Complex-Valued Embedding on Grassmann Manifolds for Pattern Set Representation

Complex-valued data arise in various domains, including signal and image processing. Analyzing and classifying such data pose unique challenges due to their inherent structural and modal characteristics. In this paper, we propose the Complex-valued Subspace Embedding (CvSE), a novel approach for fast, compact, and physically meaningful representation of complex-valued pattern sets. Our method advances the analysis and classification of complex data by employing complex subspaces. We construct complex subspaces that capture the highest variance features by applying complex Singular Value Decomposition (SVD) on pattern sets, achieving compactness and noise robustness. We validate CvSE through experiments on MNIST, Fashion-MNIST, CIFAR-10, and Washington RGBD, showcasing its potential. Our findings demonstrate that CvSE excels in handling complex data, offering improved performance in the analysis and classification of pattern sets.