Tangling-Untangling Cycle for Efficient Learning

arXiv:2404.05484v1 Announce Type: new
Abstract: The conventional wisdom of manifold learning is based on nonlinear dimensionality reduction techniques such as IsoMAP and locally linear embedding (LLE). We challenge this paradigm by exploiting the blessing of dimensionality. Our intuition is simple: it is easier to untangle a low-dimensional manifold in a higher-dimensional space due to its vastness, as guaranteed by Whitney embedding theorem. A new insight brought by this work is to introduce class labels as the context variables in the …

abstract arxiv challenge cs.lg dimensionality embedding intuition linear low manifold paradigm simple space stat.ml type