# Online Sparse Subspace Clustering

## TL;DR

This paper introduces an online algorithm for sparse subspace clustering that efficiently handles streaming data by updating similarities and clustering results without revisiting the entire dataset.

## Contribution

It proposes a novel online approach for sparse subspace clustering with convergence guarantees and dynamic regret analysis for non-strongly convex costs.

## Key findings

- Online algorithm converges to a neighborhood of batch solution
- Dynamic regret bounds are established for non-strongly convex costs
- Method enables real-time clustering of streaming data

## Abstract

This paper focuses on the sparse subspace clustering problem, and develops an online algorithmic solution to cluster data points on-the-fly, without revisiting the whole dataset. The strategy involves an online solution of a sparse representation (SR) problem to build a (sparse) dictionary of similarities where points in the same subspace are considered "similar," followed by a spectral clustering based on the obtained similarity matrix. When the SR cost is strongly convex, the online solution converges to within a neighborhood of the optimal time-varying batch solution. A dynamic regret analysis is performed when the SR cost is not strongly convex.