Data mining, hypergraph transversals, and machine learning (extended abstract)

Abstract

Several data mining problems can be formulated as problems of finding maximally specific sentences that are interesting in a database. We first show that this problem has a close relationship with the hypergraph transversal problem. We then analyze two algorithms that have been previously used in data mining, proving upper bounds on their complexity. The first algorithm is useful when the maximally specific interesting sentences are "small". We show that this algorithm can also be used to efficiently solve a special case of the hypergraph transversal problem, improving on previous results. The second algorithm utilizes a subroutine for hypergraph transversals, and is applicable in more general situations, with complexity close to a lower bound for the problem. We also relate these problems to the model of exact learning in computational learning theory, and use the correspondence to derive some corollaries.

Output-Sensitive Algorithms for Enumerating Minimal Transversals for Some Geometric Hypergraphs

“…When V is a finite set of points and each object in F is an arbitrary finite subset of V, we obtain the well-known hypergraph transversal or dualization problem [2], which calls for finding all minimal hitting sets for a given hypergraph G ⊆ 2 V , defined on a finite set of vertices V. Denote by Tr(G) the set of all minimal hitting sets of G, also known as the transversal hypergraph of G. The problem of finding Tr(G) has received considerable attention in the literature (see, e.g., [3,12,13,19,29,31]), since it is known to be polynomially or quasi-polynomially equivalent with many problems in various areas, such as artificial intelligence (e.g., [12,24]), database theory (e.g., [30]), distributed systems (e.g., [23]), machine learning and data mining (e.g., [1,7,20]), mathematical programming (e.g., [5,25]), matroid theory (e.g., [26]), and reliability theory (e.g., [9]). …”

The Minimum Consistent Subset Cover Problem: A Minimization View of Data Mining

“…As a first approach, maximal frequent patterns [9] and closed frequent patterns [18] have been introduced. These subsets of frequent patterns are more concise and allow to derive all the frequent patterns.…”

Computational Science and Data Mining

“…However, global approaches more genuinely belong to Machine Learning, where the assumption of a global generative process behind the data is better supported. Most prominent example of work in the local tradition is the research on association rule mining [13,4,1,15]. We shall be concerned in this paper with the local problem.…”

“…A direct application of computational models developed for Machine Learning is therefore not possible, for at least two reasons. First, a Data Mining task may consist of finding many weak predictors in a hypothesis space whereas in Machine Learning one strong predictor is normally sought [4]. This is the so-called local-global problem [13].…”