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.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Pierre-François Marteau
• Keywords: CORR 2011, Education, Elastic Inner Products, Euclidean Inner Product, Inner Product