# Dimensionality Reduction with Subspace Structure Preservation

arXiv: https://arxiv.org/abs/1412.2404 · HTML: https://mlsanity.com/paper/1412.2404/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2014.

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

- [Subdomain-aware representation compression for pretrained image embeddings](https://mlsanity.com/paper/2609.20213/) (2026)

## Abstract (arXiv)

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that 2K projection vectors are sufficient for the independence preservation of any K class data sampled from a union of independent subspaces. It is this non-trivial observation that we use for designing our dimensionality reduction technique. In this paper, we propose a novel dimensionality reduction algorithm that theoretically preserves this structure for a given dataset. We support our theoretical analysis with empirical results on both synthetic and real world data achieving textitstate-of-the-art results compared to popular dimensionality reduction techniques.