Theory of Spectral Method for Union of Subspaces-Based Random Geometry Graph
This work provides a theoretical foundation for subspace clustering, which is incremental as it analyzes an existing method rather than introducing a new one.
The paper tackles the problem of clustering data points near a union of subspaces using spectral methods with random geometry graphs, establishing a theoretical analysis that demonstrates the method's efficiency under broad conditions.
Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on this theory, we demonstrate the efficiency of Subspace Clustering in fairly broad conditions. The insights and analysis techniques developed in this paper might also have implications for other random graph problems. Numerical experiments demonstrate the effectiveness of our theoretical study.