Spectral clustering methods are claimed to possess ability to represent clusters of diverse shapes, densities etc.They constitute an approximation to graph cuts of various types (plain cuts, normalized cuts, ratio cuts).They are applicable to unweighted and weighted similarity graphs.We perform an evaluation of these capabilities for clustering tasks of increasing complexity.

In a former paper [1] the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we deal with a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. We state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.

In this paper we make a comparison of two NMF based techniques of dataset characterization: clustering and hulling. The characteristics of a dataset should be understood as describing the content of a data set through several characteristic representatives. Hulling (defined later) characterizes the data by saying that the data points are somewhere between the representatives, while clustering characterizes the data by saying that the data points are close to one or the other representative. The precision of such a characteristic will be measured as a deviation from the idea of characterization, i.e. the distance of the actual data points from the closest representatives in the case of clustering and from the interior of the hull spanned by the representatives. We show that for low-dimensional data the hull-based characterization precision is much better than in case of clustering. Clustering and hulling are two examples of sophisticated optimization problems. Evolutionary algorithms are an excellent tool for solving such problems. However, in the case of large, high-dimensional data sets, their usefulness decreases. In this paper, we discuss heuristics for hulling for massive data. We hope that it will inspire the creation of an effective evolutionary algorithm dedicated to solving such problems.

The paper presents an approach to knowledge integration coming from different databases. It is based on model tree construction from databases with both discrete and continuous attributes. The methodology of model trees is explained. Some information on implementation issues is given and preliminary results on a real dataset are presented.

In the literature, the optimization problem to identify a set of composite hypotheses H, which will yield the k largest P(H|Se ) where a composite hypothesis is an instantiation of all the nodes in the network except the evidence nodes [17] is of sig