A time series distance measure for efficient clustering of input output signals by their underlying dynamics

Starting from a dataset with input/output time series generated by multiple deterministic linear dynamical systems, this paper tackles the problem of automatically clustering these time series. We propose an extension to the so-called Martin cepstral distance, that allows to efficiently cluster these time series, and apply it to simulated electrical circuits data. Traditionally, two ways of handling the problem are used. The first class of methods employs a distance measure on time series (e.g. Euclidean, Dynamic Time Warping) and a clustering technique (e.g. k-means, k-medoids, hierarchical clustering) to find natural groups in the dataset. It is, however, often not clear whether these distance measures effectively take into account the specific temporal correlations in these time series. The second class of methods uses the input/output data to identify a dynamic system using an identification scheme, and then applies a model norm-based distance (e.g. H2, H-infinity) to find out which systems are similar. This, however, can be very time consuming for large amounts of long time series data. We show that the new distance measure presented in this paper performs as good as when every input/output pair is modelled explicitly, but remains computationally much less complex. The complexity of calculating this distance between two time series of length N is O(N logN).Comment: 6 pages, 4 figures, sent in for review to IEEE L-CSS (CDC 2017 option

Proceedings of Abstracts Engineering and Computer Science Research Conference 2019

© 2019 The Author(s). This is an open-access work distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. For further details please see https://creativecommons.org/licenses/by/4.0/. Note: Keynote: Fluorescence visualisation to evaluate effectiveness of personal protective equipment for infection control is © 2019 Crown copyright and so is licensed under the Open Government Licence v3.0. Under this licence users are permitted to copy, publish, distribute and transmit the Information; adapt the Information; exploit the Information commercially and non-commercially for example, by combining it with other Information, or by including it in your own product or application. Where you do any of the above you must acknowledge the source of the Information in your product or application by including or linking to any attribution statement specified by the Information Provider(s) and, where possible, provide a link to this licence: http://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/This book is the record of abstracts submitted and accepted for presentation at the Inaugural Engineering and Computer Science Research Conference held 17th April 2019 at the University of Hertfordshire, Hatfield, UK. This conference is a local event aiming at bringing together the research students, staff and eminent external guests to celebrate Engineering and Computer Science Research at the University of Hertfordshire. The ECS Research Conference aims to showcase the broad landscape of research taking place in the School of Engineering and Computer Science. The 2019 conference was articulated around three topical cross-disciplinary themes: Make and Preserve the Future; Connect the People and Cities; and Protect and Care