Improved Subspace K-Means Performance via a Randomized Matrix Decomposition

Subspace clustering algorithms provide the capability to project a dataset onto bases that facilitate clustering. Proposed in 2017, the subspace k-means algorithm simultaneously performs clustering and dimensionality reduction with the goal of finding the optimal subspace for the cluster structure; this is accomplished by incorporating a trade-off between cluster and noise subspaces in the objective function. In this study, we improve subspace k-means by estimating a critical transformation matrix via a randomized eigenvalue decomposition. Our modification results in an order of magnitude runtime improvement on high dimensional data, while retaining the simplicity, interpretable subspace projections, and convergence guarantees of the original algorithm.