Abstract
Decision implication is an elementary representation of decision knowledge in formal concept analysis. Decision implication canonical basis (DICB), a set of decision implications with completeness and non-redundancy, is the most compact representation of decision implications. The method based on true premises (MBTP) for DICB generation is the most efficient one at present. In practical applications, however, data are always changing dynamically, and MBTP, lacking an update mechanism of DICB, still needs to re-generate inefficiently the whole DICB. This paper proposes an incremental algorithm for DICB generation, which obtains a new DICB just by modifying and updating the existing one. Experimental results verify that when samples in data are much more than condition attributes, which is actually a general case in practical applications, the incremental algorithm is significantly superior to MBTP. Furthermore, we conclude that even for the data in which samples are less than condition attributes, when new samples are continually added into data, the incremental algorithm must be also more efficient than MBTP, because the incremental algorithm just needs to modify the existing DICB, which is only a part of work of MBTP.
Highlights
We study an incremental method for decision implication canonical basis (DICB) generation, which updates the existing DICB to obtain a new one, when new objects come
We proposed an incremental algorithm, which produces a new DICB by modifying and updating the existing DICB in the case of new objects being continually added into data
Experimental results verified that when samples in data are much more than condition attributes, the time consumption of generating the whole DICB by incremental algorithm will be remarkably less than that by method based on true premises (MBTP)
Summary
Formal Concept Analysis (FCA) is an order-theoretic method for concept analysis and visualization, pioneered by Wille [38] in the mid-80s. FCA comes from a philosophical understanding of a concept, which is viewed as a unit of thought constituted by its extent and intent. FCA is capable of presenting the relationship between intent and extent and visualizing the generalization and specialization of concepts by means of concept lattice. FCA attracts the interest of researchers in the fields of data mining [27, 1, 5, 36, 2, 29, 52], social networks [32], cognition-based concept learning [41, 40, 16, 23, 54, 14], knowledge reduction [11, 4, 35, 25, 17, 12, 13, 6] and decision making [50, 51]
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