Classification of time series as early as possible is a valuable goal. Indeed, in many application domains, the earliest the decision, the more rewarding it can be. Yet, often, gathering more information allows one to get a better decision. The optimization of this time vs. accuracy tradeoff must generally be solved online and is a complex problem. This paper presents a formal criterion that expresses this trade-off in all generality together with a generic sequential meta algorithm to solve it. This meta algorithm is interesting in two ways. First, it pinpoints where choices can (have to) be made to obtain a computable algorithm. As a result a wealth of algorithmic solutions can be found. Second, it seeks online the earliest time in the future where a minimization of the criterion can be expected. It thus goes beyond the classical approaches that myopically decide at each time step whether to make a decision or to postpone the call one more time step. After this general setting has been expounded, we study one simple declination of the meta-algorithm, and we show the results obtained on synthetic and real time series data sets chosen for their ability to test the robustness and properties of the technique. The general approach is vindicated by the experimental results, which allows us to point to promising perspectives.

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.

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