[Paper Review] Combining Clustering techniques and Formal Concept Analysis to characterize Interestingness Measures

Dhouha Grissa, Sylvie Guillaume+1 more|arXiv (Cornell University)|Aug 21, 2010

Rough Sets and Fuzzy Logic22 references5 citations

TL;DR

This paper proposes a formal concept analysis (FCA)-based framework to validate and refine clusters of interestingness measures (IMs) derived from hierarchical (AHC) and partitioning (k-means) clustering. By modeling 61 IMs and 19 semantic properties as a formal context, FCA reveals stable, semantically coherent groups, validates AHC/k-means results, and identifies questionable or fragmented clusters, offering a principled method for IM selection in knowledge discovery.

ABSTRACT

Formal Concept Analysis "FCA" is a data analysis method which enables to discover hidden knowledge existing in data. A kind of hidden knowledge extracted from data is association rules. Different quality measures were reported in the literature to extract only relevant association rules. Given a dataset, the choice of a good quality measure remains a challenging task for a user. Given a quality measures evaluation matrix according to semantic properties, this paper describes how FCA can highlight quality measures with similar behavior in order to help the user during his choice. The aim of this article is the discovery of Interestingness Measures "IM" clusters, able to validate those found due to the hierarchical and partitioning clustering methods "AHC" and "k-means". Then, based on the theoretical study of sixty one interestingness measures according to nineteen properties, proposed in a recent study, "FCA" describes several groups of measures.

Motivation & Objective

• To address the challenge of selecting appropriate interestingness measures (IMs) among the large number of available options in association rule mining.
• To validate the results of traditional clustering methods (AHC and k-means) applied to IMs using a formal, theory-based approach.
• To identify stable, semantically coherent groups of IMs with similar behavioral properties based on 19 semantic criteria.
• To provide researchers and practitioners with a reliable method to assess and select high-quality IMs for effective knowledge discovery.

Proposed method

• Construct a formal context from a 61×19 matrix of IMs (objects) and 19 semantic properties (attributes), where a cell indicates whether an IM satisfies a property.
• Apply Formal Concept Analysis (FCA) to generate a concept lattice that reveals conceptual relationships and hierarchical groupings of IMs based on shared properties.
• Use lattice visualization to validate or question clusters identified by AHC and k-means, particularly assessing cluster cohesion and boundary ambiguity.
• Select key concept nodes (e.g., C9, C5, C2) to analyze group membership and proximity of IMs, identifying stable vs. questionable clusters.
• Evaluate the stability of clusters by checking whether all members of a cluster share the same intent (set of properties), and assess external measures' proximity to clusters.
• Identify IMs that are ambiguous in cluster assignment (e.g., recall, informational gain) by analyzing their position in the lattice relative to multiple clusters.

Experimental results

Research questions

• RQ1 Can FCA effectively validate the clusters of interestingness measures generated by AHC and k-means clustering?
• RQ2 Which clusters of interestingness measures exhibit strong semantic cohesion based on shared properties?
• RQ3 Why are certain clusters (e.g., C2, C5) difficult to validate using FCA, and what does this imply about their structural stability?
• RQ4 How can FCA reveal ambiguous or overlapping memberships of specific interestingness measures across clusters?
• RQ5 To what extent can FCA serve as a third-party validation mechanism for clustering results in IM analysis?

Key findings

• FCA successfully validates the C1 and C4 clusters, as all members of these clusters share a common intent and form a coherent group in the lattice.
• The C9 cluster is well-validated by FCA, with all its members forming a stable concept and being closely linked in the lattice, confirming their similar behavior.
• The C2 cluster is questionable due to inconsistent property sharing and ambiguous membership; FCA reveals that its members are not fully coherent and are also close to other clusters.
• The C5 cluster is fragmented in the lattice, splitting into two subgroups: {Negative Reliability, causal confidence, causal confirmed-confidence} and {Specificity, Leverage, Putative Causal Dependency}, indicating poor cohesion.
• Measures like recall, informational gain, and Gini are found near multiple clusters (e.g., C4, C5, C8, C9), indicating ambiguous or unstable cluster membership, with proximity suggesting shared properties but no definitive assignment.
• Fukuda’s measure is closely linked to the C6 cluster (IIE, IIER, IP3E), confirming its placement in that group, while other measures like mutual information and fukuda show proximity to multiple clusters, highlighting their ambiguous positioning.