Abstract
Formal concept analysis has proven to be a very effective method for data analysis and rule extraction, but how to build formal concept lattices is a difficult and hot topic. In this paper, an efficient and rapid incremental concept lattice construction algorithm is proposed. The algorithm, named FastAddExtent, is seen as a modification of AddIntent in which we improve two fundamental procedures, including fixing the covering relation and searching the canonical generator. The proposed algorithm can locate the desired concept quickly by adding data fields to every concept. The algorithm is depicted in detail, using a formal context to show how the new algorithm works and discussing time and space complexity issues. We also present an experimental evaluation of its performance and comparison with AddExtent. Experimental results show that the FastAddExtent algorithm can improve efficiency compared with the primitive AddExtent algorithm.
Highlights
In terms of formal concept analysis (FCA) [1,2], how to generate a relation diagram that is effectively and quickly built by the formal context has been extensively studied by scholars [3,4,5,6,7,8,9,10,11]
Incremental algorithms add objects or attributes one by one from the formal context progressively, which can change the concept lattice dynamically according to the changes made to a formal context
The formal context is shown by a triple K = (G, M, I) in FCA, in which G represents the set of objects, M represents the set of attributes, and I represents the binary relation between G and M. gIm denotes that the object g has the attribute m for an object g ∈ G and an attribute m ∈ M
Summary
In terms of formal concept analysis (FCA) [1,2], how to generate a relation diagram that is effectively and quickly built by the formal context has been extensively studied by scholars [3,4,5,6,7,8,9,10,11]. The extent refers to the set of objects which has the same attributes, while the intent is the description of the concept (the set of attributes), which means the example has the common feature in this concept This structure describes the essential relationship between objects and attributes and shows the formalization of all concepts in the category of philosophy [9]. Incremental algorithms add objects or attributes one by one from the formal context progressively, which can change the concept lattice dynamically according to the changes made to a formal context. It can reduce the unnecessary computational time by avoiding rebuilding the concept lattice
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