Knowledge Extraction with Interval Temporal Logic Decision Trees

Multivariate temporal, or time, series classification is, in a way, the temporal generalization of (numeric) classification, as every instance is described by multiple time series instead of multiple values. Symbolic classification is the machine learning strategy to extract explicit knowledge from a data set, and the problem of symbolic classification of multivariate temporal series requires the design, implementation, and test of ad-hoc machine learning algorithms, such as, for example, algorithms for the extraction of temporal versions of decision trees. One of the most well-known algorithms for decision tree extraction from categorical data is Quinlan's ID3, which was later extended to deal with numerical attributes, resulting in an algorithm known as C4.5, and implemented in many open-sources data mining libraries, including the so-called Weka, which features an implementation of C4.5 called J48. ID3 was recently generalized to deal with temporal data in form of timelines, which can be seen as discrete (categorical) versions of multivariate time series, and such a generalization, based on the interval temporal logic HS, is known as Temporal ID3. In this paper we introduce Temporal C4.5, that allows the extraction of temporal decision trees from undiscretized multivariate time series, describe its implementation, called Temporal J48, and discuss the outcome of a set of experiments with the latter on a collection of public data sets, comparing the results with those obtained by other, classical, multivariate time series classification methods.