Early classification of time series

Abstract

An increasing number of applications require to recognize the class of an incoming time series as quickly as possible without unduly compromising the accuracy of the prediction. In this paper, we put forward a new optimization criterion which takes into account both the cost of misclassification and the cost of delaying the decision. Based on this optimization criterion, we derived a family of non-myopic algorithms which try to anticipate the expected future gain in information in balance with the cost of waiting. In one class of algorithms, unsupervised-based, the expectations use the clustering of time series, while in a second class, supervised-based, time series are grouped according to the confidence level of the classifier used to label them. Extensive experiments carried out on real datasets using a large range of delay cost functions show that the presented algorithms are able to solve the earliness vs. accuracy trade-off, with the supervised partition based approaches faring better than the unsupervised partition based ones. In addition, all these methods perform better in a wide variety of conditions than a state of the art method based on a myopic strategy which is recognized as being very competitive. Furthermore, our experiments show that the non-myopic feature of the proposed approaches explains in large part the obtained performances.

ECOTS: Early Classification in Open Time Series

“…In [11], the authors put forward the idea of a multi-objective criterion with an associated Pareto front with multiple dominating trade-offs. However, whereas these methods are myopic in nature, the Economy approach described in [1,4] goes one step further by (i) directly optimizing the combined cost defined in equation 1 and (ii) giving a way to estimate the combined cost for future time steps, thus leading to a non-myopic approach that outperforms the best methods known to date.…”

“…In the following, we demonstrate how the triggering strategy used in ECTS can be adapted to deal with ECOTS. For this, we consider one of the best performing myopic strategies known to date, described in [9] and the best non-myopic approach in the literature: the Economy-γ strategy described in [1]. The first one relies ultimately on confidence criteria, while the second one explicitly optimizes the accuracy versus delay cost trade-off.…”

“…Our goal is to use the ECOTS approaches to make this horizon adaptive to the observable part of the time series at hand. Evaluation criterion: Ultimately, the value of using an early classification method is defined by the average cost incurred using it, as in [1]. Given an open time series S (e.g.…”

“…Data split and extraction: We splitted the set of time series into four parts: 50% for training classifiers, 20% for testing ECOTS algorithms, 15% for validating ECOTS algorithms and 15% for estimating confusion matrices. This split is inspired from the original paper of economy [1]. Subsequences of size w were extracted from the training open time series by doing the following steps: (i) time stamps t p , aka targets, were set within the time series, spaced with w + η M time units in order to avoid overlaps between samples; (ii) η M −η m subsequences were extracted around each target, each one dedicated to the training of the classifier h η (see Figure 4).…”

“…In Section 2, we formally draw a parallel between the ECTS problem and the ECOTS one. We then review the main approaches to ECTS, and outline two competitive methods: one described in [10] and the other, the Economy method presented in [1]. We then show, in Section 4, how to adapt these methods to the ECOTS problem, before comparing their performances on experiments in Section 5.…”