Laplacian normalization for deriving thematic fuzzy clusters with an additive spectral approach
This paper presents a further investigation into computational properties of a novel fuzzy additive spectral clustering method, Fuzzy Additive Spectral clustering (FADDIS), recently introduced by authors. Specifically, we extend our analysis to ‘difficult’ data structures from the recent literature and develop two synthetic data generators simulating affinity data of Gaussian clusters and genuine additive similarity data, with a controlled level of noise. The FADDIS is experimentally verified on these data in comparison with two state-of-the-art fuzzy clustering methods. The claimed ability of FADDIS to help in determining the right number of clusters is experimentally tested, and the role of the pseudo-inverse Laplacian data transformation in this is highlighted. A potentially useful extension of the method to biclustering is introduced.
The issue of determining “the right number of clusters” in K-Means has attracted considerable interest, especially in the recent years. Cluster intermix appears to be a factor most affecting the clustering results. This paper proposes an experimental setting for comparison of different approaches at data generated from Gaussian clusters with the controlled parameters of between- and within-cluster spread to model cluster intermix. The setting allows for evaluating the centroid recovery on par with conventional evaluation of the cluster recovery. The subjects of our interest are two versions of the “intelligent” K-Means method, ik-Means, that find the “right” number of clusters by extracting “anomalous patterns” from the data one-by-one. We compare them with seven other methods, including Hartigan’s rule, averaged Silhouette width and Gap statistic, under different between- and within-cluster spread-shape conditions. There are several consistent patterns in the results of our experiments, such as that the right K is reproduced best by Hartigan’s rule – but not clusters or their centroids. This leads us to propose an adjusted version of iK-Means, which performs well in the current experiment setting.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
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
The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.
Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.