TY - JOUR
T1 - Riemannian Geodesic Discriminant Analysis–Minimum Riemannian Mean Distance
T2 - A Robust and Effective Method Leveraging a Symmetric Positive Definite Manifold and Discriminant Algorithm for Image Set Classification
AU - Liu, Zigang
AU - El-Sousy, Fayez F.M.
AU - Larik, Nauman Ali
AU - Quan, Huan
AU - Ji, Tianyao
N1 - Publisher Copyright:
© 2024 by the authors.
PY - 2024/7
Y1 - 2024/7
N2 - 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.
AB - 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.
KW - image set classification
KW - minimum Riemannian mean distance
KW - regularized local Fisher discriminant analysis
KW - Riemannian manifold
KW - symmetric positive definite matrices
KW - tangent space
UR - http://www.scopus.com/inward/record.url?scp=85199927615&partnerID=8YFLogxK
U2 - 10.3390/math12142164
DO - 10.3390/math12142164
M3 - Article
AN - SCOPUS:85199927615
SN - 2227-7390
VL - 12
JO - Mathematics
JF - Mathematics
IS - 14
M1 - 2164
ER -