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320
Towards a General Theory of Topological Maps
 Artificial Intelligence
, 2002
"... We present a general theory of topological maps whereby sensory input, topological and local metrical information are combined to define the topological maps explaining such information. Topological maps correspond to the minimal models of an axiomatic theory describing the relationships between ..."
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Cited by 67 (9 self)
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We present a general theory of topological maps whereby sensory input, topological and local metrical information are combined to define the topological maps explaining such information. Topological maps correspond to the minimal models of an axiomatic theory describing the relationships between the different sources of information explained by a map. We use a circumscriptive theory to specify the minimal models associated with this representation.
Graph drawing by stress majorization
 GRAPH DRAWING
, 2004
"... One of the most popular graph drawing methods is based of achieving graphtheoretic target ditsances. This method was used by Kamada and Kawai [15], who formulated it as an energy optimization problem. Their energy is known in the multidimensional scaling (MDS) community as the stress function. In th ..."
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Cited by 66 (11 self)
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One of the most popular graph drawing methods is based of achieving graphtheoretic target ditsances. This method was used by Kamada and Kawai [15], who formulated it as an energy optimization problem. Their energy is known in the multidimensional scaling (MDS) community as the stress function. In this work, we show how to draw graphs by stress majorization, adapting a technique known in the MDS community for more than two decades. It appears that majorization has advantages over the technique of Kamada and Kawai in running time and stability. We also present a few extensions to the basic energy model which can improve layout quality and computation speed in practice. Majorizationbased optimization is essential to these extensions.
GPS free coordinate assignment and routing in wireless sensor networks
 In IEEE INFOCOM
, 2005
"... Abstract — In this paper we consider the problem of constructing a coordinate system in a sensor network where location information is not available. To this purpose we introduce the Virtual Coordinate assignment protocol (VCap) which defines a virtual coordinate system based on hop distances. As co ..."
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Cited by 54 (0 self)
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Abstract — In this paper we consider the problem of constructing a coordinate system in a sensor network where location information is not available. To this purpose we introduce the Virtual Coordinate assignment protocol (VCap) which defines a virtual coordinate system based on hop distances. As compared to other approaches, VCap is simple and have very little requirements in terms of communication and memory overheads. We compare by simulations the performances of greedy routing using our virtual coordinate system with the one using the physical coordinates. Results show that the virtual coordinate system can be used to efficently support geographic routing. Index Terms — Wireless sensor network, virtual coordinates, hop based greedy routing, performance analysis, simulations I.
Binary Analysis and OptimizationBased Normalization of Gene Expression Data
, 2002
"... Motivation: Most approaches to gene expression analysis use realvalued expression data, produced by highthroughput screening technologies, such as microarrays. Often, some measure of similarity must be computed in order to extract meaningful information from the observed data. The choice of this si ..."
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Cited by 53 (6 self)
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Motivation: Most approaches to gene expression analysis use realvalued expression data, produced by highthroughput screening technologies, such as microarrays. Often, some measure of similarity must be computed in order to extract meaningful information from the observed data. The choice of this similarity measure frequently has a profound effect on the results of the analysis, yet no standards exist to guide the researcher.
Efficient Computation of IsometryInvariant Distances between Surfaces
"... We present an efficient computational framework for isometryinvariant comparison of smooth surfaces. We formulate the GromovHausdorff distance as a multidimensional scaling (MDS)like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical ..."
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Cited by 52 (18 self)
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We present an efficient computational framework for isometryinvariant comparison of smooth surfaces. We formulate the GromovHausdorff distance as a multidimensional scaling (MDS)like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples. For isometryinvariant comparison of surfaces in the case of partially missing data, we present the partial embedding distance, which is computed using a similar scheme. The main idea is finding a minimumdistortion mapping from one surface to another, while considering only relevant geodesic distances. We discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency.
Knowledge mining with VxInsight: Discovery through interaction
 JOURNAL OF INTELLIGENT INFORMATION SYSTEMS
, 1998
"... The explosive growth in the availability of information is overwhelming traditional information management systems. Although individual pieces of information have become easy to find, the larger context in which they exist has become harder to track. These contextual questions are ideally suited to ..."
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Cited by 42 (4 self)
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The explosive growth in the availability of information is overwhelming traditional information management systems. Although individual pieces of information have become easy to find, the larger context in which they exist has become harder to track. These contextual questions are ideally suited to visualization since the humrex visual system is remarkably adept at interpreting large quantities of information, and at detecting patterns and anomalies. The challenge is to present the information in a manner that maximally leverages our v/sual skills. This paper discusses a set of properties that such a presentation should have, and describes the design and functionality of Vxlnsight, a visualization tool built to these principles.
Correspondence analysis of genes and tissue types and finding genetic links from microarray data
 Genome Informatics
, 2000
"... In this paper, we propose and use two novel procedures for the analysis of microarray gene expression data. The first is correspondence analysis which visualizes the relationship between genes and tissues as two 2 dimensional graphs, oriented so that distances between genes are preserved, distances ..."
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Cited by 41 (1 self)
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In this paper, we propose and use two novel procedures for the analysis of microarray gene expression data. The first is correspondence analysis which visualizes the relationship between genes and tissues as two 2 dimensional graphs, oriented so that distances between genes are preserved, distances between tissues are preserved, and so that genes which primarily distinguish certain types of tissue are spatially close to those tissues. For the inference of genetic links, partial correlations rather than correlations are the key issue. A partial correlation between i and j is the relationship between i and j after the effect of surrounding genes has been subtracted out of their pairwise correlation. This leads to the area of graphical modeling. A limitation of the graphical modeling approach is that the correlation matrix of expression profiles between genes is degenerate whenever the number of genes to be analyzed exceeds the number of distinct expression measurements. This can cause considerable problems, as calculation of partial correlations typically uses the inverse of the correlation matrix. To avoid this limitation, we propose two practical multiple regression procedures with variable selection to measure the net, screened, relationship between pairs of genes. Possible biases arising from the analysis of a subset of genes from the genome are examined in the worked examples. It seems that both these approaches are more natural ways of analyzing gene expression data than the currently popular approach of two way clustering.
Beyond pairwise clustering
 in IEEE Computer Society Conference on Computer Vision and Pattern Recognition
"... We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a twostep algorithm for solving this problem. In the first step we use a nove ..."
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Cited by 41 (2 self)
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We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a twostep algorithm for solving this problem. In the first step we use a novel scheme to approximate the hypergraph using a weighted graph. In the second step a spectral partitioning algorithm is used to partition the vertices of this graph. The algorithm is capable of handling hyperedges of all orders including order two, thus incorporating information of all orders simultaneously. We present a theoretical analysis that relates our algorithm to an existing hypergraph partitioning algorithm and explain the reasons for its superior performance. We report the performance of our algorithm on a variety of computer vision problems and compare it to several existing hypergraph partitioning algorithms. 1.
Data Fusion and Multicue Data Matching by Diffusion Maps
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Data fusion and multicue data matching are fundamental tasks of highdimensional data analysis. In this paper, we apply the recently introduced diffusion framework to address these tasks. Our contribution is threefold. First, we present the LaplaceBeltrami approach for computing density invariant ..."
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Cited by 38 (4 self)
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Data fusion and multicue data matching are fundamental tasks of highdimensional data analysis. In this paper, we apply the recently introduced diffusion framework to address these tasks. Our contribution is threefold. First, we present the LaplaceBeltrami approach for computing density invariant embeddings which are essential for integrating different sources of data. Second, we describe a refinement of the Nyström extension algorithm called “geometric harmonics”. We also explain how to use this tool for data assimilation. Finally, we introduce a multicue data matching scheme based on nonlinear spectral graphs alignment. The effectiveness of the presented schemes is validated by applying it to the problems of lipreading and image sequence alignment.