# Evolutionary Self-Expressive Models for Subspace Clustering

arXiv: https://arxiv.org/abs/1810.11957 · HTML: https://mlsanity.com/paper/1810.11957/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2018.

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

- [Neural Ordinary Differential Equation Model for Evolutionary Subspace Clustering and Its Applications](https://mlsanity.com/paper/2107.10484/) (2021)

## Abstract (arXiv)

The problem of organizing data that evolves over time into clusters is encountered in a number of practical settings. We introduce evolutionary subspace clustering, a method whose objective is to cluster a collection of evolving data points that lie on a union of low-dimensional evolving subspaces. To learn the parsimonious representation of the data points at each time step, we propose a non-convex optimization framework that exploits the self-expressiveness property of the evolving data while taking into account representation from the preceding time step. To find an approximate solution to the aforementioned non-convex optimization problem, we develop a scheme based on alternating minimization that both learns the parsimonious representation as well as adaptively tunes and infers a smoothing parameter reflective of the rate of data evolution. The latter addresses a fundamental challenge in evolutionary clustering -- determining if and to what extent one should consider previous clustering solutions when analyzing an evolving data collection. Our experiments on both synthetic and real-world datasets demonstrate that the proposed framework outperforms state-of-the-art static subspace clustering algorithms and existing evolutionary clustering schemes in terms of both accuracy and running time, in a range of scenarios.