Laplacian Eigenmaps

Laplacian Eigenmaps are dimensionality reduction techniques that embed high-dimensional data onto a lower-dimensional manifold by leveraging the graph Laplacian, effectively capturing the data's underlying structure. Current research focuses on extending the method's capabilities through integrations with other techniques, such as optimal transport, contrastive learning, and various graph embedding algorithms (e.g., shortest path methods), to improve performance in tasks like data alignment, anomaly detection, and visualization of large graphs. These advancements enhance the applicability of Laplacian Eigenmaps across diverse fields, including computer vision, bioinformatics, and robotics, by enabling more robust and efficient analysis of complex datasets. The resulting improved data representations facilitate better performance in downstream machine learning tasks.