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an input the completed time series to be classified. This may be a severe
drawback if the classifiers are to be use on line in a dynamic environment
and a classification is needed as soon as possible. This work shows how the
original method can be extended to cope with these weaknesses.
Regarding variable length time series, it is always possible to prepro-
cess the data set in order to obtain a new one with fixed length series.
Nevertheless, this cannot be considered as a generic solution, because, usu-
ally, the own length of the series provides essential information for its clas-
sification. The method can now be used with variable length series because
the literals are allowed to abstain (that is, the result of their evaluation can
be true, false or an abstention) if the series is not long enough to evaluate
some literal. A variant of boosting that can work with base classifiers with
abstentions is used.
Regarding the classification of partial examples, or early classification,
the system has been modified to add it the capacity of assigning a prelim-
inary classification to an incomplete example. This feature is crucial when
the examples to classify are being generated dynamically and the time nec-
essary to generate an example is long. For instance, consider a supervision
task of a dynamic system. In this case, the example to classify is the current
state, considering the historical values of the variables. For this problem, it
is necessary to indicate a possible problem as soon as possible. In order to
confirm the problem, it will be necessary to wait and see how the variables
evolve. Hence, it is necessary to obtain classifications using as input series
of different lengths. Again, the capability of the literals to abstain allows
tackling this problem.
The rest of the chapter is organized as follows. Section 2 is a brief intro-
duction to boosting, suited to our method. The base classifiers, interval
literals, are described in Section 3. Sections 4 and 5 deal, respectively, with
variable length series and early classification. Section 6 presents experimen-
tal results. Finally, we give some concluding remarks in Section 7.
2. Boosting
At present, an active research topic is the use of ensembles of classifiers.
They are obtained by generating and combining base classifiers, constructed
using other machine learning methods. The target of these ensembles is to
increase the accuracy with respect to the base classifiers.
One of the most popular methods for creating ensembles is boosting
[Schapire (1999)], a family of methods, of which A
da
B
oost
is the most
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