12746246
JRV: an interactive tool for data mining visualization
In this paper, we demonstrate JRV, a new data mining visualization tool for the knowledge discovery process where the user and computer can cooperate with each other. First, the computer can be instructed by the user interactively to compute values of several evaluation functions. Then, the user can take advantage of domain knowledge and assess the intermediate results obtained. Furthermore, by providing effective and efficient data visualization, the pattern recognition capacities of users can be greatly improved. Instead of being limited to two attributes at a given time in independence diagrams, this novel tool will allow simultaneous analyses of multiple attribute dependencies using four different drawing panels. Also, by utilizing the existing techniques of data visualization, we design a general model which can handle both categorical and numerical attributes in an intuitive way. With this model, we can identify patterns of interests efficiently. Through actual examples, we show that it might help users to find novel attribute relationships. This work is supported by NIH grant #RO1-CA98932-01.
1796961
Dynamically Constructing Classification Rules with Visualization Techniques
11260681
Mining Multi-dimensional Data with Visualization Techniques
This paper describes a method to generate classification rules by using an interactive multidimensional data visualization and classification tool, called PolyCluster. PolyCluster is a system that adopts state-of-the-art algorithms for data visualization and integrates human domain knowledge into the construction process of classification rules. In addition, PolyCluster proposes a pair of novel and robust measurements, called the Average External Connecting Distance and the Average Internal Connecting Distance to evaluate the quality of the induced clusters. Experimental evaluation shows that PolyCluster is a visual-based approach that offers numerous improvements over previous visual-based techniques.
36089150
Hamiltonicity and circular distance two labellings
Abstract A k -circular distance two labelling (or k -c-labelling) of a graph G is a vertex-labelling such that the circular difference ( mod k ) of the labels is at least two for adjacent vertices, and at least one for vertices at distance two. Given G , denote σ(G) the minimum k for which there exists a k -c-labelling of G . Suppose G has n vertices, we prove σ(G)⩽n if G c is Hamiltonian; and σ(G)=n+p v (G c ) otherwise, where p v (G) is the path covering number of G . We give exact values of σ(G) for some families of graphs such that G c is Hamiltonian, and discuss injective k -c-labellings especially for joins and unions of graphs.
18107138
A Framework for Web-Based Interactive Applications of High-Resolution 3D Medical Image Data
With the advances in medical imaging devices, large volumes of high-resolution 3D medical image data have been produced. These high-resolution 3D data are very large in size, and severely stress storage systems and networks. Most existing Web-based 3D medical image interactive applications therefore deal with only low- or medium-resolution image data. While it is possible to download the whole 3D high-resolution image data from the server and perform the image visualization and analysis at the client site, such an alternative is infeasible when the high-resolution data are very huge, and many users concurrently access the server. In this paper, we propose a novel framework for Web-based interactive applications of high-resolution 3D medical image data. Specifically, we first partition the whole 3D data into buckets, and then compress each bucket separately. We also propose an indexing structure for these buckets to efficiently support typical queries such as 3D slicer and region of interest (ROI), and only the relevant buckets are transmitted instead of the whole high-resolution 3D medical image data. Furthermore, in order to better support concurrent accesses and to improve the average response time, we also propose some techniques for bucket group access on the server side and incremental transmission. Our experimental study based on a human brain MRI data set indicates that the proposed framework can significantly reduce storage and communication requirements, and can enable real-time interaction with remote high-resolution 3D medical image data for many concurrent users
35821065
Criteria for asymptotic stability of a class of discrete systems with multiple independent variables
This paper investigates the problem of asymptotic stability for a class of linear shift-invariant discrete systems with multiple independent variables. We first establish the equivalence of this problem and the problem of robust stability for a class of ordinary linear shift-varying discrete systems with the matrix uncertainty set defined by the coefficient matrices of the original system. On the basis of this equivalence, by using the variational method and the Lyapunov Second Method, necessary and sufficient conditions for asymptotic stability are obtained in different forms for the class of systems considered in the present paper. The parametric classes of Lyapunov functions which define the necessary and sufficient conditions of asymptotic stability are determined. We use the piecewise linear polyhedral Lyapunov functions of the infinity vector norm type to derive an algebraic criterion for asymptotic stability of the given class of discrete systems in the form of solvability conditions of a set of matrix equations.
16699960
Circular chromatic number for iterated Mycielski graphs
Abstract For a graph G , let M( G ) denote the Mycielski graph of G . The t th iterated Mycielski graph of G , M t ( G ), is defined recursively by M 0 ( G )= G , and M t ( G )=M(M t −1 ( G )) for t ⩾1. Let χ c ( G ) denote the circular chromatic number of G . We prove two main results: (1) If G has a universal vertex x , then χ c (M( G ))= χ (M( G )) if χ c (G−x)>χ(G)− 1 2 and G is not a star, otherwise χ c ( M (G))=χ( M (G))− 1 2 ; and (2) χ c (M t ( K m ))= χ (M t ( K m )) if m ⩾2 t −1 +2 t −2 and t ⩾2.
14012169
Efficient k nearest neighbor queries on remote spatial databases using range estimation
We propose a k-NN query processing algorithm that uses one or more window queries to retrieve the nearest neighbors of a given query point. We also propose two different methods to estimate the ranges to be used by the window queries. Each range estimation method requires different statistical knowledge about the spatial databases. Our experiments on the TIGER data allow us to study the behavior of the proposed algorithm using different range estimation methods. Apart from not requiring direct access to the spatial indices, the window queries used in the proposed algorithm can be easily supported by non-spatial database systems containing spatial objects.