Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/degenerating-families-of-dendrograms-4ucsNvbgDJ
References (29)
-
D. Banks, F. McMorris, P. Arabie, W. Gaul (2004)
Classification, Clustering, and Data Mining Applications -
P. Griffiths (1989)
Introduction to Algebraic Curves -
V. Berkovich (1990)
Spectral Theory and Analytic Geometry over Non-Archimedean Fields -
(2004)
Thinking ultrametrically -
L. Gerritzen, F. Herrlich, M. Put (1988)
Stable n-pointed trees of projective lines, 91
-
Fakultät für Architektur, Englerstr. 7, D-76128 Karlsruhe, Germany E-mail: bradley@ifib.uni-karlsruhe -
G. Cornelissen, Fumiharu Kato (2005)
The p-adic icosahedronNotices of the American Mathematical Society, 52
-
John Bruce (1990)
INTRODUCTION TO ALGEBRAIC CURVES (Translations of Mathematical Monographs 76)Bulletin of The London Mathematical Society, 22
-
Rumely, R: Potential theory on the Berkovich projective line. Book in preparation -
V. Berkovich (1999)
Smooth p-adic analytic spaces are locally contractibleInventiones mathematicae, 137
-
(1974)
Automatische Klassifikation. Studia Mathematica/Mathematische Lehrbücher, Band XXIV -
D. MUMFORD (1999)
The Red Book of Varieties and Schemes, (2nd ed., expanded) Lecture Notes in Mathematics, 1358 -
J. Harris, I. Morrison (1998)
Moduli of curves -
Fumiharu Kato (2005)
Non-archimedean orbifolds covered by mumford curvesJournal of Algebraic Geometry, 14
-
Frank Herrlich (1980)
Endlich erzeugbarep-adische diskontinuierliche GruppenArchiv der Mathematik, 35
-
L. Gerritzen (1978)
Unbeschränkte Steinsche Gebiete von P1 und nichtarchimedische automorphe Formen.Journal für die reine und angewandte Mathematik (Crelles Journal), 1978
-
John Deely (1966)
The Red BookOryx, 8
-
R. Rumely, M. Baker (2004)
Analysis and dynamics on the Berkovich projective linearXiv: Number Theory
-
P. Bradley (2007)
Families of Dendrograms -
A. Mathew (2009)
The p-adic Numbers -
B. Dragovich, A. Dragovich (2006)
A p-adic model of DNA sequence and genetic codeP-Adic Numbers, Ultrametric Analysis, and Applications, 1
-
G. CORNELISSEN, F. KATO (2005)
The p-adic IcosahedronNotices of the AMS, 52
-
F.Q. GOUVÊA (1993)
p-adic Numbers. An Introduction -
F. Kirwan (2000)
MODULI OF CURVES (Graduate Texts in Mathematics 187)Bulletin of The London Mathematical Society, 32
-
P. Bradley (2007)
Mumford DendrogramsArXiv, abs/0707.3540
-
L. GERRITZEN (1978)
Unbeschr�nkte Steinsche Gebiete vonJournal für die Reine und Angewandte Mathematik, 297
-
D. Mumford (1988)
The red book of varieties and schemesLecture Notes in Mathematics
-
F. Murtagh (2004)
On Ultrametricity, Data Coding, and ComputationJournal of Classification, 21
-
Institut für Industrielle Bauproduktion, Fakultät für Architektur
- Publisher
- Springer Journals
- Copyright
- Copyright © 2008 by Springer Science+Business Media, LLC
- Subject
- Statistics; Marketing ; Psychometrics; Signal, Image and Speech Processing; Bioinformatics; Pattern Recognition; Statistical Theory and Methods
- ISSN
- 0176-4268
- eISSN
- 1432-1343
- DOI
- 10.1007/s00357-008-9009-5
- Publisher site
- See Article on Publisher Site
Abstract
Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist p-adic representations of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the p-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are in fact p-adic parameter spaces of dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.
Journal
Journal of Classification – Springer Journals
Published: Jun 26, 2008