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Semi-supervised Spectral Connectivity Projection Pursuit

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We propose a projection pursuit method based on semi-supervised spectral connectivity. The projection index is given by the second eigenvalue of the graph Laplacian of the projected data. An incomplete label set is used to modify pairwise similarities between data in such a way that penalises projections which do not admit a separation of the classes (within the training data). We show that the global optimum of the proposed problem converges to the Transductive Support Vector Machine solution, as the scaling parameter is reduced to zero. We evaluate the performance of the proposed method on benchmark data sets.