Grassmann Manifold

The Grassmann manifold, a mathematical space representing linear subspaces, is increasingly used in machine learning to model and analyze data sets characterized by inherent variability, such as image sets or time series. Current research focuses on developing efficient algorithms for dimensionality reduction, classification, and optimization on this manifold, including adaptations of Principal Component Analysis (PCA) and gradient descent methods, often within federated learning frameworks. These advancements enable improved performance in various applications, such as anomaly detection in IoT networks, human action recognition, and robust image set classification, while also offering enhanced interpretability and computational efficiency compared to traditional methods.