Section: Scientific Foundations

Methods for Knowledge Discovery guided by Domain Knowledge

Classification problems can be formalized by means of a class of individuals (or objects), a class of properties (or attributes), and a binary correspondence between the two classes, indicating for each individual-property pair whether the property applies to the individual or not. The properties may be features that are present or absent, or the values of a property that have been transformed into binary variables. Formal Concept Analysis (FCA) relies on the analysis of such binary tables and may be considered as a symbolic data mining technique to be used for extracting (from a binary database) a set of formal concepts organized within a concept lattice hierarchy [91] . Concept lattices are sometimes also called Galois lattices [81] .

The search for frequent itemsets and the extraction of association rules are well-known symbolic data mining methods, related to FCA (actually searching for frequent itemsets may be understood as traversing a concept lattice). Both processes usually produce a large number of items and rules, leading to the associated problems of “mining the sets of extracted items and rules”. Some subsets of itemsets, e.g. frequent closed itemsets (FCIs), allow to find interesting subsets of association rules, e.g. informative association rules. This is why several algorithms are needed for mining data depending on specific applications [120] , [119] .

Among useful patterns extracted from a database, frequent itemsets are usually thought to unfold “regularities” in the data, i.e. they are the witnesses of recurrent phenomena and they are consistent with the expectations of the domain experts. In some situations however, it may be interesting to search for “rare” itemsets, i.e. itemsets that do not occur frequently in the data (contrasting frequent itemsets). These correspond to unexpected phenomena, possibly contradicting beliefs in the domain. In this way, rare itemsets are related to “exceptions” and thus may convey information of high interest for experts in domains such as biology or medicine [121] , [122] .

From the numerical point of view, a Hidden Markov Model (HMM2) is a stochastic process aimed at extracting and modeling a stationary distribution of events. These models can be used for data mining purposes, especially for spatial and temporal data as they show good capabilities to locate stationary segments [100] ). one special research effort focuses on the study of the application of HMM2 to composite data, both in the temporal and spatial domain, to produce a multi-dimensional classification based on multiple attributes.