TY  - JOUR
A1  - Laub, Julian
A1  - Roth, Volker
A1  - Buhmann, Joachim
A1  - Müller, Klaus-Robert
T1  - On the information and representation of non-Euclidean pairwise data
N2  - Two common data representations are mostly used in intelligent data analysis, namely the vectorial and the pairwise representation. Pairwise data which satisfy the restrictive conditions of Euclidean spaces can be faithfully translated into a Euclidean vectorial representation by embedding. Non-metric pairwise data with violations of symmetry, reflexivity or triangle inequality pose a substantial conceptual problem for pattern recognition since the amount of predictive structural information beyond what can be measured by embeddings is unclear. We show by systematic modeling of non-Euclidean pairwise data that there exists metric violations which can carry valuable problem specific information. Furthermore, Euclidean and non-metric data can be unified on the level of structural information contained in the data. Stable component analysis selects linear subspaces which are particularly insensitive to data fluctuations. Experimental results from different domains support our pattern recognition strategy.
Y1  - 2006
UR  - http://www.sciencedirect.com/science/journal/00313203
U6  - https://doi.org/10.1016/j.patcog.2006.04.016
SN  - 0031-3203
ER  -