Applying binary decision diagram to extract concepts from triadic formal context

Neves, Julio C. V.; Ananias, Kaio H. A.; Nobre, Cristiane Neri; Zárate, Luis Enrique; Song, Mark A. J.

doi:10.1145/3341105.3374086

Cited by 1 publication

(10 citation statements)

References 9 publications

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“…Recently a successful TCA-adaption of ProperIm [13], an improved FCA algorithm based on the binary decision diagram (BDD) [1] has been conducted. The adaption was named TRIAS-BDD, which saves about 25% of running time compared to the baseline TRIAS algorithm [14]. We find this research meaningful but still has space for further improvements mainly for the following two reasons.…”

Section: Introductionmentioning

confidence: 93%

“…[8] and is now still considered the most natural and stateof-the-art working flow for TCA. To the furthest of our knowledge, all later TCA algorithms are based on this prototype algorithm [7], [14]. A sample pseudocode for this prototype algorithm is presented as Algorithm 1 for a clearer view of the process.…”

Section: The Prototype Algorithm For Tcamentioning

confidence: 99%

“…The two previous algorithms are originally proposed for FCA, while they can be easily adapted to TCA following the procedure of the prototype algorithm for TCA introduced in Algorithm 1. Previous research has successfully adapted the ProperIm algorithm to TCA and proved it effective in speeding up the process [14]. However, we are to theoretically analyze that a direct adaption of these two improved FCA algorithms to TCA must encounter some problems which may slow down the process in some cases.…”

Section: Zdd-based Improved Tca Algorithmsmentioning

confidence: 99%

“…However, in terms of solving real problems, it is often considered impractical due to the lack of a fast algorithm. According to the previous studies, it costs longer than a day to conduct TCA on a 10,000 × 15 × 5 context with the baseline TRIAS algorithm [7], [14]. This is because the TCA process is proved to be equivalent to a nested FCA process [9], which means that the complexity of TCA will be square to that of FCA.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, its time complexity is linear to the number of all concepts, reaching the lower bound of the complexity of an FCA algorithm. Till now, most TCA algorithms choose to apply the NextClosure algorithm for their FCA components [7], [8], [14].…”

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confidence: 99%

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Z-TCA: Fast Algorithm for Triadic Concept Analysis Using Zero-suppressed Decision Diagrams

Peng,

Yamamoto

2023

Journal of Information Processing

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We propose a fast algorithm called Z-TCA for triadic concept analysis (TCA). TCA is an extension of formal concept analysis (FCA), aiming at extracting ontologies by using mathematical order theories from a collection of ternary relations of three groups of variables: the object, attributes, and conditions. It finds various applications in fields like data mining and knowledge representation. However, the state-of-the-art TCA algorithms are suffering from the problem of low efficiency due to the complexity of the task. Attempts have been made to speed up the TCA process using a Binary Decision Diagram (BDD) or its improved version Zero-suppressed Decision Diagram (ZDD), while in this paper, we propose a new way to apply ZDD to TCA, named the Z-TCA algorithm. We conduct experiments on a real-world triadic context built from the IMDb database as well as some randomly-generated contexts and the results show that our Z-TCA algorithm can speed up the TCA process about 3 times compared to the baseline TRIAS algorithm. We also discover that when the density of the context exceeds 5%, our algorithm outperforms all other ZDD-based improved TCA algorithms and becomes the fastest choice for TCA.

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Section: Introductionmentioning

confidence: 93%