# An iterative coordinate descent algorithm to compute sparse low-rank approximations

arXiv: https://arxiv.org/abs/2107.14608 · HTML: https://mlsanity.com/paper/2107.14608/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 43 references that are in the map.
- First posted on arXiv 30 Jul 2021.

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

- [On the Computational Intractability of Exact and Approximate Dictionary Learning](https://mlsanity.com/paper/1405.6664/) (2014)
- [Sparse Generalized Eigenvalue Problem via Smooth Optimization](https://mlsanity.com/paper/1408.6686/) (2014)
- [Orthogonal Sparse PCA and Covariance Estimation via Procrustes Reformulation](https://mlsanity.com/paper/1602.03992/) (2016)
- [Learning Fast Sparsifying Transforms](https://mlsanity.com/paper/1611.08230/) (2016)
- [Multi-Rank Sparse and Functional PCA: Manifold Optimization and Iterative Deflation Techniques](https://mlsanity.com/paper/1907.12012/) (2019)
- [A Dictionary-Based Generalization of Robust PCA Part II: Applications to Hyperspectral Demixing](https://mlsanity.com/paper/1902.10238/) (2019)
- [Fast approximation of orthogonal matrices and application to PCA](https://mlsanity.com/paper/1907.08697/) (2019)
- [Constructing fast approximate eigenspaces with application to the fast graph Fourier transforms](https://mlsanity.com/paper/2002.09723/) (2020)

## Abstract (arXiv)

In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz algorithm to build an approximate singular value decomposition for a few principal components. We show the performance of the proposed algorithm to recover sparse principal components on various datasets from the literature and perform dimensionality reduction for classification applications.