MANIFOLD MATCHING COMPLEXES

Chessboard Complexes and Matching Complexes

Manifold Matching for High-Dimensional Pattern Recognition

In pattern recognition, a kind of classical classifier called k-nearest neighbor rule (kNN) has been applied to many real-life problems because of its good performance and simple algorithm. In kNN, a test sample is classified by a majority vote of its k-closest training samples. This approach has the following advantages: (1) It was proved that the error rate of kNN approaches the Bayes error w...

Shape Matching by Variational Computation of Geodesics on a Manifold

Klassen et al. [9] recently developed a theoretical formulation to model shape dissimilarities by means of geodesics on appropriate spaces. They used the local geometry of an infinite dimensional manifold to measure the distance dist(A,B) between two given shapes A and B. A key limitation of their approach is that the computation of distances developed in the above work is inherently unstable, ...

The mirror matching system: A shared manifold for intersubjectivity

Empathy is the phenomenal experience of mirroring ourselves into others. It can be explained in terms of simulations of actions, sensations, and emotions which constitute a shared manifold for intersubjectivity. Simulation, in turn, can be sustained at the subpersonal level by a series of neural mirror matching systems. The article by Preston & de Waal (P&deW) has the merit of raising the issue...

Efficiency investigation of manifold matching for text document classification

Manifold matching works to identify embeddings of multiple disparate data spaces into the same low-dimensional space, where joint inference can be pursued. It is an enabling methodology for fusion and inference from multiple and massive disparate data sources. In this paper three methods of manifold matching are considered: PoM, which stands for Multidimensional Scaling (MDS) composed with Proc...