Classification of 'Short' Time Series via the Epsilon-Complexity of Continuous Functions

• Activity Number: 601
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Alexandra Piryatinska*+ and Boris Darkhovsky
• Companies: San Francisco State University and Institute for Systems Analysis, Russian Academy of Sciences
• Keywords: time series ; complexity ; classification

Abstract

In applications we often need to classify short time series into segments depending on the unknown mechanisms (stochastic or deterministic) that generated them. In such a case it is hard to find characteristics of the time series that can be used for classification purposes. A new approach to this problem, based on the novel concept of the epsilon-complexity of a continuous function, is proposed. The complexity of a continuous function is defined as the fraction of the function values necessary to recover the original function via a certain fixed family of approximation methods without exceeding a given error. It is shown that the dependence of the complexity of a function on the reconstruction error can be well approximated in logarithmic coordinates by an affine function. Its parameters are then used as the classifier. Effectiveness of this procedure is verified by simulations. We apply this procedure to the EEG study which examines the genetic predisposition to alcoholism.