Inductive Sparse Subspace Clustering

TL;DR

This paper introduces inductive Sparse Subspace Clustering (iSSC), a scalable method that extends SSC to efficiently cluster out-of-sample data by leveraging low-dimensional manifold assumptions.

Contribution

The paper proposes iSSC, an inductive extension of SSC, enabling efficient clustering of new data without recomputing the entire similarity graph.

Findings

iSSC effectively clusters out-of-sample data.

iSSC maintains high clustering quality comparable to SSC.

iSSC is suitable for online and scalable clustering applications.

Abstract

Sparse Subspace Clustering (SSC) has achieved state-of-the-art clustering quality by performing spectral clustering over a $\ell^{1}$-norm based similarity graph. However, SSC is a transductive method which does not handle with the data not used to construct the graph (out-of-sample data). For each new datum, SSC requires solving $n$ optimization problems in O(n) variables for performing the algorithm over the whole data set, where $n$ is the number of data points. Therefore, it is inefficient to apply SSC in fast online clustering and scalable graphing. In this letter, we propose an inductive spectral clustering algorithm, called inductive Sparse Subspace Clustering (iSSC), which makes SSC feasible to cluster out-of-sample data. iSSC adopts the assumption that high-dimensional data actually lie on the low-dimensional manifold such that out-of-sample data could be grouped in the embedding space learned from in-sample data. Experimental results show that iSSC is promising in clustering out-of-sample data.