# Transformed Subspace Clustering

arXiv: https://arxiv.org/abs/1912.04734 · HTML: https://mlsanity.com/paper/1912.04734/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2019.

## Built on by (most cited first, 3 of 3)

- [Subspace Clustering of Subspaces: Unifying Canonical Correlation Analysis and Subspace Clustering](https://mlsanity.com/paper/2509.18653/) (2025)
- [Transformed K-means Clustering](https://mlsanity.com/paper/2111.13921/) (2021)
- [Subspace Clustering in Wavelet Packets Domain](https://mlsanity.com/paper/2406.03819/) (2024)

## Abstract (arXiv)

Subspace clustering assumes that the data is sepa-rable into separate subspaces. Such a simple as-sumption, does not always hold. We assume that, even if the raw data is not separable into subspac-es, one can learn a representation (transform coef-ficients) such that the learnt representation is sep-arable into subspaces. To achieve the intended goal, we embed subspace clustering techniques (locally linear manifold clustering, sparse sub-space clustering and low rank representation) into transform learning. The entire formulation is jointly learnt; giving rise to a new class of meth-ods called transformed subspace clustering (TSC). In order to account for non-linearity, ker-nelized extensions of TSC are also proposed. To test the performance of the proposed techniques, benchmarking is performed on image clustering and document clustering datasets. Comparison with state-of-the-art clustering techniques shows that our formulation improves upon them.