Fuzzy Granule Manifold Alignment Preserving Local Topology

Manifold Alignment Preserving Global Geometry

This paper proposes a novel algorithm for manifold alignment preserving global geometry. This approach constructs mapping functions that project data instances from different input domains to a new lower-dimensional space, simultaneously matching the instances in correspondence and preserving global distances between instances within the original domains. In contrast to previous approaches, whi...

Triangulated manifold meshing method preserving molecular surface topology.

Generation of manifold mesh is an urgent issue in mathematical simulations of biomolecule using boundary element methods (BEM) or finite element method (FEM). Defects, such as not closed mesh, intersection of elements and missing of small structures, exist in surface meshes generated by most of the current meshing method. Usually the molecular surface meshes produced by existing methods need to...

Manifold Alignment

Manifold Warping: Manifold Alignment over Time

Knowledge transfer is computationally challenging, due in part to the curse of dimensionality, compounded by source and target domains expressed using different features (e.g., documents written in different languages). Recent work on manifold learning has shown that data collected in real-world settings often have high-dimensional representations, but lie on low-dimensional manifolds. Furtherm...

Generalized Unsupervised Manifold Alignment

In this paper, we propose a Generalized Unsupervised Manifold Alignment (GUMA) method to build the connections between different but correlated datasets without any known correspondences. Based on the assumption that datasets of the same theme usually have similar manifold structures, GUMA is formulated into an explicit integer optimization problem considering the structure matching and preserv...