Analysis of Data Clusters Obtained by Self-Organizing Methods

The self-organizing methods were used for the investigation of financial market. As an example we consider data time-series of Dow Jones index for the years 2002-2003 (R. Mantegna, cond-mat/9802256). In order to reveal new structures in stock market behavior of the companies drawing up Dow Jones index we apply SOM (Self-Organizing Maps) and GMDH (Group Method of Data Handling) algorithms. Using SOM techniques we obtain SOM-maps that establish a new relationship in market structure. Analysis of the obtained clusters was made by GMDH.Comment: 10 pages, 4 figure

Data structures

We discuss data structures and their methods of analysis. In particular, we treat the unweighted and weighted dictionary problem, self-organizing data structures, persistent data structures, the union-find-split problem, priority queues, the nearest common ancestor problem, the selection and merging problem, and dynamization techniques. The methods of analysis are worst, average and amortized case

Growing Self-Organizing Maps for Data Analysis

Currently, there exist many research areas that produce large multivariable datasets that are difficult to visualize in order to extract useful information. Kohonen self organizing maps have been used successfully in the visualization and analysis of multidimensional data. In this work, a projection technique that compresses multidimensional datasets into two dimensional space using growing self-organizing maps is described. With this embedding scheme, traditional Kohonen visualization methods have been implemented using growing cell structures networks. New graphical map display have been compared with Kohonen graphs using two groups of simulated data and one group of real multidimensional data selected from a satellite scene

Self-Organizing Legal Systems: Precedent and Variation in Bankruptcy

Models of legal ordering are frequently hierarchical. These models do not explain two prominent realities: (1) variation in the content of a legal system, and (2) patterns of non-hierarchical ordering that we observe. As a supplement to hierarchical explanations of legal order, this Article, drawing from physical and social science research on complex systems, offers a self-organizing model. The self-organizing model focuses on variation in the content of legal systems and attempts to explain the relationship between that variation and patterns of ordering. The self-organizing model demonstrates that variation and ordering are not opposite categories, but rather constitute one continuous phenomenon. Working with bankruptcy data and institutions, this Article describes self-organizing structures as overlapping networks of legal and extra-legal actors, and self-organizing dynamics as involving the twin processes of form innovation and norm emergence. This Article adduces empirical evidence (including a substantial case study and statistical analysis of a quantitative database) showing that bankruptcy is a self-organizing system. Finally, this Article suggests that self-organization may state a general theory of trial court behavior, and that the self-organizing model may illuminate legal research in areas such as discretion, doctrine, and legal change

Topological Chaos in a Three-Dimensional Spherical Fluid Vortex

In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are techniques which exploit the topology of dynamically invariant structures. However, the path to extending many such topological techniques to three dimensions is filled with roadblocks that prevent their application to a wider variety of physical systems. Here, we overcome these roadblocks and successfully analyze a realistic model of 3D fluid advection, by extending the homotopic lobe dynamics (HLD) technique, previously developed for 2D area-preserving dynamics, to 3D volume-preserving dynamics. We start with numerically-generated finite-time chaotic-scattering data for particles entrained in a spherical fluid vortex, and use this data to build a symbolic representation of the dynamics. We then use this symbolic representation to explain and predict the self-similar fractal structure of the scattering data, to compute bounds on the topological entropy, a fundamental measure of mixing, and to discover two different mixing mechanisms, which stretch 2D material surfaces and 1D material curves in distinct ways.Comment: 14 pages, 11 figure

How do we think : Modeling Interactions of Perception and Memory

A model of artificial perception based on self-organizing data into hierarchical structures is generalized to abstract thinking. This approach is illustrated using a two-level perception model, which is justified theoretically and tested empirically. The model can be extended to an arbitrary number of levels, with abstract concepts being understood as patterns of stable relationships between data aggregates of high representation levels

Median topographic maps for biomedical data sets

Median clustering extends popular neural data analysis methods such as the self-organizing map or neural gas to general data structures given by a dissimilarity matrix only. This offers flexible and robust global data inspection methods which are particularly suited for a variety of data as occurs in biomedical domains. In this chapter, we give an overview about median clustering and its properties and extensions, with a particular focus on efficient implementations adapted to large scale data analysis

Business Ecosystem & Data Ecosystem: Introduction to International Workshop on Big Data for Business Ecosystems

The possibilities of integrating business ecosystems and data ecosystems are considered. Their interaction is considered in the aspect of information exchange in open complex sociotechnical self-organizing systems. Modeling the interaction in such network structures makes it possible to determine the mechanisms of self-regulation that allow to ensure the sustainability of the ecosystem. Two models of network interaction are given, based on the analogy with information exchange in the models of production systems, presented as holon systems integrated with agents