Discrete Time Elastic Vector Spaces

This paper proposes a framework dedicated to the construction of what we call time elastic inner products allowing one to embed 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 or prospective applications, while generalizing the Euclidean inner product.