Geodesic Fuzzy Rough Sets for Discriminant Feature Extraction

Feature extraction is a fundamental and challenging task in machine learning, which aims at extracting a subset of significant and discriminant features from raw data for various downstream tasks. The extraction process involves mapping the original data into a space with lower dimensions while preserving the desirable information. However, the data often has hidden manifold structures, which contain neighbor sample information within the same class. Most existing methods that extract data features without considering the potentially significant manifold structures would result in poorly discriminative features. To address these challenges, we propose a novel geodesic fuzzy rough set model (GFRS) to capture those complex manifold structures embed in the data. Given GFRS, we further design a discriminant feature extraction algorithm based on graph embedding to enhance the discriminative performance of the extracted features. Extensive experiments on fourteen real-world datasets and visualization results on modified national institute of standards and technology (MNIST) digits demonstrate the effectiveness of the proposed algorithm and its superiority over baselines methods.