Multi-task manifold learning using hierarchical modeling for insufficient samples

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In this paper, we propose a method for multi-task manifold learning. For a set of tasks of dimensionality reduction, the aim of the method is to model each given dataset as a manifold, and map it to a low-dimensional space. For this purpose, we use a hierarchical manifold modeling approach. Thus, while each data distribution is represented by a manifold model, the obtained models are further modeled by a higher-order manifold in a function space. The higher-order model mediates the information transfer between tasks, and as a result, the performance of each task is improved. The results of simulations show that the proposed method can estimate manifolds approximately, even in cases in which a tiny number of samples are provided for each task.

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