Kernelized transformed subspace clustering with geometric weights for non-linear manifolds

Abstract

The naive assumption of subspace clustering is that the data should be separable into separate subspaces. Another consideration of the conventional subspace clustering methods is the linear manifolds. What if, the data doesn’t hold this assumption? We propose a novel subspace clustering framework that works even if the raw data is not separable into separate subspaces. It also generalizes it for non-linear manifolds. To achieve the intended goal, we embed subspace clustering techniques into kernelized transform learning with weighting matrix regularization which accounts for nonlinearity. For the weighting matrix, we use similarity between tangent spaces on data manifolds for local structure and euclidean distances for capturing global geometric structure. The complete optimization problem is solved using alternate minimization. The weighted norm regularization is solved by designing a fixed-point continuation algorithm to obtain an approximate closed solution. To test the performance of the proposed framework, we provide the experimental results on handwritten digits clustering, face image clustering, and motion segmentation. The superiority of the results proves the effectiveness of the weighting matrix in kernelized transformed subspace clustering formulation.