While temporal classification may be relatively unexplored, time series have been studied extensively in different fields, including statistics, signal processing and control theory.
The study of time series in statistics has a long history [BJ76,And76]. The two main goals of time series analysis in statistics are (a) to characterise, describe and interpret time series (b) to forecast future time series behaviour [Sta02]. The focus in most of the time series analysis work is on long-duration historical data (months/years), because it was typically modelling time series from fields such as biology, economics and demographics. Approaches typically tried to model time series as an underlying ``trend'' - a long term pattern - together with a seasonailty - short term patterns. The most popular techniques in this type of analysis are Autoregressive Integrated Moving Averages (ARIMA) and Autocorrelation. Many of the techniques, however, make assumptions of stationarity.
The field of signal processing has also explored time series. The objective of signal processing is to characterise time series in such a manner as to allow transformations and modifications of them for particular purposes; e.g. optimal transmission over a phone line. One of the oldest techniques for time series analysis is the Fourier transform [Bra65]. The Fourier transform converts from a time-series representation to a frequency representation. Fourier's Theory states that any periodic time series can be represented as a sum of sinusoidal waves of different frequencies and phases. Converting from a time series representation to a frequency representation allowed certain patterns to be observed more easily. However, the limitation of periodicity is quite significant, and so recently much work has focused on wavelet analysis [Mal99], where any time series can be represented not as a sum of sinusoidal waves, but ``wavelets'' - non-periodic signals that approach zero in the positive and negative limits. Signal processing has seen applications in the design of electrical circuits, building of audio amplifiers, the design of telecommunications equipment and more.
Control theory is another field that has explored time series. Control theory studies systems that produce output values at regular time intervals on the basis of certain inputs. However, the relationship between outputs and inputs depends on previous values of the outputs and inputs. Control theory observes patterns in the past inputs and outputs to try to set new inputs so as to achieve a desired output. Typical applications of control theory are to operating industrial equipment such as steel mills and food production processes. Recent work has seen a move towards ``adaptive control'' [GRC80]; approaches that modify the control theory on the basis of past observations.
All of these fields relate closely to the current work in their study of time series; however, our work differs in that its objective is not to predict future values or to modify behaviour, but rather to classify new time series based on past observations of time series, rather than analysing a single time series' patterns.