Paper Info
Title
Self-Organizing Mappings On The Grassmannian With Applications To Data Analysis In High Dimensions
Abstract
We propose a method for extending Kohonen's self-organizing mapping to the geometric framework of the Grassmannian. The resulting algorithm serves as a prototype of the extension of the SOM to the setting of abstract manifolds. The ingredients required for this are a means to measure distance between two points, and a method to move one point in the direction of another. In practice, the data are not required to have a representation in Euclidean space. We discuss in detail how a point on a Grassmannian is moved in the direction of another along a geodesic path. We demonstrate the implementation of the algorithm on several illustrative data sets, hyperspectral images and gene expression data sets.
Year
DOI
Venue
2020
10.1007/s00521-019-04444-x
NEURAL COMPUTING & APPLICATIONS
Keywords
DocType
Volume
Grassmannian, Self-organizing mappings, Geodesic, Data visualization, Gene expression
Journal
32
Issue
ISSN
Citations 
24
0941-0643
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Xiaofeng Ma121.76
Michael Kirby213714.40
Chris Peterson3296.26
Louis L. Scharf42525414.45