Geometric and combinatorial tiles in 0-1 data

Authors:
Aristides Gionis;Heikki Mannila;Jouni K. Seppänen
Affiliations:
Helsinki Institute for Information Technology, University of Helsinki and Helsinki University of Technology, Finland;Helsinki Institute for Information Technology, University of Helsinki and Helsinki University of Technology, Finland;Helsinki Institute for Information Technology, University of Helsinki and Helsinki University of Technology, Finland
Venue:
PKDD '04 Proceedings of the 8th European Conference on Principles and Practice of Knowledge Discovery in Databases
Year:
2004

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Abstract

In this paper we introduce a simple probabilistic model, hierarchical tiles, for 0-1 data. A basic tile (X,Y,p) specifies a subset X of the rows and a subset Y of the columns of the data, i.e., a rectangle, and gives a probability p for the occurrence of 1s in the cells of X × Y. A hierarchical tile has additionally a set of exception tiles that specify the probabilities for subrectangles of the original rectangle. If the rows and columns are ordered and X and Y consist of consecutive elements in those orderings, then the tile is geometric; otherwise it is combinatorial. We give a simple randomized algorithm for finding good geometric tiles. Our main result shows that using spectral ordering techniques one can find good orderings that turn combinatorial tiles into geometric tiles. We give empirical results on the performance of the methods.