Goto

Collaborating Authors

Global Versus Local Methods in Nonlinear Dimensionality Reduction

Neural Information Processing Systems

Recently proposed algorithms for nonlinear dimensionality reduction fall broadly into two categories which have different advantages and disadvantages: global (Isomap [1]), and local (Locally Linear Embedding [2], Laplacian Eigenmaps [3]). We present two variants of Isomap which combine the advantages of the global approach with what have previously been exclusive advantages of local methods: computational sparsity and the ability to invert conformal maps.


Global Versus Local Methods in Nonlinear Dimensionality Reduction

Neural Information Processing Systems

Recently proposed algorithms for nonlinear dimensionality reduction fall broadly into two categories which have different advantages and disadvantages: global (Isomap [1]), and local (Locally Linear Embedding [2], Laplacian Eigenmaps [3]). We present two variants of Isomap which combine the advantages of the global approach with what have previously been exclusive advantages of local methods: computational sparsity and the ability to invert conformal maps.


Global Versus Local Methods in Nonlinear Dimensionality Reduction

Neural Information Processing Systems

Recently proposed algorithms for nonlinear dimensionality reduction fall broadly into two categories which have different advantages and disadvantages: global(Isomap [1]), and local (Locally Linear Embedding [2], Laplacian Eigenmaps [3]). We present two variants of Isomap which combine the advantages of the global approach with what have previously beenexclusive advantages of local methods: computational sparsity and the ability to invert conformal maps.


S-Isomap++: Multi Manifold Learning from Streaming Data

arXiv.org Machine Learning

Manifold learning based methods have been widely used for non-linear dimensionality reduction (NLDR). However, in many practical settings, the need to process streaming data is a challenge for such methods, owing to the high computational complexity involved. Moreover, most methods operate under the assumption that the input data is sampled from a single manifold, embedded in a high dimensional space. We propose a method for streaming NLDR when the observed data is either sampled from multiple manifolds or irregularly sampled from a single manifold. We show that existing NLDR methods, such as Isomap, fail in such situations, primarily because they rely on smoothness and continuity of the underlying manifold, which is violated in the scenarios explored in this paper. However, the proposed algorithm is able to learn effectively in presence of multiple, and potentially intersecting, manifolds, while allowing for the input data to arrive as a massive stream.