Reviews: Solving Interpretable Kernel Dimensionality Reduction

Summary: [19] has proposed recently an efficient iterative spectral (eigendecomposition) method (ISM) for the non-convex interpretable kernel dimensionality reduction (IKDR) objective in the context of alternative clustering. It established theoretical guarantees of ISM for the Gaussian kernel. The paper extends the theoretical guarantees of ISM to a family of kernels [Definition 1]. Each kernel in the ISM family has an associated surrogate matrix \Phi and the optimal projection is formed by the most dominant eigenvectors of \Phi [Theorem 1 and 2]. They showed that any conic combination of the ISM kernels is still an ISM kernel [Proposition 1] and therefore ISM can be extend to conic combination of kernels.