# Two-way Spectrum Pursuit for CUR Decomposition and Its Application in Joint Column/Row Subset Selection

arXiv: https://arxiv.org/abs/2106.06983 · HTML: https://mlsanity.com/paper/2106.06983/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 13 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Optimal CUR Matrix Decompositions](https://mlsanity.com/paper/1405.7910/) (2014)
- [Improving CUR Matrix Decomposition and the Nystr"om Approximation via Adaptive Sampling](https://mlsanity.com/paper/1303.4207/) (2013)
- [Dissimilarity-based Sparse Subset Selection](https://mlsanity.com/paper/1407.6810/) (2014)
- [Spectrum Cartography via Coupled Block-Term Tensor Decomposition](https://mlsanity.com/paper/1911.12468/) (2019)
- [Column subset selection is NP-complete](https://mlsanity.com/paper/1701.02764/) (2017)
- [Iterative Projection and Matching: Finding Structure-preserving Representatives and Its Application to Computer Vision](https://mlsanity.com/paper/1811.12326/) (2018)
- [Transduction with Matrix Completion Using Smoothed Rank Function](https://mlsanity.com/paper/1805.07561/) (2018)
- [Polynomial Time Algorithms for Dual Volume Sampling](https://mlsanity.com/paper/1703.02674/) (2017)
- [Column Selection via Adaptive Sampling](https://mlsanity.com/paper/1510.04149/) (2015)

## Built on by (most cited first, 2 of 2)

- [CNLL: A Semi-supervised Approach For Continual Noisy Label Learning](https://mlsanity.com/paper/2204.09881/) (2022)
- [RF Signal Transformation and Classification using Deep Neural Networks](https://mlsanity.com/paper/2204.03564/) (2022)

## Abstract (arXiv)

The problem of simultaneous column and row subset selection is addressed in this paper. The column space and row space of a matrix are spanned by its left and right singular vectors, respectively. However, the singular vectors are not within actual columns/rows of the matrix. In this paper, an iterative approach is proposed to capture the most structural information of columns/rows via selecting a subset of actual columns/rows. This algorithm is referred to as two-way spectrum pursuit (TWSP) which provides us with an accurate solution for the CUR matrix decomposition. TWSP is applicable in a wide range of applications since it enjoys a linear complexity w.r.t. number of original columns/rows. We demonstrated the application of TWSP for joint channel and sensor selection in cognitive radio networks, informative users and contents detection, and efficient supervised data reduction.