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Conference Papers Year : 2012

## Extending Set-Based Dualization: Application to Pattern Mining

Lhouari Nourine
Jean-Marc Petit

#### Abstract

Dualization problems have been intensively studied in combinatorics, AI and pattern mining for years. Roughly speaking, for a partial order $(P,\preceq)$ and some monotonic predicate $Q$ over $P$, the dualization consists in identifying all maximal elements of $P$ verifying $Q$ from all minimal elements of $P$ not verifying $Q$, and vice versa. The dualization is equivalent to the enumeration of minimal transversal of hypergraphs whenever $(P,\preceq)$ is a boolean lattice. In the setting of interesting pattern mining in databases, $P$ represents a set of patterns and whenever $P$ is isomorphic to a boolean lattice, the pattern mining problem is said to be \emph{representable as sets}. The class of such problems is denoted by \RAS. In this paper, we introduce a \emph{weak representation as sets} for pattern mining problems which extends the \RAS\ class to a wider and significantly larger class of problems, called \WRAS. We also identify \EWRAS, an \emph{efficient} subclass of \WRAS\ for which the dualization problem is still quasi-polynomial. Finally, we point out that one representative pattern mining problem known not to be in \RAS, namely \emph{frequent rigid sequences with wildcard}, belongs to \EWRAS. These new classes might prove to have large impact in unifying existing pattern mining approaches.

#### Domains

Computer Science [cs]

### Dates and versions

hal-01353000 , version 1 (10-08-2016)

### Identifiers

• HAL Id : hal-01353000 , version 1
• DOI :

### Cite

Lhouari Nourine, Jean-Marc Petit. Extending Set-Based Dualization: Application to Pattern Mining. ECAI 2012, Aug 2012, Montpellier, France. pp.630-635, ⟨10.3233/978-1-61499-098-7-630⟩. ⟨hal-01353000⟩

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