We describe a simple algorithm based on a Markov chain process to generate simply connected acycl... more We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non necessarily connected.
We express any general characteristic sturmian word as a unique infinite non-increasing product o... more We express any general characteristic sturmian word as a unique infinite non-increasing product of Lyndon words. Using this identity, we give a new ω-division for characteristic sturmian words. We also give a short proof of a result by Berstel and de Luca (Sturmian words, Lyndon words and trees, Theoret. Comput. Sci., 178 (1997) 171–203.); more precisely, we show that the set of factors of sturmian words that qualify as Lyndon words is the set of primitive Christoffel words.
Viennot factorization of infinite words. Guy Melancon Information Processing Letters 60:22, 53-57... more Viennot factorization of infinite words. Guy Melancon Information Processing Letters 60:22, 53-57, 1996. The results presented in this paper generalize the Lyndon factorization theorem for infinite words to Viennot factorizations. ...
Discrete Mathematics and Theoretical Computer Science 1, 1997, 4352 ... Lyndon factorization of ... more Discrete Mathematics and Theoretical Computer Science 1, 1997, 4352 ... Lyndon factorization of the ThueMorse word ... LaBRI, URA 1304 CNRS Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France E-Mail: [email protected]
Mining relational data often boils down to computing clusters, that is finding sub-communities of... more Mining relational data often boils down to computing clusters, that is finding sub-communities of data elements forming cohesive sub-units, while being well separated from one another. The clusters themselves are sometimes terms "communities" and the way clusters relate to one another is often referred to as a "community structure". We study a modularity criterion M Q introduced by Mancoridis et al. in order to infer community structure on relational data.
We describe an exploratory technique based on the direct interaction with a 2D modified scatterpl... more We describe an exploratory technique based on the direct interaction with a 2D modified scatterplot computed from two different metrics calculated over the elements of a network. The scatterplot is transformed into an image by applying standard image processing techniques resulting into blurring effects. Segmentation of the image allows to easily select patches on the image as a way to extract sub-networks. We were inspired by the work of Wattenberg and Fisher showing that the blurring process builds into a multiscale perceptual scheme, making this type of interaction intuitive to the user. We explain how the exploration of the network can be guided by the visual analysis of the blurred scatterplot and by its possible interpretations.
We present a multiscale MDS method extending Chalmers . Our multiscale strategy is itself based o... more We present a multiscale MDS method extending Chalmers . Our multiscale strategy is itself based on a O(N log N ) hybrid MDS approach. Our algorithm clearly improves over its predecessors with respect to time, while producing layouts of a comparable quality.
Information and Computation/information and Control, 2000
Many applications, from everyday file system browsers to visual programming tools, require the di... more Many applications, from everyday file system browsers to visual programming tools, require the display of network and graph structures. The Graph Visualization Framework 2 (GVF) is an architecture that supports the tasks common to most graph browsers and editors. This article gives a brief overview of the design of the GVF and focuses on the core classes that are used to represent and manipulate graphs. The design of the core classes is justified by the requirements for navigation and visualization.
Mining relational data often boils down to computing clusters, that is finding subcommunities of ... more Mining relational data often boils down to computing clusters, that is finding subcommunities of data elements forming cohesive sub-units, while being well separated from one another. The clusters themselves are sometimes termed "communities" and the way clusters relate to one another is often referred to as a "community structure". Methods for identifying communities or subgroups in network data is the focus of intense research is different scientific communities and for different purposes. The present paper focuses on two novel algorithms producing multilevel community structures from raw network data. The two algorithms exploit an edge metric extending Watts's clustering coefficient to edges of a graph. The full benefit of the method comes from the multilevel nature of the community structure as it facilitates the visual interaction and navigation of the network by zooming in and out of components at any level. This multilevel navigation proves to be useful when visually exploring a network in search for structural patterns.
Two tasks in Graph Visualization require partitioning: the assignment of visual attributes and di... more Two tasks in Graph Visualization require partitioning: the assignment of visual attributes and divisive clustering. Often, we would like to assign a color or other visual attributes to a node or edge that indicates an associated value. In an application involving divisive clustering, we would like to partition the graph into subsets of graph elements based on metric values in such a way that all subsets are evenly populated. Assuming a uniform distribution of metric values during either partitioning or coloring can have undesired effects such as empty clusters or only one level of emphasis for the entire graph. Probability density functions derived from statistics about a metric can help systems succeed at these tasks.
In this paper, we present an algorithm, called Bubble Tree, for the drawing of general rooted tre... more In this paper, we present an algorithm, called Bubble Tree, for the drawing of general rooted trees. A large variety of algorithms already exists in this field. However, the goal of this algorithm is to obtain a better drawing which makes a trade off between the angular resolution and the length of the edges. We show that the Bubble Tree drawing algorithm provides a planar drawing with at most one bend per edge in linear running time.
We describe an algorithm producing circular layouts for trees, that is drawings, where subtrees o... more We describe an algorithm producing circular layouts for trees, that is drawings, where subtrees of a node lie within circles, and these circles are themselves placed on the circumference of a circle. The complexity and methodology of our algorithm compares to Reingold and ...
Information and Computation/information and Control, 2000
A clustered graph can be used to build an abstract view of its non-clustered counterpart and redu... more A clustered graph can be used to build an abstract view of its non-clustered counterpart and reduce visual complexity. The classic approach to interaction with a clustered graph is limited in scalability and efficacy, underlining the need for an overview diagram. We present a technique for the automatic generation of an overview diagram based on hierarchical clustering and discuss its application to graphs. Hierarchical clustering induces a tree structure that is useful as a map to navigate the original data set. Because the resulting overview diagram is itself a graph, it can be manipulated by the same tools that are available for graphs.
We describe a simple, fast computing and easy to implement method for finding relatively good clu... more We describe a simple, fast computing and easy to implement method for finding relatively good clusterings of software systems. Our method relies on the ability to compute the strength of an edge in a graph by applying a straightforward metric defined in terms of the neighborhoods of its end vertices. The metric is used to identify the weak edges of the graph, which are momentarily deleted to break it into several components. We study the quality metric M Q introduced in and exhibit mathematical properties that make it a good measure for clustering quality. Letting the threshold weakness of edges vary defines a path, i.e. a sequence of clusterings in the solution space (of all possible clustering of the graph). This path is described in terms of a curve linking M Q to the weakness of the edges in the graph.
Many networks under study in Information Visualization are "small world" networks. These networks... more Many networks under study in Information Visualization are "small world" networks. These networks first appeared in the study social networks and were shown to be relevant models in other application domains such as software reverse engineering and biology. Furthermore, many of these networks actually have a multiscale nature: they can be viewed as a network of groups that are themselves small world networks. We describe a metric that has been designed in order to identify the weakest edges in a small world network leading to an easy and low cost filtering procedure that breaks up a graph into smaller and highly connected components. We show how this metric can be exploited through an interactive navigation of the network based on semantic zooming. Once the network is decomposed into a hierarchy of sub-networks, a user can easily find groups and subgroups of actors and understand their dynamics.
This paper presents some of the most important features of a tree visualisation system called Lat... more This paper presents some of the most important features of a tree visualisation system called Latour, developed for the purposes of information visualisation. This system includes a number of interesting and unique characteristics, for example the provision for visual cues based on complexity metrics on graphs, which represent general principles that, in our view, graph based information visualisation systems should generally offer.
When dealing with a graph, any visualization strategy must rely on a layout procedure at least to... more When dealing with a graph, any visualization strategy must rely on a layout procedure at least to initiate the process. Because the visualization process evolves within an interactive environment the choice of this layout procedure is critical and will often be based on efficiency. This ...
We describe an exploratory technique based on the direct interaction with a 2D modified scatterpl... more We describe an exploratory technique based on the direct interaction with a 2D modified scatterplot computed from two different metrics calculated over the elements of a network. The scatterplot is transformed into an image by applying standard image processing techniques resulting into blurring effects. Segmentation of the image allows to easily select patches on the image as a way to extract sub-networks. We were inspired by the work of Wattenberg and Fisher showing that the blurring process builds into a multiscale perceptual scheme, making this type of interaction intuitive to the user. We explain how the exploration of the network can be guided by the visual analysis of the blurred scatterplot and by its possible interpretations.
Many applications, from everyday file system browsers to visual programming tools, require the di... more Many applications, from everyday file system browsers to visual programming tools, require the display of network and graph structures. The Graph Visualization Framework 2 (GVF) is an architecture that supports the tasks common to most graph browsers and editors. This article gives a brief overview of the design of the GVF and focuses on the core classes that are used to represent and manipulate graphs. The design of the core classes is justified by the requirements for navigation and visualization.
We describe a simple algorithm based on a Markov chain process to generate simply connected acycl... more We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non necessarily connected.
We express any general characteristic sturmian word as a unique infinite non-increasing product o... more We express any general characteristic sturmian word as a unique infinite non-increasing product of Lyndon words. Using this identity, we give a new ω-division for characteristic sturmian words. We also give a short proof of a result by Berstel and de Luca (Sturmian words, Lyndon words and trees, Theoret. Comput. Sci., 178 (1997) 171–203.); more precisely, we show that the set of factors of sturmian words that qualify as Lyndon words is the set of primitive Christoffel words.
Viennot factorization of infinite words. Guy Melancon Information Processing Letters 60:22, 53-57... more Viennot factorization of infinite words. Guy Melancon Information Processing Letters 60:22, 53-57, 1996. The results presented in this paper generalize the Lyndon factorization theorem for infinite words to Viennot factorizations. ...
Discrete Mathematics and Theoretical Computer Science 1, 1997, 4352 ... Lyndon factorization of ... more Discrete Mathematics and Theoretical Computer Science 1, 1997, 4352 ... Lyndon factorization of the ThueMorse word ... LaBRI, URA 1304 CNRS Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France E-Mail: [email protected]
Mining relational data often boils down to computing clusters, that is finding sub-communities of... more Mining relational data often boils down to computing clusters, that is finding sub-communities of data elements forming cohesive sub-units, while being well separated from one another. The clusters themselves are sometimes terms "communities" and the way clusters relate to one another is often referred to as a "community structure". We study a modularity criterion M Q introduced by Mancoridis et al. in order to infer community structure on relational data.
We describe an exploratory technique based on the direct interaction with a 2D modified scatterpl... more We describe an exploratory technique based on the direct interaction with a 2D modified scatterplot computed from two different metrics calculated over the elements of a network. The scatterplot is transformed into an image by applying standard image processing techniques resulting into blurring effects. Segmentation of the image allows to easily select patches on the image as a way to extract sub-networks. We were inspired by the work of Wattenberg and Fisher showing that the blurring process builds into a multiscale perceptual scheme, making this type of interaction intuitive to the user. We explain how the exploration of the network can be guided by the visual analysis of the blurred scatterplot and by its possible interpretations.
We present a multiscale MDS method extending Chalmers . Our multiscale strategy is itself based o... more We present a multiscale MDS method extending Chalmers . Our multiscale strategy is itself based on a O(N log N ) hybrid MDS approach. Our algorithm clearly improves over its predecessors with respect to time, while producing layouts of a comparable quality.
Information and Computation/information and Control, 2000
Many applications, from everyday file system browsers to visual programming tools, require the di... more Many applications, from everyday file system browsers to visual programming tools, require the display of network and graph structures. The Graph Visualization Framework 2 (GVF) is an architecture that supports the tasks common to most graph browsers and editors. This article gives a brief overview of the design of the GVF and focuses on the core classes that are used to represent and manipulate graphs. The design of the core classes is justified by the requirements for navigation and visualization.
Mining relational data often boils down to computing clusters, that is finding subcommunities of ... more Mining relational data often boils down to computing clusters, that is finding subcommunities of data elements forming cohesive sub-units, while being well separated from one another. The clusters themselves are sometimes termed "communities" and the way clusters relate to one another is often referred to as a "community structure". Methods for identifying communities or subgroups in network data is the focus of intense research is different scientific communities and for different purposes. The present paper focuses on two novel algorithms producing multilevel community structures from raw network data. The two algorithms exploit an edge metric extending Watts's clustering coefficient to edges of a graph. The full benefit of the method comes from the multilevel nature of the community structure as it facilitates the visual interaction and navigation of the network by zooming in and out of components at any level. This multilevel navigation proves to be useful when visually exploring a network in search for structural patterns.
Two tasks in Graph Visualization require partitioning: the assignment of visual attributes and di... more Two tasks in Graph Visualization require partitioning: the assignment of visual attributes and divisive clustering. Often, we would like to assign a color or other visual attributes to a node or edge that indicates an associated value. In an application involving divisive clustering, we would like to partition the graph into subsets of graph elements based on metric values in such a way that all subsets are evenly populated. Assuming a uniform distribution of metric values during either partitioning or coloring can have undesired effects such as empty clusters or only one level of emphasis for the entire graph. Probability density functions derived from statistics about a metric can help systems succeed at these tasks.
In this paper, we present an algorithm, called Bubble Tree, for the drawing of general rooted tre... more In this paper, we present an algorithm, called Bubble Tree, for the drawing of general rooted trees. A large variety of algorithms already exists in this field. However, the goal of this algorithm is to obtain a better drawing which makes a trade off between the angular resolution and the length of the edges. We show that the Bubble Tree drawing algorithm provides a planar drawing with at most one bend per edge in linear running time.
We describe an algorithm producing circular layouts for trees, that is drawings, where subtrees o... more We describe an algorithm producing circular layouts for trees, that is drawings, where subtrees of a node lie within circles, and these circles are themselves placed on the circumference of a circle. The complexity and methodology of our algorithm compares to Reingold and ...
Information and Computation/information and Control, 2000
A clustered graph can be used to build an abstract view of its non-clustered counterpart and redu... more A clustered graph can be used to build an abstract view of its non-clustered counterpart and reduce visual complexity. The classic approach to interaction with a clustered graph is limited in scalability and efficacy, underlining the need for an overview diagram. We present a technique for the automatic generation of an overview diagram based on hierarchical clustering and discuss its application to graphs. Hierarchical clustering induces a tree structure that is useful as a map to navigate the original data set. Because the resulting overview diagram is itself a graph, it can be manipulated by the same tools that are available for graphs.
We describe a simple, fast computing and easy to implement method for finding relatively good clu... more We describe a simple, fast computing and easy to implement method for finding relatively good clusterings of software systems. Our method relies on the ability to compute the strength of an edge in a graph by applying a straightforward metric defined in terms of the neighborhoods of its end vertices. The metric is used to identify the weak edges of the graph, which are momentarily deleted to break it into several components. We study the quality metric M Q introduced in and exhibit mathematical properties that make it a good measure for clustering quality. Letting the threshold weakness of edges vary defines a path, i.e. a sequence of clusterings in the solution space (of all possible clustering of the graph). This path is described in terms of a curve linking M Q to the weakness of the edges in the graph.
Many networks under study in Information Visualization are "small world" networks. These networks... more Many networks under study in Information Visualization are "small world" networks. These networks first appeared in the study social networks and were shown to be relevant models in other application domains such as software reverse engineering and biology. Furthermore, many of these networks actually have a multiscale nature: they can be viewed as a network of groups that are themselves small world networks. We describe a metric that has been designed in order to identify the weakest edges in a small world network leading to an easy and low cost filtering procedure that breaks up a graph into smaller and highly connected components. We show how this metric can be exploited through an interactive navigation of the network based on semantic zooming. Once the network is decomposed into a hierarchy of sub-networks, a user can easily find groups and subgroups of actors and understand their dynamics.
This paper presents some of the most important features of a tree visualisation system called Lat... more This paper presents some of the most important features of a tree visualisation system called Latour, developed for the purposes of information visualisation. This system includes a number of interesting and unique characteristics, for example the provision for visual cues based on complexity metrics on graphs, which represent general principles that, in our view, graph based information visualisation systems should generally offer.
When dealing with a graph, any visualization strategy must rely on a layout procedure at least to... more When dealing with a graph, any visualization strategy must rely on a layout procedure at least to initiate the process. Because the visualization process evolves within an interactive environment the choice of this layout procedure is critical and will often be based on efficiency. This ...
We describe an exploratory technique based on the direct interaction with a 2D modified scatterpl... more We describe an exploratory technique based on the direct interaction with a 2D modified scatterplot computed from two different metrics calculated over the elements of a network. The scatterplot is transformed into an image by applying standard image processing techniques resulting into blurring effects. Segmentation of the image allows to easily select patches on the image as a way to extract sub-networks. We were inspired by the work of Wattenberg and Fisher showing that the blurring process builds into a multiscale perceptual scheme, making this type of interaction intuitive to the user. We explain how the exploration of the network can be guided by the visual analysis of the blurred scatterplot and by its possible interpretations.
Many applications, from everyday file system browsers to visual programming tools, require the di... more Many applications, from everyday file system browsers to visual programming tools, require the display of network and graph structures. The Graph Visualization Framework 2 (GVF) is an architecture that supports the tasks common to most graph browsers and editors. This article gives a brief overview of the design of the GVF and focuses on the core classes that are used to represent and manipulate graphs. The design of the core classes is justified by the requirements for navigation and visualization.
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Papers by Guy Melançon