Dimensionality Reduction with Subspace Structure Preservation
This addresses a theoretical gap in subspace-based data modeling for applications like clustering or classification, though it appears incremental as it builds on existing subspace assumptions.
The paper tackles the problem of dimensionality reduction for data from a union of independent subspaces by proving that 2K projection vectors suffice to preserve independence, and proposes a novel algorithm that achieves state-of-the-art results on synthetic and real-world data.
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that $2K$ projection vectors are sufficient for the independence preservation of any $K$ class data sampled from a union of independent subspaces. It is this non-trivial observation that we use for designing our dimensionality reduction technique. In this paper, we propose a novel dimensionality reduction algorithm that theoretically preserves this structure for a given dataset. We support our theoretical analysis with empirical results on both synthetic and real world data achieving \textit{state-of-the-art} results compared to popular dimensionality reduction techniques.