A Scalable Unsupervised Feature Selection with Orthogonal Graph Representation for Hyperspectral Images

Feature selection (FS) is essential in various fields of science and engineering, from remote sensing to computer vision. Reducing data dimensionality by removing redundant features and selecting the most informative ones improves machine learning algorithms’ performance, especially in supervised classification tasks, while lowering storage needs. Graph-embedding (GE) techniques have recently been found efficient for FS since they preserve the geometric structure of the original feature space while embedding data into a low-dimensional subspace. However, the main drawback is the high computational cost of solving an eigenvalue decomposition problem, especially for large-scale problems. This article addresses this issue by combining the GE framework and representation theory for a novel FS method. Inspired by the high-dimensional model representation (HDMR), the feature transformation is assumed to be a linear combination of a set of univariate orthogonal functions carried out in the GE framework. As a result, an explicit embedding function is created, which can be utilized to embed out-of-samples into low-dimensional space and provide a feature relevance score. The significant contribution of the proposed method is to divide an $n$ -dimensional generalized eigenvalue problem into $n$ small-sized eigenvalue problems. With this property, the computational complexity (CC) of the GE is significantly reduced, resulting in a scalable FS method, which could be easily parallelized too. The performance of the proposed method is compared favorably to its counterparts in high-dimensional hyperspectral image (HSI) processing in terms of classification accuracy, feature stability, and computational time.