Fast Feature Extraction for Time Series Analysis Using Least-Squares Approximations with Orthogonal Basis Functions | IEEE Conference Publication | IEEE Xplore

Fast Feature Extraction for Time Series Analysis Using Least-Squares Approximations with Orthogonal Basis Functions


Abstract:

Many efforts have been made during the past decades to investigate the use of orthogonal basis functions in the field of least-squares approximation. Certain bases of ort...Show More

Abstract:

Many efforts have been made during the past decades to investigate the use of orthogonal basis functions in the field of least-squares approximation. Certain bases of orthogonal functions allow for a definition of fast update algorithms for approximations of time series in sliding or growing time windows. In fields such as technical data analytics, temporal data mining, or pattern recognition in time series, appropriate time series representations are needed to measure the similarity of time series or to segment them. This article bridges the gap between mathematical basic research and applications by making fast update techniques for standard polynomials and trigonometric polynomials accessible for time series classification or regression (e.g., forecasting), anomaly or motif detection in time series, etc. This is of utmost importance for online or big data applications. Time series or segments of time series will be represented by features derived from the orthogonal expansion coefficients of the approximating polynomials which capture the essential behavior in the time or spectral domain, i.e. trends and periodic behavior, using standard or trigonometric polynomials. Our experiments show that a reliable computation is possible at a very low runtime compared to a conventional least-squares approach. The algorithms are implemented in Java, C(++), Matlab, and Python and made publicly available.
Date of Conference: 23-25 September 2015
Date Added to IEEE Xplore: 07 January 2016
ISBN Information:
Print ISSN: 1530-1311
Conference Location: Kassel, Germany

I. Introduction

Time series can be found in many applications such as medical and biological diagnostics, analysis of financial time series, speech processing, or sensor analysis. Many steps in time series analysis, such as segmentation, representation, similarity measurement, etc. are often based on appropriate features extracted. From the time series, examples for features individual statistical measures (e.g., mean variance, number of zero crossings), features in the time domain (e.g., slope, curve), or spectral features (e.g., amplitudes attributed to certain frequency components of a time series). The run-time efficiency of algorithms for time series analysis is an important issue for two reasons:

The amount of data including time series data increases rapidly nowadays. The analysis of large time series data sets (i.e., big data in a time series context such as smart grid data) requires algorithms that fulfill harsh space and run-time constraints.

On-line algorithms (e.g., streaming algorithms) require a fast (often non-reversible) decision with strict runtime requirements (e.g., in the fields of ubiquitous or pervasive computing).

References

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