Spectral clustering has taken an important place in the context of pattern recognition, being a good alternative to solve problems with non-linearly separable groups. Because of its unsupervised nature, clustering methods are often parametric, requiring then some initial parameters. Thus, clustering performance is greatly dependent on the selection of those initial parameters. Furthermore, tuning such parameters is not an easy task when the initial data representation is not adequate. Here, we propose a new projection for input data to improve the cluster identification within a kernel spectral clustering framework. The proposed projection is done from a feature extraction formulation, in which a generalized distance involving the kernel matrix is used. Data projection shows to be useful for improving the performance of kernel spectral clustering.