Discrete Time Elastic Vector Spaces

Pierre-François Marteau (1)

1 VALORIA - Laboratoire de Recherche en Informatique et ses Applications de Vannes et Lorient

We propose in this paper a framework dedicated to the construction of what we call time elastic inner products that allows embedding sets of non-uniformly sampled multivariate time series of varying lengths into vector space structures. This framework is based on a recursive definition that covers the case of multiple embedded time elastic dimensions. We prove that such inner products exist in our framework and show how a simple instance of this inner product class operates on some toy applications, while generalizing the Euclidean inner product.

Mots clés: Elastic Inner Product; Time Warping; Vector Space; Discrete Time Series; Non Uniform Sampling

Domaines: Mathématique discrète [cs.DM]

Pierre-François Marteau. Discrete Time Elastic Vector Spaces. 2011. ⟨hal-00556007v3⟩