Linear methods of dimension reduction for classification (2024)
For classification problems, traditional dimension reduction methods often take into account only the feature information, while ignoring the class label. This poses an opportunity for improvement. In this thesis, we explore new methods that aim to find linear orthogonal projections that maximize optimal transportation distances (Wasserstein and Sinkhorn) feature subsamples corresponding to the categories. These methods employ ubgradient ascent and stochastic subgradient ascent algorithms. We detail the calculation of the subgradient of these distances with respect to the projection and implement these methods in Python. To validate our approach, we test these methods on various datasets. Our results demonstrate that the proposed methods effectively enhance classification performance by incorporating class information into the dimension reduction process.