Date: PM 4:00-, April 13, 2005
Place: Ce605, IIS, University of Tokyo
Invited Speaker:Dr. Julian Laub(Fraunhofer FIRST)

Title: Analyzing Non-Euclidean Pairwise Data

Abstract:
There are two common data representations in intelligent data
analysis,  namely the vectorial representation and the pairwise
representation.  Pairwise data satisfying the restrictive conditions
of Euclidean spaces can be faithfully translated into a Euclidean vectorial
representation by way of embedding.
Pairwise data, for which no loss-free embeddings exist, are called
non-Euclidean pairwise data.

This paper investigates and explores non-Euclidean pairwise data
and common paradigms related to them,  based on both conceptual and
empirical considerations.
The major focus lies on apprehending the nature and consequences of
metric violations. Such violations have commonly been considered an
accidental byproduct of measurement noise and have received
corresponding mathematical treatment.  It is shown by simple modeling
of metric violations that this assumption is misleading, not only in
pathological cases but even for naturally constructed similarity
measures.

Furthermore it is shown that even though in general there exists no
unification on a representational level, non-metric pairwise data and
vectorial data
can be unified with respect to the structural information contained in
the data, that is, the entity we are really interested in machine learning.