# Orientation-Aware Sparse Tensor PCA for Efficient Unsupervised Feature Selection

arXiv: https://arxiv.org/abs/2407.16985 · HTML: https://mlsanity.com/paper/2407.16985/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 58 references that are in the map.
- First posted on arXiv 24 Jul 2024.

## Builds on (most cited first, 8 of 8)

- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data](https://mlsanity.com/paper/1508.07416/) (2015)
- [Sparse PCA via l2,p-Norm Regularization for Unsupervised Feature Selection](https://mlsanity.com/paper/2012.14595/) (2020)
- [A Convex Sparse PCA for Feature Analysis](https://mlsanity.com/paper/1411.6233/) (2014)
- [High-Dimensional Low-Rank Tensor Autoregressive Time Series Modeling](https://mlsanity.com/paper/2101.04276/) (2021)
- [Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection](https://mlsanity.com/paper/2309.06202/) (2023)
- [Blind Direction-of-Arrival Estimation in Acoustic Vector-Sensor Arrays via Tensor Decomposition and Kullback-Leibler Divergence Covariance Fitting](https://mlsanity.com/paper/2005.08318/) (2020)
- [Genetic algorithm for feature selection of EEG heterogeneous data](https://mlsanity.com/paper/2103.07117/) (2021)

## Built on by (most cited first, 1 of 1)

- [Unpaired Image Deraining Using Reward-Guided Self-Reinforcement Strategy](https://mlsanity.com/paper/2605.00719/) (2026)

## Abstract (arXiv)

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. 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 preserve the data tensor structure, they do not consider the influence of data orientation and thus have difficulty in handling orientation-specific data such as time series. To solve the above problem, we utilize the orientation-dependent tensor-tensor product from Tensor Singular Value Decomposition based on *M-product (T-SVDM) and extend the one-dimensional Sparse Principal Component Analysis (SPCA) to a tensor form. The proposed sparse tensor PCA model can constrain sparsity at the specified mode and yield sparse tensor principal components, enhancing flexibility and accuracy in learning feature relations. To ensure fast convergence and a flexible description of feature correlation, we develop a convex version specially designed for general UFS tasks and propose an efficient slice-by-slice algorithm that performs dual optimization in the transform domain. Experimental results on real-world datasets demonstrate the effectiveness and remarkable computational efficiency of the proposed method for tensor data of diverse structures over the state-of-the-art. When transform axes align with feature distribution patterns, our method is promising for various applications. The codes related to our proposed methods and the experiments are available at https://github.com/zjj20212035/STPCA.git.