Querying Triadic Concepts through Partial or Complete Matching of Triples

TL;DR

This work tackles efficient querying of triadic concepts by introducing an inverted-index approach for partial and complete matching of triples within a triadic context $K=(K_1,K_2,K_3,Y)$ and triadic concepts $(A_1,A_2,A_3)$. The method supports one-, two-, and three-dimensional queries, ranking retrieved triadic concepts with a novel similarity-based metric and a Re-rank procedure, without storing the full triadic context or performing derivations or factorization during queries. Compared to the state-of-the-art approximation method, the approach demonstrates substantially better efficiency and scalability on large datasets, as shown in empirical studies on the Mushroom and Groceries datasets, with fast index construction and millisecond-level query times. The work also furnishes a practical workflow and a ranking mechanism that makes the search results immediately useful, providing a foundation for big-data pattern mining in Triadic Concept Analysis and enabling open-source exploration tools in this domain.

Abstract

In this paper, we introduce a new method for querying triadic concepts through partial or complete matching of triples using an inverted index, to retrieve already computed triadic concepts that contain a set of terms in their extent, intent, and/or modus. As opposed to the approximation approach described in Ananias, this method (i) does not need to keep the initial triadic context or its three dyadic counterparts, (ii) avoids the application of derivation operators on the triple components through context exploration, and (iii) eliminates the requirement for a factorization phase to get triadic concepts as the answer to one-dimensional queries. Additionally, our solution introduces a novel metric for ranking the retrieved triadic concepts based on their similarity to a given query. Lastly, an empirical study is primarily done to illustrate the effectiveness and scalability of our approach against the approximation one. Our solution not only showcases superior efficiency, but also highlights a better scalability, making it suitable for big data scenarios.

Figures (3)

• Figure 1: The Hasse diagram of triadic concepts
• Figure 2: Workflow of our proposed solution
• Figure 3: Process of creating the Inverted-Index from triadic concepts and retrieving a matched concept