A Tangent Distance Preserving Dimensionality Reduction Algorithm
This addresses the problem of visualizing complex manifold structures for researchers in machine learning, though it appears incremental compared to existing methods like LLE and ISOMAP.
The paper tackles nonlinear dimensionality reduction by preserving the manifold's nonlinear structure in high-dimensional space, introducing Tangent Distance Preserving Mapping (TDPM) which uses tangent distance with MDS to map the manifold while showing its folding.
This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear structure of the manifold, and shows how the manifold is folded in the high dimensional space. We call this method Tangent Distance Preserving Mapping (TDPM). TDPM uses tangent distance instead of geodesic distance, and then applies MDS to the tangent distance matrix to map the manifold into a low dimensional space in which we can get its nonlinear structure.