Shamap: Shape-based Manifold Learning

Fortunately, in many cases such data are essentially low dimensional; i.e., they stay on a low-dimensional manifold embedded in the high dimensional space [1]. This key observation suggests the possibility of dimensionality reduction to facilitate visualization and analysis of the data. Manifold learning is one of the mainstream nonlinear dimensionality reduction techniques [2]. Driven by major academic and practical motives, many algorithms [3-9] were developed to flatten an embedded manifold and reveal an intrinsic structure. One of the representative methods, Isomap combines the Floyd-Warshall algorithm with multidimensional scaling (MDS [10]) to compress high-dimensional data.