1 Nat-Bijection: Bijections between natural numbers and other types 13 1.1 Type nat × nat . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2 Type nat + nat . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3 Type int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Type nat list . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5 Finite sets of naturals...

Design of Cellular Manufacturing System involves four major decisions: Cell formation (CF), Group layout (GL), Group scheduling (Gs) and Resource assignment (RA).  These problems should be regarded, concurrently, in order to obtain an optimal solution in a CM environment. In this paper a two stage heuristic procedure is proposed for CF and RA decisions problem. The solution approach contains a ...

Visualization and clustering of multivariate data are usually based on mutual distances of samples, measured by heuristic means such as the Euclidean distance of vectors of extracted features. Our recently developed methods remove this arbitrariness by learning to measure important differences. The effect is equivalent to changing the metric of the data space. It is assumed that variation of th...

A huge number of clustering methods have been applied to many different kinds of data set including multivariate images, such as magnetic resonance images and remote sensing images. However, not many methods include spatial information of the image data. In this tutorial, the major types of clustering techniques are summarized. Particular attention will be devoted to the extension of clustering...

A huge number of clustering methods have been applied to many different kinds of data set including multivariate images, such as magnetic resonance images (MRI) and remote sensing images. However, not many methods include spatial information of the image data. In this tutorial, the major types of clustering techniques are summarized. Particular attention will be devoted to the extension of clus...

MOTIVATION Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, model-based clustering assumes that the data is generated by a finite mixture of underlying pro...