Mixing matrix estimation in instantaneous blind source separation (BSS) can be performed by exploiting the sparsity and disjoint orthogonality of source signals. As a result, approaches for estimating the unknown mixing process typically employ clustering algorithms on the mixtures in a parametric domain, where the signals can be sparsely represented. In this paper, we propose two algorithms to perform discriminative clustering of the mixture signals for estimating the mixing matrix. For the case of overdetermined BSS, we develop an algorithm to perform linear discriminant analysis based on similarity measures and combine it with K-hyperline clustering. Furthermore, we propose to perform discriminative clustering in a high-dimensional feature space obtained by an implicit mapping, using the kernel trick, for the case of underdetermined source separation. Using simulations on synthetic data, we demonstrate the improvements in mixing matrix estimation performance obtained using the proposed algorithms in comparison to other clustering methods. Finally we perform mixing matrix estimation from speech mixtures, by clustering single source points in the time-frequency domain, and show that the proposed algorithms achieve higher signal to interference ratio when compared to other baseline algorithms.