Some Remarks on Diffusion Distances
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-09-23
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
As a diffusion distance, we propose to use a metric (closely related to cosine similarity) which is defined as the L2 distance between two L2-normalized vectors.
We provide a mathematical explanation as to why the normalization makes diffusion distances more meaningful.
Our proposal is in contrast to that made some years ago by R.
Coifman which finds the L2 distance between certain L1 unit vectors.
In the second part of the paper, we give two proofs that an extension of mean first passage time to mean first passage cost satisfies the triangle inequality; we do not assume that the underlying Markov matrix is diagonalizable.
We conclude by exhibiting an interesting connection between the (normalized) mean first passage time and the discretized solution of a certain Dirichlet-Poisson problem and verify our result numerically for the simple case of the unit circle.
American Psychological Association (APA)
Goldberg, Maxim J.& Kim, Seonja. 2010. Some Remarks on Diffusion Distances. Journal of Applied Mathematics،Vol. 2010, no. 2010, pp.1-17.
https://search.emarefa.net/detail/BIM-473681
Modern Language Association (MLA)
Goldberg, Maxim J.& Kim, Seonja. Some Remarks on Diffusion Distances. Journal of Applied Mathematics No. 2010 (2010), pp.1-17.
https://search.emarefa.net/detail/BIM-473681
American Medical Association (AMA)
Goldberg, Maxim J.& Kim, Seonja. Some Remarks on Diffusion Distances. Journal of Applied Mathematics. 2010. Vol. 2010, no. 2010, pp.1-17.
https://search.emarefa.net/detail/BIM-473681
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473681