MPI für biologische Kybernetik / Biologische Kybernetik |
|Multi-way set enumeration in real-valued tensors|
|Authors:||Georgii, E.; Tsuda, K.; Schölkopf, B.|
|Editors:||Ding, C.; Li, T.|
|Date of Publication (YYYY-MM-DD):||2009-06|
|Title of Proceedings:||Proceedings of the 2nd Workshop on Data Mining using Matrices and Tensors (DMMT 2009)|
|Intended Educational Use:||No|
|Abstract / Description:||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. An n-set pattern consists of
specific subsets of the n instance sets such that all possible n-ary associations between the corresponding instances are
observed. This provides a higher-level view of the data, revealing associative relationships between groups of
instances. Here we generalize this approach in two aspects. First, we tolerate missing observations to a certain degree, thet means we
are also interested in n-sets where most (although not all) of the possible combinations have been recorded in the data.
Second, we take association weights into account. More precisely, we propose a method to enumerate all n-sets
that satisfy a minimum treshold with respect to the average association weight. Non-observed associations
obtain by default a weight of zero. Technically, we solve the enumeration task using a reverse search strategy,
which allows for effective pruning of 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 data sets from different domains.
|External Publication Status:||published|
|Communicated by:||Holger Fischer|
|Affiliations:||MPI für biologische Kybernetik/Empirical Inference (Dept. Schölkopf)|
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