Canonical Variates in Wasserstein Metric Space

This paper introduces a novel dimension reduction technique for classification tasks using the Wasserstein metric, focusing on maximizing Fisher's ratio to enhance classification accuracy for distributions in vector spaces. The proposed method employs an iterative algorithm that alternates between optimal transport and ratio maximization, demonstrating improved performance over traditional algorithms that utilize vector representations. This approach is particularly significant for practitioners as it provides a robust framework for handling complex distributional data, such as those represented by Gaussian mixture models.