# Scalable variable selection for two-view learning tasks with projection operators

arXiv: https://arxiv.org/abs/2307.01558 · HTML: https://mlsanity.com/paper/2307.01558/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 55 references that are in the map.
- First posted on arXiv 4 Jul 2023.

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

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [Feature Selection: A Data Perspective](https://mlsanity.com/paper/1601.07996/) (2016)
- [Randomized Nonlinear Component Analysis](https://mlsanity.com/paper/1402.0119/) (2014)
- [A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learning](https://mlsanity.com/paper/1401.8066/) (2014)
- [MISSION: Ultra Large-Scale Feature Selection using Count-Sketches](https://mlsanity.com/paper/1806.04310/) (2018)
- [Vector-Valued Least-Squares Regression under Output Regularity Assumptions](https://mlsanity.com/paper/2211.08958/) (2022)
- [On the Self-Penalization Phenomenon in Feature Selection](https://mlsanity.com/paper/2110.05852/) (2021)
- [Large-Scale Approximate Kernel Canonical Correlation Analysis](https://mlsanity.com/paper/1511.04773/) (2015)
- [Saturating Splines and Feature Selection](https://mlsanity.com/paper/1609.06764/) (2016)

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

- [From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identification](https://mlsanity.com/paper/2512.14404/) (2025)

## Abstract (arXiv)

In this paper we propose a novel variable selection method for two-view settings, or for vector-valued supervised learning problems. Our framework is able to handle extremely large scale selection tasks, where number of data samples could be even millions. In a nutshell, our method performs variable selection by iteratively selecting variables that are highly correlated with the output variables, but which are not correlated with the previously chosen variables. To measure the correlation, our method uses the concept of projection operators and their algebra. With the projection operators the relationship, correlation, between sets of input and output variables can also be expressed by kernel functions, thus nonlinear correlation models can be exploited as well. We experimentally validate our approach, showing on both synthetic and real data its scalability and the relevance of the selected features. Keywords: Supervised variable selection, vector-valued learning, projection-valued measure, reproducing kernel Hilbert space