Abstract:
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We develop support histogram machines based on the Wasserstein-Kantorovich distance, which can classify histogram-valued data. The main difference of our proposed method from standard SVM is that we use a kernel, designed for histogram-valued data, induced by Wasserstein-Kantorovich distance in the dual form of objective function. Additionally, to mitigate risk of mislabeling due to choice of the ill-suited number of bins, we propose an approach to introduce case-specific parameters into the objective function in order to identify possible mislabels, making our model robust. Simulation results and real data analysis approve adequacy of our method.
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