# Subspace Clustering via Optimal Direction Search

arXiv: https://arxiv.org/abs/1706.03860 · HTML: https://mlsanity.com/paper/1706.03860/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2017.

## Built on by (most cited first, 5 of 5)

- [Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees](https://mlsanity.com/paper/2301.11911/) (2023)
- [Provable Data Clustering via Innovation Search](https://mlsanity.com/paper/2108.06888/) (2021)
- [Fitting Multiple Machine Learning Models with Performance Based Clustering](https://mlsanity.com/paper/2411.06572/) (2024)
- [Closed-Form, Provable, and Robust PCA via Leverage Statistics and Innovation Search](https://mlsanity.com/paper/2106.12190/) (2021)
- [Provable Clustering of a Union of Linear Manifolds Using Optimal Directions](https://mlsanity.com/paper/2201.02745/) (2022)

## Abstract (arXiv)

This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in the span of the data that has minimum projection on the other data points and non-vanishing projection on d. The obtained directions are subsequently leveraged to identify a neighborhood set for each data point. An alternating direction method of multipliers framework is provided to efficiently solve for the optimal directions. The proposed method is shown to notably outperform the existing subspace clustering methods, particularly for unwieldy scenarios involving high levels of noise and close subspaces, and yields the state-of-the-art results for the problem of face clustering using subspace segmentation.