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Learning Evaluation Functions to Improve Optimization by Local Search
 Journal of Machine Learning Research
, 2000
"... This paper describes algorithms that learn to improve search performance on largescale optimization tasks. The main algorithm, Stage, works by learning an evaluation function that predicts the outcome of a local search algorithm, such as hillclimbing or Walksat, from features of states visited durin ..."
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Cited by 56 (0 self)
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This paper describes algorithms that learn to improve search performance on largescale optimization tasks. The main algorithm, Stage, works by learning an evaluation function that predicts the outcome of a local search algorithm, such as hillclimbing or Walksat, from features of states visited during search. The learned evaluation function is then used to bias future search trajectories toward better optima on the same problem. Another algorithm, XStage, transfers previously learned evaluation functions to new, similar optimization problems. Empirical results are provided on seven largescale optimization domains: binpacking, channel routing, Bayesian network structurefinding, radiotherapy treatment planning, cartogram design, Boolean satisfiability, and Boggle board setup.
Cartodraw: A fast algorithm for generating contiguous cartograms
 IEEE Transactions on Visualization and Computer Graphics
, 2004
"... Abstract—Cartograms are a wellknown technique for showing geographyrelated statistical information, such as population demographics and epidemiological data. The basic idea is to distort a map by resizing its regions according to a statistical parameter, but in a way that keeps the map recognizabl ..."
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Cited by 22 (6 self)
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Abstract—Cartograms are a wellknown technique for showing geographyrelated statistical information, such as population demographics and epidemiological data. The basic idea is to distort a map by resizing its regions according to a statistical parameter, but in a way that keeps the map recognizable. In this study, we formally define a family of cartogram drawing problems. We show that even simple variants are unsolvable in the general case. Because the feasible variants are NPcomplete, heuristics are needed to solve the problem. Previously proposed solutions suffer from problems with the quality of the generated drawings. For a cartogram to be recognizable, it is important to preserve the global shape or outline of the input map, a requirement that has been overlooked in the past. To address this, our objective function for cartogram drawing includes both global and local shape preservation. To measure the degree of shape preservation, we propose a shape similarity function, which is based on a Fourier transformation of the polygons’ curvatures. Also, our application is visualization of dynamic data, for which we need an algorithm that recalculates a cartogram in a few seconds. None of the previous algorithms provides adequate performance with an acceptable level of quality for this application. In this paper, we therefore propose an efficient iterative scanline algorithm to reposition edges while preserving local and global shapes. Scanlines may be generated automatically or entered interactively to guide the optimization process more closely. We apply our algorithm to several example data sets and provide a detailed comparison of the two variants of our algorithm and previous approaches. Index Terms—Information visualization, visualization of georelated information, continuous cartograms, valuebyarea cartograms, visualization and cartography. 1
A VARIABLESCALE MAP FOR SMALLDISPLAY CARTOGRAPHY
, 2002
"... The aim of this paper is to develop methods for presenting geodata for personal navigation in realtime to a mobile user. Ideally, the user should have an overview map in the vicinity of his position; required for e.g. choosing the right road in a crossing. At the same time the user requires a small ..."
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Cited by 12 (1 self)
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The aim of this paper is to develop methods for presenting geodata for personal navigation in realtime to a mobile user. Ideally, the user should have an overview map in the vicinity of his position; required for e.g. choosing the right road in a crossing. At the same time the user requires a smallscale map where he can see the final target of his route. A solution to obtain these user requirements is to create a variablescale map that is constantly changing to make the user position always be in the largescale part of the map. In the paper a formula for a variablescale map is derived and its properties are demonstrated. Furthermore, realtime generalisation methods are described, these methods are used to adapt the original cartographic data to the smallscale areas of the map. A prototype system of a variablescale approach was created using the emerging XMLbased vectordata standards (GML and SVG), where the generalisation and scalevariations were performed in an XSLT transformation. The paper describes a minor case study which shows that variablescale maps have a potential for personal navigation.
AreaNormalized Thematic Views
 In Proceedings of International Cartography Assembly
, 1999
"... Thematic variables are commonly used to encode additional information such as population density within the spatial layout of a map. Such themes» are typically encoded using colourmaps. We will explore techniques for using this thematic information to directly define spatial transformations so that ..."
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Cited by 6 (0 self)
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Thematic variables are commonly used to encode additional information such as population density within the spatial layout of a map. Such themes» are typically encoded using colourmaps. We will explore techniques for using this thematic information to directly define spatial transformations so that areas of map regions are proportional to their thematic variables, thus making the view more consistent with the thematic encodings. Our method emphasizes interactivity as a primary mechanism for allowing the user to better realize the distribution of the thematic variable, rather than relying on static views of the map. Introduction A common problem in cartography occurs when a thematic variable is used to control the shading of regions of the map; this can very often lead to a situation where the areas used to represent the various thematic values are not consistent with the values themselves, possibly leading the viewer to misinterpret the information that the map designer is trying to ...
A constraintbased approach to constructing continuous cartograms
 In Proc. Symp. Spatial Data Handling
, 1998
"... We present a new constraintbased continuous area cartogram construction method that is unique in its ability to preserve essential cues for recognition of region shapes. It automatically achieves desired region areas while maintaining correct map topology. The algorithm is compared with a number of ..."
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Cited by 5 (0 self)
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We present a new constraintbased continuous area cartogram construction method that is unique in its ability to preserve essential cues for recognition of region shapes. It automatically achieves desired region areas while maintaining correct map topology. The algorithm is compared with a number of existing methods, and results are shown to be superior in both accuracy and preservation of shape recognition cues. Through hierarchical resolution, we first perform gross adjustments upon a coarsely resampled map and later refine the map at progressively higher levels of detail. 1
CartoSom  Cartogram creation using selforganizing maps
"... ... In this article we have presented a general method for constructing densityequalizing projections or cartograms, using the basic SOM algorithm, providing a tool for geographic data presentation and analysis ..."
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Cited by 4 (0 self)
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... In this article we have presented a general method for constructing densityequalizing projections or cartograms, using the basic SOM algorithm, providing a tool for geographic data presentation and analysis
Learning Evaluation Functions to Improve Local Search
"... This paper describes Stage, a learning algorithm that automatically improves search performance on largescale optimization problems. Stage learns an evaluation function that predicts the outcome of a local search algorithm, such as hillclimbing or Walksat, from features of states visited during sea ..."
Abstract
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This paper describes Stage, a learning algorithm that automatically improves search performance on largescale optimization problems. Stage learns an evaluation function that predicts the outcome of a local search algorithm, such as hillclimbing or Walksat, from features of states visited during search. The learned evaluation function is used to bias future search trajectories toward better optima on the same problem. This paper presents the Stage algorithm; an extension, XStage, that transfers learned evaluation functions to new, similar optimization problems; and empirical results on seven largescale optimization domains: binpacking, channel routing, Bayes network structurefinding, radiotherapy treatment planning, cartogram design, Boolean satisfiability, and Boggle board setup.
Medial Axesbased Cartograms
, 2003
"... Cartograms are a wellknown technique for showing geographyrelated statistical information, such as population demographics and epidemiological data. The basic idea is to distort a map by resizing its regions according to a statistical parameter, but in a way that keeps the map recognizable. In t ..."
Abstract
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Cartograms are a wellknown technique for showing geographyrelated statistical information, such as population demographics and epidemiological data. The basic idea is to distort a map by resizing its regions according to a statistical parameter, but in a way that keeps the map recognizable. In this paper, we deal with the continuous cartogram problem which strictly retains the topology of the polygon mesh. We develop an algorithm to solve the problem which uses an iterative relocation of the vertices based on a modified medial axes transformation of the polygon mesh. Experiments using real data sets show that our algorithm is capable of producing highquality cartograms in interactive time even for very large polygon meshes. A number of application examples show the high potential of our algorithm.
Cartogram data projection for . . .
, 2012
"... The SelfOrganizing Map (SOM) is very often visualized by applying Ultsch’s Unified Distance Matrix (UMatrix) shading and labeling the cells of the 2D grid with training data observations nearest to that node in feature space. Although powerful and the de facto standard visualization for SOMs, thi ..."
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The SelfOrganizing Map (SOM) is very often visualized by applying Ultsch’s Unified Distance Matrix (UMatrix) shading and labeling the cells of the 2D grid with training data observations nearest to that node in feature space. Although powerful and the de facto standard visualization for SOMs, this does not provide for two key pieces of information when considering real world data mining applications: (a) While the UMatrix indicates the location of possible clusters on the map, it typically does not accurately convey the size of the underlying data population within these clusters. (b) When mapping training data observations onto the 2D grid of the SOM it often occurs that multiple observations are mapped onto a single cell of the grid. Simply labeling the observations on a single cell does not provide any insights of the featurespace distribution of observations within that cell and in practical data mining applications it is often desirable to understand the distribution or “goodness of fit ” of the observations as they are mapped to the individual SOM cells. We address these problems with two complementary innovations. First, we increase or decrease the 2D size of each cell according to the number of data elements it contains; an approach derived from the cartogram techniques in geography. Second, we determine the withincell location of each datum according to its similarity in ndimensional feature space to each of the neighboring nodes that surround it on the 2D SOM grid. When multiple observations are mapped to a single cell then the plot locations will convey a sense of the data distribution within that cell. One way to view plotting of the data distribution within a cell is as a visualization of the quantization error of the map. Finally, we found that these techniques lend themselves to additional applications and uses within the context of SOMs and we will explore them briefly.