Induction of formal concepts by lattice computing techniques for tunable classification

Abstract

This work proposes an enhancement of Formal Concept Analysis (FCA) by Lattice Computing (LC) techniques. More specifically, a novel Galois connection is introduced toward defining tunable metric distances as well as tunable inclusion measure functions between formal concepts induced from hybrid (i.e., nominal and numerical) data. An induction of formal concepts is pursued here by a novel extension of the Karnaugh map, or K-map for short, technique from digital electronics. In conclusion, granular classification can be pursued. The capacity of a classifier based on formal concepts is demonstrated here with promising results. The formal concepts are interpreted as descriptive decisionmaking knowledge (rules) induced from the training data.

Lattice computing (LC) meta-representation for pattern classification

“…Since the introduction of the LC, a lot of work has been reported in reformulating some traditional classifier models to operate according to LC framework [10]- [14]. Among these models the Minimum Distance Classifier (MDC), which is equivalent with the 1-NN classifier, is selected for this study due to its simplicity.…”

“…This meta-representation enables the usage of some useful tools defined in lattice space, such as distance and similarity measures, able to distinguish the patterns of each class. Based on these distance and similarity measures, traditional classifier models have been adopted [10]- [14] and applied in pattern classification applications with success.…”

Hyperbox Granular Computing Based on Distance Measure

“…The training data are generated by the method proposed in [7]. The training set and the testing set in reference [8] are used to evaluate the performance of GrC.…”

“…Pedrtcz computed information granules based on sets, fuzzy sets or relations, and fuzzy relations [3]. Karburlasos and his colleage use the fuzzy relation between two granules to realize the transformation between two granule spaces with different granularities [4][5][6][7][8][9]. These studies enable us to map the complexities of the world around us into simple theories.…”

WINkNN: Windowed Intervals’ Number kNN Classifier for Efficient Time-Series Applications

“…LC models are expected to be useful in CPS applications including human-robot interaction because they can (1) deal with both numerical data (regarding physical system components) as well as with non-numerical data (regarding cyber system components), (2) compute with semantics, represented by a partial-order relation, (3) rigorously deal with ambiguity represented by information granules, (4) naturally engage logic and reasoning, and (5) process data fast. LC suggests useful instruments for analysis and design of new technologies including formal concepts [25,26], type-2 fuzzy sets [23,27], and other. In the context of the LC framework, intervals' numbers, or INs for short, have been studied as explained next.…”