# A Subspace-based Approach for Dimensionality Reduction and Important Variable Selection

arXiv: https://arxiv.org/abs/2106.01584 · HTML: https://mlsanity.com/paper/2106.01584/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 57 references that are in the map.
- First posted on arXiv 3 Jun 2021.

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

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Correlation and variable importance in random forests](https://mlsanity.com/paper/1310.5726/) (2013)
- [Using stacking to average Bayesian predictive distributions](https://mlsanity.com/paper/1704.02030/) (2017)
- [Unbiased Measurement of Feature Importance in Tree-Based Methods](https://mlsanity.com/paper/1903.05179/) (2019)
- [A State-of-the-Art Survey on Multidimensional Scaling Based Localization Techniques](https://mlsanity.com/paper/1906.03585/) (2019)
- [High-Dimensional Estimation, Basis Assets, and the Adaptive Multi-Factor Model](https://mlsanity.com/paper/1804.08472/) (2018)
- [Robustness of Random Forest-based gene selection methods](https://mlsanity.com/paper/1305.4525/) (2013)
- [Time-Invariance Coefficients Tests with the Adaptive Multi-Factor Model](https://mlsanity.com/paper/2011.04171/) (2020)

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

- [The Adaptive Multi-Factor Model and the Financial Market](https://mlsanity.com/paper/2107.14410/) (2021)

## Abstract (arXiv)

An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few important features, but they are limited due to the lack of interpretability and connectivity to actual decision making associated with each physical variable. Variable selection techniques, as an alternative, can maintain the interpretability, but they often involve a greedy search that is susceptible to failure in capturing important interactions or a metaheuristic search that requires extensive computations. This research proposes a new method that produces subspaces, reduced-dimensional physical spaces, based on a randomized search and leverages an ensemble of critical subspace-based models, achieving dimensionality reduction and variable selection. When applied to high-dimensional data collected from the failure prediction of a composite/metal hybrid structure exhibiting complex progressive damage failure under loading, the proposed method outperforms the existing and potential alternatives in prediction and important variable selection.