Multi-way set enumeration in weight tensors

Abstract

The analysis of n-ary relations receives attention in many different fields, for instance biology, web mining, and social studies. In the basic setting, there are n sets of instances, and each observation associates n instances, one from each set. A common approach to explore these n-way data is the search for n-set patterns, the n-way equivalent of itemsets. More precisely, an n-set pattern consists of specific subsets of the n instance sets such that all possible associations between the corresponding instances are observed in the data. In contrast, traditional itemset mining approaches consider only two-way data, namely items versus transactions. The n-set patterns provide a higher-level view of the data, revealing associative relationships between groups of instances. Here, we generalize this approach Learn (2011) 82: 123-155 in two respects. First, we tolerate missing observations to a certain degree, that means we are also interested in n-sets where most (although not all) of the possible associations have been recorded in the data. Second, we take association weights into account. In fact, we propose a method to enumerate all n-sets that satisfy a minimum threshold with respect to the average association weight. Technically, we solve the enumeration task using a reverse search strategy, which allows for effective pruning of the search space. In addition, our algorithm provides a ranking of the solutions and can consider further constraints. We show experimental results on artificial and real-world datasets from different domains.

Bigfoot Climbing the Hill with ILP to Grow Patterns in Fuzzy Tensors

“…It enforces as well a closedness constraint, which discards all strict sub-patterns of a valid pattern, and can prune the search with additional relevance constraints that every pattern must satisfy, e. g., the minimal size constraint -"involving at least γ i ∈ N elements of D i ". DCE [6] is the only other complete algorithm to mine patterns in fuzzy tensors. Cerf and Meira [3] show that DCE's definition catches patterns that are not sub-patterns of any pattern planted in a synthetic dataset, even if there is little noise affecting that dataset.…”

“…Constraint (5) forces the returned pattern X to be a super-pattern of the grown fragment F , i. e., X ⊇ F . Constraint (6) forces the returned pattern…”

Decision rules extraction from data stream in the presence of changing context for diabetes treatment

“…Graph-based methods were used for rules induction [54,58], clustering [23], substructure detection [16,34]. However, for such methods, there is still a need for developing proper forgetting mechanisms and a method for applying incremental learning.…”

“…The first approach is the OLIN algorithm, which applies graphs to represent rules [42]. The second one is the work of Georgii et al who use a graph as a space search and an inverse search method for finding clusters [23]. Last but not least, the presented approach is strongly influenced by Pawlak's flow graphs [52].…”

Triadic Formal Concept Analysis and triclustering: searching for optimal patterns

“…There are several recent efficient algorithms for mining closed ternary sets (triconcepts) and even more general algorithms than Trias. Thus, Data-Peeler (Cerf et al 2009) is able to mine n-ary formal concepts and its descendant mines fault-tolerant n-sets (Cerf et al 2013); the latter was compared with DCE algorithm for fault-tolerant n-sets mining from Georgii et al (2011). The paper (Spyropoulou et al 2014) generalises n-ary formal concept mining to multi-relational setting in databases.…”