Sparse Tensor PCA via Tensor Decomposition for Unsupervised Feature Selection

• URL: http://arxiv.org/abs/2407.16985v1
• Date: Wed, 24 Jul 2024 04:04:56 GMT
• Title: Sparse Tensor PCA via Tensor Decomposition for Unsupervised Feature Selection
• Authors: Junjing Zheng, Xinyu Zhang, Weidong Jiang,
• Abstract summary: We develop two Sparse Principal Component Analysis (STPCA) models that utilize the projection directions in the factor matrices to perform unsupervised feature selection. For both models, we prove the optimal solution of each subproblem falls onto the Hermitian Positive Semidefinite Cone (HPSD) According to the experimental results, the two proposed methods are suitable for handling different data tensor scenarios and outperform the state-of-the-art UFS methods.
• Score: 8.391109286933856
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Recently, introducing Tensor Decomposition (TD) methods into unsupervised feature selection (UFS) has been a rising research point. A tensor structure is beneficial for mining the relations between different modes and helps relieve the computation burden. However, while existing methods exploit TD to minimize the reconstruction error of a data tensor, they don't fully utilize the interpretable and discriminative information in the factor matrices. Moreover, most methods require domain knowledge to perform feature selection. To solve the above problems, we develop two Sparse Tensor Principal Component Analysis (STPCA) models that utilize the projection directions in the factor matrices to perform UFS. The first model extends Tucker Decomposition to a multiview sparse regression form and is transformed into several alternatively solved convex subproblems. The second model formulates a sparse version of the family of Tensor Singular Value Decomposition (T-SVDs) and is transformed into individual convex subproblems. For both models, we prove the optimal solution of each subproblem falls onto the Hermitian Positive Semidefinite Cone (HPSD). Accordingly, we design two fast algorithms based on HPSD projection and prove their convergence. According to the experimental results on two original synthetic datasets (Orbit and Array Signal) and five real-world datasets, the two proposed methods are suitable for handling different data tensor scenarios and outperform the state-of-the-art UFS methods.

Related papers

• Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models [50.90868087591973]
  We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation.
  arXiv  Detail & Related papers  (2024-08-20T19:06:02Z)
• Variational Laplace Autoencoders [53.08170674326728]
  Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. We present a novel approach that addresses the limited posterior expressiveness of fully-factorized Gaussian assumption. We also present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models.
  arXiv  Detail & Related papers  (2022-11-30T18:59:27Z)
• PARAFAC2-based Coupled Matrix and Tensor Factorizations [1.7188280334580195]
  We propose an algorithmic framework for fitting PARAFAC2-based CMTF models with the possibility of imposing various constraints on all modes and linear couplings. Through numerical experiments, we demonstrate that the proposed algorithmic approach accurately recovers the underlying patterns using various constraints and linear couplings.
  arXiv  Detail & Related papers  (2022-10-24T09:20:17Z)
• Partial Least Square Regression via Three-factor SVD-type Manifold Optimization for EEG Decoding [4.0204191666595595]
  We propose a new method to solve the partial least square regression, named PLSR via optimization on bi-Grassmann manifold (PLSRbiGr) qlPLSRbiGr is validated with a variety of experiments for decoding EEG signals at motor imagery (MI) and steady-state visual evoked potential (SSVEP) task.
  arXiv  Detail & Related papers  (2022-08-09T11:57:02Z)
• Semi-orthogonal Embedding for Efficient Unsupervised Anomaly Segmentation [6.135577623169028]
  We generalize an ad-hoc method, random feature selection, into semi-orthogonal embedding for robust approximation. With the scrutiny of ablation studies, the proposed method achieves a new state-of-the-art with significant margins for the MVTec AD, KolektorSDD, KolektorSDD2, and mSTC datasets.
  arXiv  Detail & Related papers  (2021-05-31T07:02:20Z)
• Sparse PCA via $l_{2,p}$-Norm Regularization for Unsupervised Feature Selection [138.97647716793333]
  We propose a simple and efficient unsupervised feature selection method, by combining reconstruction error with $l_2,p$-norm regularization. We present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically.
  arXiv  Detail & Related papers  (2020-12-29T04:08:38Z)
• A Bayesian Approach with Type-2 Student-tMembership Function for T-S Model Identification [47.25472624305589]
  fuzzyc-regression clustering based on type-2 fuzzyset has been shown the remarkable results on non-sparse data. Aninnovative architecture for fuzzyc-regression model is presented and a novel student-tdistribution based membership functionis designed for sparse data modelling.
  arXiv  Detail & Related papers  (2020-09-02T05:10:13Z)
• Model Fusion with Kullback--Leibler Divergence [58.20269014662046]
  We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors.
  arXiv  Detail & Related papers  (2020-07-13T03:27:45Z)
• Simple and Effective Prevention of Mode Collapse in Deep One-Class Classification [93.2334223970488]
  We propose two regularizers to prevent hypersphere collapse in deep SVDD. The first regularizer is based on injecting random noise via the standard cross-entropy loss. The second regularizer penalizes the minibatch variance when it becomes too small.
  arXiv  Detail & Related papers  (2020-01-24T03:44:47Z)
• A Unified Framework for Coupled Tensor Completion [42.19293115131073]
  Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The TR has powerful expression ability and achieves success in some multi-dimensional data processing applications. The proposed method is validated on numerical experiments on synthetic data, and experimental results on real-world data demonstrate its superiority over the state-of-the-art methods in terms of recovery accuracy.
  arXiv  Detail & Related papers  (2020-01-09T02:15:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.