Two Semi-supervised Dimensionality Reduction Methods For Tensor And Multiple View Data

As an important research direction which integrates the knowledge from both statistics and computer science, dimensionality reduction for high-dimensional data has become a hot issue. Semi-supervised dimensionality reduction methods, which can employ information underlying the unlabeled data thus can generally outperform the supervised methods on the same data, have recently drawn more and more attention from researchers. However, the data in real-world applications bear not only exceedingly high dimensionality, but also complicated natural intrinsic structures which always challenge the traditional semi-supervised dimensionality reduction methods. Among these intrinsic structures, tensor structure and multiple view structure are typical ones. The dissertation will propose two semi-supervised dimensionality reduction methods for the two types of data. The main contributions include:1. Based on Local Tensor Discriminant Analysis (LTDA) proposed by Nie, et. al., this thesis will propose Tensor Dimensionality Reduction via Harmonic Function (TDRHF), which first employs harmonic function to propagate the labels of the labeled data to the unlabeled data and then conducts semi-supervised dimensionality reduction, thus extends Nie's method to the realm of semi-supervised dimensionality reduction.2. Based on Multiple View Semi-supervised Dimensionality Reduction (MVSSDR) proposed by Hou, et. al., this thesis will propose Multiple View Dimensionality Reduction via Harmonic Function (MVDRHF), which substitutes the soft label gained in the harmonic-function-based label propagation technique for the link information in MVSSDR, thus avoids the transformation from label information to link information to preserve the prior information as much as possible and finally guarantee better dimensionality reduction power.