Maximum Margin Embedding
We propose a new dimensionality reduction method called maximum margin embedding (MME), which targets to projecting data samples into the most discriminative subspace, where clusters are most well-separated. Specifically, MME projects input patterns onto the normal of the maximum margin separating hyperplanes. As a result, MME only depends on the geometry of the optimal decision boundary and not on the distribution of those data points lying further away from this boundary. Technically, MME is formulated as an integer programming problem and we propose a cutting plane algorithm to solve it. Moreover, we prove theoretically that the computational time of MME scales linearly with the dataset size. Experimental results on both toy and real world datasets demonstrate the effectiveness of MME.