Pattern/rule relation analysis [5-7] focuses on analyzing the structural, distributional, logical, semantic and other coupling relationships between patterns/rules and between their constituent items, elements, subsequences/itemsets, sequences, and patterns/rules. Two to multiple patterns/rules could be associated, correlated, dependent, or coupled for various reasons and factors through analyzing pattern couplings and interactions .
In the classic literature, pattern/rule mining and pattern recognition focus on individual patterns/rules based on the downward closure (Apriori) property, which essentially assumes pattern/rule elements and patterns/rules are independent. For example, association rule mining and general frequent pattern mining only evaluate and select individual patterns/rules.
In reality, patterns/rules may be dependent, coupled and relevant for various reasons. As an example, interaction patterns between clients and service providers evolve with circumstance and scenario changes, health and medical treatment protocols evolve per patients’ conditions and service options. Pattern/rule relation analysis can either couple multiple relevant patterns/rules for a richer representation and comparison between condition/scenario-specific pattern/rule descriptions or present an evolving path of patternable behavior evolution from one condition/scenario to another as shown in the above example.
Pattern/rule relations may be measured in terms of pattern/rule similarity or difference, e.g., attributed pattern/rule similarity by involving item/element/pattern/rule attributes, logical relations; or representations. Explicit and implicit pattern/rule relations may be modeled.
Combined Pattern/Rule Mining
Combined patterns/rules [5-7] can be discovered that consist of a pair or cluster of patterns/rules, which are coupled in terms of explicit or implicit item/element relations and pattern/rule relations. Pair patterns/rules (e.g., two patterns/rules p1= –> high risk and p2= –> low risk should be combined to view the risk mitigation) and cluster patterns/rules can be coupled with their couplings formalized, which can then be used to select patterns, form combined patterns/rule, construct pattern evolution, and suggest decision-making actions.
Combined patterns/rules can be discovered in positive (sequential) patterns/rules, negative (sequential) patterns/rules, graph-based linkage patterns, tree-based rules, and interaction patterns/rules, etc.
Although rarely explored in research, various topics could be relevant to pattern relation/rule analysis, e.g.:
- Pattern/rule coupling and interaction learning: learning explicit and implicit, sequential and unordered, heterogeneous and hierarchical couplings and interactions within and between pattern elements, itemsets, subpatterns, and patterns;
- Combined pattern/rule mining: discovering patterns/rules consisting of two to multiple patterns/rules to form super combined patterns/rules, e.g., pair patterns/rules, cluster patterns/rules;
- Mining pair patterns/rules: discovering a pair of patterns/rules with certain relations that couple the patterns/rules, e.g., co-occurrences or logic connections; and different types of pair patterns/rules, e.g., contrast patterns/rules, underlying-derivative patterns/rules, impact-contrast patterns/rules, impact-reversed patterns/rules, etc.;
- Mining cluster patterns/rules: discovering a cluster of patterns/rules that are coupled, e.g., progression between events over time;
- Graph-based pattern/rule analysis: analyzing the relations between patterns/rules based on their graph representation, relations modeling, and path selection, etc.;
- Tree-based pattern/rule analysis: analyzing the relations between patterns/rules based on their tree representation, relations modeling, and tree branch selection, etc.;
- Item/element contribution modeling: measuring the contribution of an item or element in a pattern/rule and a combined pattern/rule;
- Explicit pattern/rule relation learning: modeling pattern/rule relations based on explicit (direct, observable, attributed) relations;
- Implicit pattern/rule relation learning: modeling pattern/rule relations based on implicit (hidden, indirect, representation-based) relations;
- Pattern/rule selection: analyzing the relations between patterns/rules to select pattern subsets or item/element subsets;
- Actionable pattern/rule discovery: discovering patterns/rules that are actionable by quantifying the high-contributing elements and items;
 Shoujin Wang, Longbing Cao. Inferring Implicit Rules by Learning Explicit and Hidden Item Dependency. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(3): 935-946, 2020.
 Jingyu Shao, Junfu Yin, Wei Liu,, Longbing Cao. Mining actionable combined patterns of high utility and frequency. DSAA 2015: 1-10. BibTeX
 Jinjiu Li, Can Wang, Longbing Cao, Philip S. Yu. Efficient Selection of Globally Optimal Rules on Large Imbalanced Data Based on Rule Coverage Relationship Analysis, SDM 2013. BibTeX
 Wei Li, Longbing Cao, Dazhe Zhao. CRNN: Integrating classification rules into neural network, IJCNN 2013. BibTeX
 Longbing Cao. Combined Mining: Analyzing Object and Pattern Relations for Discovering and Constructing Complex but Actionable Patterns, WIREs Data Mining and Knowledge Discovery, 3(2): 140-155, 2013. BibTeX
 Longbing Cao, Huaifeng Zhang, Yanchang Zhao, Dan Luo, and Chengqi Zhang. Combined Mining: Discovering Informative Knowledge in Complex Data, IEEE Trans. SMC Part B, 41(3): 699 – 712, 2011. BibTeX
 Longbing Cao. Zhao Y., Zhang, C. Mining Impact-Targeted Activity Patterns in Imbalanced Data, IEEE Trans. on Knowledge and Data Engineering, 20(8): 1053-1066, 2008. BibTeX
 Yanchang Zhao, Huaifeng Zhang, Longbing Cao, and Chengqi Zhang. Combined Pattern Mining: from Learned Rules to Actionable Knowledge, LNCS 5360/2008, 393-403, 2008. BibTeX
 Huaifeng Zhang, Yanchang Zhao, Longbing Cao and Chengqi Zhang. Combined Association Rule Mining, PAKDD2008. BibTeX
 Longbing Cao. Coupling Learning of Complex Interactions, Journal of Information Processing and Management, 51(2): 167-186 (2015). BibTeX