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## A-Wardpβ: Effective hierarchical clustering using the Minkowski metric and a fast k-means initialisation

In this paper we make two novel contributions to hierarchical clustering. First, we introduce an anomalous pattern initialisation method for hierarchical clustering algorithms, called A-Ward, capable of substantially reducing the time they take to converge. This method generates an initial partition with a sufficiently large number of clusters. This allows the cluster merging process to start from this partition rather than from a trivial partition composed solely of singletons.

Our second contribution is an extension of the Ward and Ward*p* algorithms to the situation where the feature weight exponent can differ from the exponent of the Minkowski distance. This new method, called A-Ward*pβ*, is able to generate a much wider variety of clustering solutions. We also demonstrate that its parameters can be estimated reasonably well by using a cluster validity index.

We perform numerous experiments using data sets with two types of noise, insertion of noise features and blurring within-cluster values of some features. These experiments allow us to conclude: (i) our anomalous pattern initialisation method does indeed reduce the time a hierarchical clustering algorithm takes to complete, without negatively impacting its cluster recovery ability; (ii) A-Ward*pβ* provides better cluster recovery than both Ward and Ward*p*.

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Recently, a three-stage version of K-Means has been introduced, at which not only clusters and their centers, but also feature weights are adjusted to minimize the summary p-th power of the Minkowski p-distance between entities and centroids of their clusters. The value of the Minkowski exponent p appears to be instrumental in the ability of the method to recover clusters hidden in data. This paper advances into the problem of finding the best p for a Minkowski metric-based version of K-Means, in each of the following two settings: semi-supervised and unsupervised. This paper presents experimental evidence that solutions found with the proposed approaches are sufficiently close to the optimum.

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Over the last few decades, performance-based funding models of universities have been introduced and have made universities build and implement different strategies to enable them to compete and be viable in changing circumstances. In turn, national governments are focused on providing universities with more opportunities to run efficient programmes that advance higher education. This paper includes a detailed review of various taxonomies for structuring university. More importantly, it develops a typology of higher education institutions that is relevant for the Russian context. The Ward method is used to cluster universities on the basis of university distinctions in terms of the availability of resources, education, and research and development. This typology of universities is verified by assessing their efficiency score gained from modified Data Envelopment Analysis,incorporating universities' heterogeneity. Finally, the paper gives a decision tree for classifying universities bearing in mind their diversity. It might be expanded for abroader set of inputs and outputs, namely external projectbased research funding modes and cooperation between universities and industry to pursue the development of innovation. The results can be used for shaping targeted policies aimed at particular university groups

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Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

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It is well-known that the class of sets that can be computed by polynomial size circuits is equal to the class of sets that are polynomial time reducible to a sparse set. It is widely believed, but unfortunately up to now unproven, that there are sets in EXPNP, or even in EXP that are not computable by polynomial size circuits and hence are not reducible to a sparse set. In this paper we study this question in a more restricted setting: what is the computational complexity of sparse sets that are *selfreducible*? It follows from earlier work of Lozano and Torán (in: Mathematical systems theory, 1991) that EXPNP does not have sparse selfreducible hard sets. We define a natural version of selfreduction, tree-selfreducibility, and show that NEXP does not have sparse tree-selfreducible hard sets. We also construct an oracle relative to which all of EXP is reducible to a sparse tree-selfreducible set. These lower bounds are corollaries of more general results about the computational complexity of sparse sets that are selfreducible, and can be interpreted as super-polynomial circuit lower bounds for NEXP.