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Article Dans Une Revue International Journal of Approximate Reasoning Année : 2024

Data complexity: An FCA-based approach

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In this paper we propose different indices for measuring the complexity of a dataset in terms of Formal Concept Analysis (FCA). We extend the lines of the research about the ``closure structure'' and the ``closure index'' based on minimum generators of intents (aka closed itemsets). We would try to capture statistical properties of a dataset, not just extremal characteristics, such as the size of a passkey. For doing so we introduce an alternative approach where we measure the complexity of a dataset w.r.t. five significant elements that can be computed in a concept lattice, namely intents (closed sets of attributes), pseudo-intents, proper premises, keys (minimal generators), and passkeys (minimum generators). Then we define several original indices allowing us to estimate the complexity of a dataset. Moreover we study the distribution of all these different elements and indices in various real-world and synthetic datasets. Finally, we investigate the relations existing between these significant elements and indices, and as well the relations with implications and association rules.
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Dates et versions

hal-03985980 , version 1 (20-02-2023)
hal-03985980 , version 2 (24-04-2024)

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Alexey Buzmakov, Egor Dudyrev, Sergei O Kuznetsov, Tatiana Makhalova, Amedeo Napoli. Data complexity: An FCA-based approach. International Journal of Approximate Reasoning, 2024, 165, ⟨10.1016/j.ijar.2023.109084⟩. ⟨hal-03985980v2⟩
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