Riemannian Geodesic Discriminant Analysis–Minimum Riemannian Mean Distance: A Robust and Effective Method Leveraging a Symmetric Positive Definite Manifold and Discriminant Algorithm for Image Set Classification

Zigang Liu, Fayez F. M. El-Sousy, Nauman Ali Larik, Huan Quan and Tianyao Ji ()
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Zigang Liu: School of Electric Power Engineering, South China University of Technology, Guangzhou 510641, China
Fayez F. M. El-Sousy: Department of Electrical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Al Kharj 16273, Saudi Arabia
Nauman Ali Larik: School of Electric Power Engineering, South China University of Technology, Guangzhou 510641, China
Huan Quan: School of Electric Power Engineering, South China University of Technology, Guangzhou 510641, China
Tianyao Ji: School of Electric Power Engineering, South China University of Technology, Guangzhou 510641, China

Mathematics, 2024, vol. 12, issue 14, 1-25

Abstract: This study introduces a novel method for classifying sets of images, called Riemannian geodesic discriminant analysis–minimum Riemannian mean distance (RGDA-MRMD). This method first converts image data into symmetric positive definite (SPD) matrices, which capture important features related to the variability within the data. These SPD matrices are then mapped onto simpler, flat spaces (tangent spaces) using a mathematical tool called the logarithm operator, which helps to reduce their complexity and dimensionality. Subsequently, regularized local Fisher discriminant analysis (RLFDA) is employed to refine these simplified data points on the tangent plane, focusing on local data structures to optimize the distances between the points and prevent overfitting. The optimized points are then transformed back into a complex, curved space (SPD manifold) using the exponential operator to enhance robustness. Finally, classification is performed using the minimum Riemannian mean distance (MRMD) algorithm, which assigns each data point to the class with the closest mean in the Riemannian space. Through experiments on the ETH-80 (Eidgenössische Technische Hochschule Zürich-80 object category), AFEW (acted facial expressions in the wild), and FPHA (first-person hand action) datasets, the proposed method demonstrates superior performance, with accuracy scores of 97.50%, 37.27%, and 88.47%, respectively. It outperforms all the comparison methods, effectively preserving the unique topological structure of the SPD matrices and significantly boosting image set classification accuracy.

Keywords: image set classification; Riemannian manifold; tangent space; symmetric positive definite matrices; regularized local Fisher discriminant analysis; minimum Riemannian mean distance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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