Kernel spectral clustering is a model-based spectral clustering method formulated in a primal-dual framework. It has a powerful out-of-sample extension property and a model selection procedure based on the balanced line fit criterion. This paper is an improvement of a previous work which sparsified the kernel spectral clustering method using the line structure of the data projections in the eigenspace. However, the previous method works only in the case of well formed and well separated clusters as in other cases the line structure is lost. In this paper, we propose two highly sparse extensions of kernel spectral clustering that can overcome these limitations. For the selection of the reduced set we use the concept of angles between the data projections in the eigenspace. We show the effectiveness and the amount of sparsity obtained by the proposed methods for several synthetic and real world datasets.