Title :

Measuring dissimilarity with diffeomorphism invariance

Author(s) :

Cantelobre, Théophile [Auteur]
Statistical Machine Learning and Parsimony [SIERRA]
MOdel for Data Analysis and Learning [MODAL]
The Inria London Programme [Inria-London]
Ciliberto, Carlo [Auteur]
Department of Computer science [University College of London] [UCL-CS]
University College of London [London] [UCL]
Guedj, Benjamin [Auteur]
University College of London [London] [UCL]
Department of Computer science [University College of London] [UCL-CS]
The Alan Turing Institute
The Inria London Programme [Inria-London]
MOdel for Data Analysis and Learning [MODAL]
Rudi, Alessandro [Auteur]
Statistical Machine Learning and Parsimony [SIERRA]

HAL domain(s) :

Informatique [cs]/Apprentissage [cs.LG]
Statistiques [stat]/Machine Learning [stat.ML]
Statistiques [stat]/Théorie [stat.TH]

English abstract : [en]

Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data's ...
Show more >Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data's internal structure to be invariant to diffeomorphisms. We prove that DID enjoys properties which make it relevant for theoretical study and practical use. By representing each datum as a function, DID is defined as the solution to an optimization problem in a Reproducing Kernel Hilbert Space and can be expressed in closed-form. In practice, it can be efficiently approximated via Nystr\"om sampling. Empirical experiments support the merits of DID.Show less >

Language :

Anglais

Comment :

A pre-print

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL