…”

Section: Convergence Analysismentioning

confidence: 89%

“…Now, we present an optimization algorithm to solve Problem (14). Generally, we combine derivative with PSD projection iterations, the unconstrained solution may not be a PSD matrix.…”

Section: Optimization Algorithmmentioning

confidence: 99%

“…The optimization algorithm to solve Problem (14) Input: Data matrix X ∈ R d×n , regularization parameters λ and η. Output: h features of the data set 1: Initialize S = XHX T , randomly initialize Ω ∈ S d + and calculate W using the elements in Ω.…”

Section: Algorithmmentioning

confidence: 99%

“…With Algorithm 1, the updated Ω can decrease the value of the objective function in Problem (14) until converge.…”

Section: Convergence Analysismentioning

confidence: 99%

“…However, it requires the training data to be fully labeled, which raises serious limitations for some practical applications. Therefore, Unsupervised Feature Selection (UFS) [12]- [14] without the need for any human annotations has gained increasing attention in recent years.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection

Zheng,

Zhang,

Jiang

et al. 2023

Preprint

View full text Add to dashboard Cite

<p>In the field of unsupervised feature selection, sparse principal component analysis (SPCA) methods have attracted more and more attention recently. Compared to spectral-based methods, SPCA methods don’t rely on the construction of a similarity matrix and show better feature selection ability on real-world data. Existing convex SPCA methods reformulate SPCA as a convex model by regarding the reconstruction matrix as an optimization variable. However, they are lack of constraints equivalent to the orthogonality restriction in SPCA, leading to larger solution space. In this paper, a standard convex SPCA-based model for unsupervised feature selection is proposed and proven to have its optimal solution falling onto the Positive Semidefinite (PSD) Cone. Further, a two-step fast optimization algorithm via PSD projection is presented to solve the proposed model (SPCA-PSD), whose computational complexity is linear to the number of samples. Two other existing convex SPCA-based models’ optimal solution space is also proven to be the PSD cone. Therefore, the PSD versions of these two models are proposed to accelerate their convergence. Experiments on synthetic and real-world datasets demonstrate the effectiveness and efficiency of the proposed methods. </p>

show abstract

Section: Convergence Analysismentioning

confidence: 89%

“…Now, we present an optimization algorithm to solve Problem (14). Generally, we combine derivative with PSD projection iterations, the unconstrained solution may not be a PSD matrix.…”

Section: Optimization Algorithmmentioning

confidence: 99%

Section: Algorithmmentioning

confidence: 99%

“…With Algorithm 1, the updated Ω can decrease the value of the objective function in Problem (14) until converge.…”

Section: Convergence Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations