Path finding on a spherical SOM using the distance transform and floodplain analysis

Data visualization has become an important tool for analyzing very complex data. In particular, spatial visualization enables users to view data in a intuitive manner. It has typically been used to externalize clusters and their relationships which exist in highly complex multidimensional data. We envisage that not only cluster formation and relationships but also other types of information, such as temporal changes of datum, can be extracted through the spatialization. In this paper, we investigate an application of trajectory/path analysis carried out using a Self-Organizing Map as a spatialization method. We propose an application of distance transformations to the Geodesic Self-Organizing Map. This new approach allows a user to visually inspect the trajectory of multidimensional knowledge pieces on a two-dimensional space. The trajectories discovered through this approach are essentially the shortest paths between two points on the Self-Organizing Map. However, those paths might go outside of the input dataspace due to the connectivity of neurons imposed by the grid structure. We also present a method to find the shortest path, which falls within the input dataspace using simple floodplain analysis

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

Path finding on a spherical self-organizing map using distance transformations

Spatialization methods create visualizations that allow users to analyze high-dimensional data in an intuitive manner and facilitates the extraction of meaningful information. Just as geographic maps are simpli ed representations of geographic spaces, these visualizations are esssentially maps of abstract data spaces that are created through dimensionality reduction. While we are familiar with geographic maps for path planning/ nding applications, research into using maps of high-dimensional spaces for such purposes has been largely ignored. However, literature has shown that it is possible to use these maps to track temporal and state changes within a high-dimensional space. A popular dimensionality reduction method that produces a mapping for these purposes is the Self-Organizing Map. By using its topology preserving capabilities with a colour-based visualization method known as the U-Matrix, state transitions can be visualized as trajectories on the resulting mapping. Through these trajectories, one can gather information on the transition path between two points in the original high-dimensional state space. This raises the interesting question of whether or not the Self-Organizing Map can be used to discover the transition path between two points in an n-dimensional space. In this thesis, we use a spherically structured Self-Organizing Map called the Geodesic Self-Organizing Map for dimensionality reduction and the creation of a topological mapping that approximates the n-dimensional space. We rst present an intuitive method for a user to navigate the surface of the Geodesic SOM. A new application of the distance transformation algorithm is then proposed to compute the path between two points on the surface of the SOM, which corresponds to two points in the data space. Discussions will then follow on how this application could be improved using some form of surface shape analysis. The new approach presented in this thesis would then be evaluated by analyzing the results of using the Geodesic SOM for manifold embedding and by carrying out data analyses using carbon dioxide emissions data

Path finding on a spherical self-organizing map using distance transformations

Spatialization methods create visualizations that allow users to analyze high-dimensional data in an intuitive manner and facilitates the extraction of meaningful information. Just as geographic maps are simpli ed representations of geographic spaces, these visualizations are esssentially maps of abstract data spaces that are created through dimensionality reduction. While we are familiar with geographic maps for path planning/ nding applications, research into using maps of high-dimensional spaces for such purposes has been largely ignored. However, literature has shown that it is possible to use these maps to track temporal and state changes within a high-dimensional space. A popular dimensionality reduction method that produces a mapping for these purposes is the Self-Organizing Map. By using its topology preserving capabilities with a colour-based visualization method known as the U-Matrix, state transitions can be visualized as trajectories on the resulting mapping. Through these trajectories, one can gather information on the transition path between two points in the original high-dimensional state space. This raises the interesting question of whether or not the Self-Organizing Map can be used to discover the transition path between two points in an n-dimensional space. In this thesis, we use a spherically structured Self-Organizing Map called the Geodesic Self-Organizing Map for dimensionality reduction and the creation of a topological mapping that approximates the n-dimensional space. We rst present an intuitive method for a user to navigate the surface of the Geodesic SOM. A new application of the distance transformation algorithm is then proposed to compute the path between two points on the surface of the SOM, which corresponds to two points in the data space. Discussions will then follow on how this application could be improved using some form of surface shape analysis. The new approach presented in this thesis would then be evaluated by analyzing the results of using the Geodesic SOM for manifold embedding and by carrying out data analyses using carbon dioxide emissions data

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

Indexability, concentration, and VC theory

Degrading performance of indexing schemes for exact similarity search in high dimensions has long since been linked to histograms of distributions of distances and other 1-Lipschitz functions getting concentrated. We discuss this observation in the framework of the phenomenon of concentration of measure on the structures of high dimension and the Vapnik-Chervonenkis theory of statistical learning.Comment: 17 pages, final submission to J. Discrete Algorithms (an expanded, improved and corrected version of the SISAP'2010 invited paper, this e-print, v3

Path finding on a spherical SOM using the distance transform and floodplain analysis

Data visualization has become an important tool for analyzing very complex data. In particular, spatial visualization enables users to view data in a intuitive manner. It has typically been used to externalize clusters and their relationships which exist in highly complex multidimensional data. We envisage that not only cluster formation and relationships but also other types of information, such as temporal changes of datum, can be extracted through the spatialization. In this paper, we investigate an application of trajectory/path analysis carried out using a Self-Organizing Map as a spatialization method. We propose an application of distance transformations to the Geodesic Self-Organizing Map. This new approach allows a user to visually inspect the trajectory of multidimensional knowledge pieces on a two-dimensional space. The trajectories discovered through this approach are essentially the shortest paths between two points on the Self-Organizing Map. However, those paths might go outside of the input dataspace due to the connectivity of neurons imposed by the grid structure. We also present a method to find the shortest path, which falls within the input dataspace using simple floodplain analysis

A unified learning framework for content based medical image retrieval using a statistical model

AbstractThis paper presents a unified learning framework for heterogeneous medical image retrieval based on a Full Range Autoregressive Model (FRAR) with the Bayesian approach (BA). Using the unified framework, the color autocorrelogram, edge orientation autocorrelogram (EOAC) and micro-texture information of medical images are extracted. The EOAC is constructed in HSV color space, to circumvent the loss of edges due to spectral and chromatic variations. The proposed system employed adaptive binary tree based support vector machine (ABTSVM) for efficient and fast classification of medical images in feature vector space. The Manhattan distance measure of order one is used in the proposed system to perform a similarity measure in the classified and indexed feature vector space. The precision and recall (PR) method is used as a measure of performance in the proposed system. Short-term based relevance feedback (RF) mechanism is also adopted to reduce the semantic gap. The Experimental results reveal that the retrieval performance of the proposed system for heterogeneous medical image database is better than the existing systems at low computational and storage cost

The use of modern polymer materials and wood in the construction of buildings in the form of geodesic domes

Spherical structures have been used by mankind since time immemorial in religious and public buildings, as well as in engineering structures. With the development of lightweight design and construction, non-standard architectural and planning solutions are used. More and more frequently they are being successfully implemented in private home projects and becoming a fact of everyday life. This may be explained by certain advantages of the form, as well as by the opportunities offered to the construction industry by the age of new materials and technologies for the works performance. The functional and architectural-structural design of round-shaped buildings in the form of geodesic domes will allow creating comfortable, cost-effective, energy-efficient and environmentally expedient conditions for human habitation taking into account the shortage of land areas and increased demand for alternative housing options due to the environmental situation around the world. This article analyzes the experience of building spherical buildings of different types and scales. The authors present the results of research carried out in the field of the geodesic dome design improvement with the use of wood and polymer materials