Accelerated sparse Kernel Spectral Clustering for large scale data clustering problems

An improved version of the sparse multiway kernel spectral clustering (KSC) is presented in this brief. The original algorithm is derived from weighted kernel principal component (KPCA) analysis formulated within the primal-dual least-squares support vector machine (LS-SVM) framework. Sparsity is achieved then by the combination of the incomplete Cholesky decomposition (ICD) based low rank approximation of the kernel matrix with the so called reduced set method. The original ICD based sparse KSC algorithm was reported to be computationally far too demanding, especially when applied on large scale data clustering problems that actually it was designed for, which has prevented to gain more than simply theoretical relevance so far. This is altered by the modifications reported in this brief that drastically improve the computational characteristics. Solving the alternative, symmetrized version of the computationally most demanding core eigenvalue problem eliminates the necessity of forming and SVD of large matrices during the model construction. This results in solving clustering problems now within seconds that were reported to require hours without altering the results. Furthermore, sparsity is also improved significantly, leading to more compact model representation, increasing further not only the computational efficiency but also the descriptive power. These transform the original, only theoretically relevant ICD based sparse KSC algorithm applicable for large scale practical clustering problems. Theoretical results and improvements are demonstrated by computational experiments on carefully selected synthetic data as well as on real life problems such as image segmentation.