Effects of Irregular Topology in Spherical Self-Organizing Maps

We explore the effect of different topologies on properties of self-organizing maps (SOM). We suggest several diagnostics for measuring topology-induced errors in SOM and use these in a comparison of four different topologies. The results show that SOM is less sensitive to localized irregularities in the network structure than the literature may otherwise suggest. Further, the results support the use of spherical topologies as a solution to the boundary problem in traditional SOM.

Self-Organizing Maps and the US Urban Spatial Structure

This article considers urban spatial structure in US cities using a multi- dimensional approach. We select six key variables (commuting costs, den- sity, employment dispersion/concentration, land-use mix, polycentricity and size) from the urban literature and define measures to quantify them. We then apply these measures to 359 metropolitan areas from the 2000 US Census. The adopted methodological strategy combines two novel techniques for the social sciences to explore the existence of relevant pat- terns in such multi-dimensional datasets. Geodesic self-organizing maps (SOM) are used to visualize the whole set of information in a meaningful way, while the recently developed clustering algorithm of the max-p is applied to draw boundaries within the SOM and analyze which cities fall into each of them. JEL C45, R0, R12, R14. Keywords Urban spatial structure, self-organizing maps, US metropolitan areas

Spherical similarity explorer for comparative case analysis

Comparative Case Analysis (CCA) is an important tool for criminal investigation and crime theory extraction. It analyzes the commonalities and differences between a collection of crime reports in order to understand crime patterns and identify abnormal cases. A big challenge of CCA is the data processing and exploration. Traditional manual approach can no longer cope with the increasing volume and complexity of the data. In this paper we introduce a novel visual analytics system, Spherical Similarity Explorer (SSE) that automates the data processing process and provides interactive visualizations to support the data exploration. We illustrate the use of the system with uses cases that involve real world application data and evaluate the system with criminal intelligence analysts

Spherical similarity explorer for comparative case analysis

Comparative Case Analysis (CCA) is an important tool for criminal investigation and crime theory extraction. It analyzes the commonalities and differences between a collection of crime reports in order to understand crime patterns and identify abnormal cases. A big challenge of CCA is the data processing and exploration. Traditional manual approach can no longer cope with the increasing volume and complexity of the data. In this paper we introduce a novel visual analytics system, Spherical Similarity Explorer (SSE) that automates the data processing process and provides interactive visualizations to support the data exploration. We illustrate the use of the system with uses cases that involve real world application data and evaluate the system with criminal intelligence analysts

Document Collection Visualization and Clustering Using An Atom Metaphor for Display and Interaction

Visual Data Mining have proven to be of high value in exploratory data analysis and data mining because it provides an intuitive feedback on data analysis and support decision-making activities. Several visualization techniques have been developed for cluster discovery such as Grand Tour, HD-Eye, Star Coordinates, etc. They are very useful tool which are visualized in 2D or 3D; however, they have not simple for users who are not trained. This thesis proposes a new approach to build a 3D clustering visualization system for document clustering by using k-mean algorithm. A cluster will be represented by a neutron (centroid) and electrons (documents) which will keep a distance with neutron by force. Our approach employs quantified domain knowledge and explorative observation as prediction to map high dimensional data onto 3D space for revealing the relationship among documents. User can perform an intuitive visual assessment of the consistency of the cluster structure

A review of data visualization: opportunities in manufacturing sequence management.

Data visualization now benefits from developments in technologies that offer innovative ways of presenting complex data. Potentially these have widespread application in communicating the complex information domains typical of manufacturing sequence management environments for global enterprises. In this paper the authors review the visualization functionalities, techniques and applications reported in literature, map these to manufacturing sequence information presentation requirements and identify the opportunities available and likely development paths. Current leading-edge practice in dynamic updating and communication with suppliers is not being exploited in manufacturing sequence management; it could provide significant benefits to manufacturing business. In the context of global manufacturing operations and broad-based user communities with differing needs served by common data sets, tool functionality is generally ahead of user application

Steklov Spectral Geometry for Extrinsic Shape Analysis

We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification. Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable property of this operator is that it completely encodes volumetric geometry. We use the boundary element method (BEM) to discretize the operator, accelerated by hierarchical numerical schemes and preconditioning; this pipeline allows us to solve eigenvalue and linear problems on large-scale meshes despite the density of the Dirichlet-to-Neumann discretization. We further demonstrate that our operators naturally fit into existing frameworks for geometry processing, making a shift from intrinsic to extrinsic geometry as simple as substituting the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde