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22
Least square projection: A fast highprecision multidimensional projection technique and its application to document mapping
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2008
"... The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analysis of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations c ..."
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Cited by 24 (8 self)
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The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analysis of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections (LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing highquality methods, particularly where it was mostly tested, that is, for mapping text sets.
Exploring 3d dti fiber tracts with linked 2d representations
 IEEE TVCG (Proc. of Visualization
"... Fig. 1: Brain fiber tracts and ventricle landmark with three different linked visual representations. Abstract—We present a visual exploration paradigm that facilitates navigation through complex fiber tracts by combining traditional 3D model viewing with lower dimensional representations. To this e ..."
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Fig. 1: Brain fiber tracts and ventricle landmark with three different linked visual representations. Abstract—We present a visual exploration paradigm that facilitates navigation through complex fiber tracts by combining traditional 3D model viewing with lower dimensional representations. To this end, we create standard streamtube models along with two twodimensional representations, an embedding in the plane and a hierarchical clustering tree, for a given set of fiber tracts. We then link these three representations using both interaction and color obtained by embedding fiber tracts into a perceptually uniform color space. We describe an anecdotal evaluation with neuroscientists to assess the usefulness of our method in exploring anatomical and functional structures in the brain. Expert feedback indicates that, while a standalone clinical use of the proposed method would require anatomical landmarks in the lower dimensional representations, the approach would be particularly useful in accelerating tract bundle selection. Results also suggest that combining traditional 3D model viewing with lower dimensional representations can ease navigation through the complex fiber tract models, improving exploration of the connectivity in the brain. Index Terms—DTI fiber tracts, embedding, coloring, interaction. 1
Exemplarbased Visualization of Large Document Corpus
"... Abstract—With the rapid growth of the World Wide Web and electronic information services, text corpus is becoming available online at an incredible rate. By displaying text data in a logical layout (e.g., color graphs), text visualization presents a direct way to observe the documents as well as und ..."
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Cited by 15 (2 self)
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Abstract—With the rapid growth of the World Wide Web and electronic information services, text corpus is becoming available online at an incredible rate. By displaying text data in a logical layout (e.g., color graphs), text visualization presents a direct way to observe the documents as well as understand the relationship between them. In this paper, we propose a novel technique, Exemplarbased Visualization (EV), to visualize an extremely large text corpus. Capitalizing on recent advances in matrix approximation and decomposition, EV presents a probabilistic multidimensional projection model in the lowrank text subspace with a sound objective function. The probability of each document proportion to the topics is obtained through iterative optimization and embedded to a low dimensional space using parameter embedding. By selecting the representative exemplars, we obtain a compact approximation of the data. This makes the visualization highly efficient and flexible. In addition, the selected exemplars neatly summarize the entire data set and greatly reduce the cognitive overload in the visualization, leading to an easier interpretation of large text corpus. Empirically, we demonstrate the superior performance of EV through extensive experiments performed on the publicly available text data sets. Index Terms—Exemplar, largescale document visualization, multidimensional projection. 1
TwoPhase Mapping for Projecting Massive Data Sets
, 2010
"... Most multidimensional projection techniques rely on distance (dissimilarity) information between data instances to embed highdimensional data into a visual space. When data are endowed with Cartesian coordinates, an extra computational effort is necessary to compute the needed distances, making m ..."
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Cited by 12 (1 self)
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Most multidimensional projection techniques rely on distance (dissimilarity) information between data instances to embed highdimensional data into a visual space. When data are endowed with Cartesian coordinates, an extra computational effort is necessary to compute the needed distances, making multidimensional projection prohibitive in applications dealing with interactivity and massive data. The novel multidimensional projection technique proposed in this work, called PartLinear Multidimensional Projection (PLMP), has been tailored to handle multivariate data represented in Cartesian highdimensional spaces, requiring only distance information between pairs of representative samples. This characteristic renders PLMP faster than previous methods when processing large data sets while still being competitive in terms of precision. Moreover, knowing the range of variation for data instances in the highdimensional space, we can make PLMP a truly streaming data projection technique, a trait absent in previous methods.
The Projection Explorer: A Flexible Tool for Projectionbased Multidimensional Visualization
"... Multidimensional projections map data points, defined in a highdimensional data space, into a 1D, 2D or 3D representation space. Such a mapping may be typically achieved with dimensional reduction, clustering, or force directed point placement. Projections can be displayed and navigated by data ana ..."
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Cited by 11 (2 self)
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Multidimensional projections map data points, defined in a highdimensional data space, into a 1D, 2D or 3D representation space. Such a mapping may be typically achieved with dimensional reduction, clustering, or force directed point placement. Projections can be displayed and navigated by data analysts by means of visual representations, which may vary from points on a plane to graphs, surfaces or volumes. Typically, projections strive to preserve distance relationships amongst data points, as defined in the original space. Information loss is inevitable and the projection approach defines the extent to which the distance preserving goal is attained. We introduce PEx – the Projection Explorer – a visualization tool for mapping and exploration of highdimensional data via projections. A set of examples – on both structured (table) and unstructured (text) data – illustrate how projection based visualizations, coupled with appropriate exploration tools, offer a flexible setup for multidimensional data exploration. The projections in PEx handle relatively large data sets at a computational cost adequate to user interaction.
A Coloring Solution to the Edge Crossing Problem
"... We introduce the concept of coloring close and crossing edges in graph drawings with perceptually opposing colors making them individually more distinguishable and reducing edgecrossing effects. We define a “closeness ” metric on edges as a combination of distance, angle and crossing. We use the in ..."
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Cited by 6 (1 self)
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We introduce the concept of coloring close and crossing edges in graph drawings with perceptually opposing colors making them individually more distinguishable and reducing edgecrossing effects. We define a “closeness ” metric on edges as a combination of distance, angle and crossing. We use the inverse of this metric to compute a color embedding in the L*a*b* color space and assign “close ” edges colors that are perceptually far apart. We present the following results: a distance metric on graph edges, a method of coloring graph edges, and anecdotal evidence that this technique can improve the reading of graph edges. Keywords graphs, colors, color embeddings. 1.
NONATO L.: Piecewise laplacianbased projection for interactive data exploration and organization
 Computer Graphics Forum
"... Multidimensional projection is emerging as an important visualization tool in applications involving the visual analysis of highdimensional data. However, existing projection methods are either computationally expensive or not flexible enough to enable fully interactive data manipulation. That is, ..."
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Cited by 4 (0 self)
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Multidimensional projection is emerging as an important visualization tool in applications involving the visual analysis of highdimensional data. However, existing projection methods are either computationally expensive or not flexible enough to enable fully interactive data manipulation. That is, they do not support the feedback of user interaction into the projection process. A mechanism that dynamically adapts the projection based on direct user interaction would go a long way towards making the technique more useful with a large range of applications and data sets. In this paper we propose the Piecewise Laplacianbased Projection (PLP), a novel multidimensional projection technique, that, due to the local nature of its formulation, enables a versatile mechanism to interact with projected data and to allow interactive changes to dynamically alter the projection map, a unique capability of the technique. We exploit the flexibility provided by PLP in two interactive projectionbased applications, one designed to organize pictures visually and another to build music playlists. These applications illustrate the usefulness of PLP in handling highdimensional data in a flexible and highly visual way. We also compare PLP with the currently most promising projections in terms of precision and speed. The results show that PLP perform very well also according to these quality criteria.
TimeAware Visualization of Document Collections
"... Scientific articles are the major mechanism for researchers to report their results, and a collection of papers on a discipline can reveal a lot about its evolution, such as the emergence of new topics. Nonetheless, given a broad collection of papers it is typically very difficult to grasp importa ..."
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Scientific articles are the major mechanism for researchers to report their results, and a collection of papers on a discipline can reveal a lot about its evolution, such as the emergence of new topics. Nonetheless, given a broad collection of papers it is typically very difficult to grasp important information that could help readers to globally interpret, navigate and then focus on the relevant items for their task. Contentbased document maps are visual representations created from evaluating the (dis)similarity amongst the documents, and have been shown to support exploratory tasks in this scenario. Documents are represented by visual markers placed in the 2D space so that documents close share similar content. Albeit the maps allow visually identifying groups of related documents and frontiers between groups, they do not explicitly convey the temporal evolution of a collection. We propose a technique for creating contentbased similarity maps of document collections that highlight temporal changes along time. Our solution constructs a sequence of maps from timestamped subsets of the data. It adopts a cumulative backwards strategy to preserve user context across successive timestamps, i.e., maps do not change drastically from one time stamp to the next, favouring user perception of changes.
A Survey of Dimension Reduction Methods for Highdimensional Data Analysis and Visualization ∗
"... Dimension reduction is commonly defined as the process of mapping highdimensional data to a lowerdimensional embedding. Applications of dimension reduction include, but are not limited to, filtering, compression, regression, classification, feature analysis, and visualization. We review methods th ..."
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Dimension reduction is commonly defined as the process of mapping highdimensional data to a lowerdimensional embedding. Applications of dimension reduction include, but are not limited to, filtering, compression, regression, classification, feature analysis, and visualization. We review methods that compute a pointbased visual representation of highdimensional data sets to aid in exploratory data analysis. The aim is not to be exhaustive but to provide an overview of basic approaches, as well as to review select stateoftheart methods. Our survey paper is an introduction to dimension reduction from a visualization point of view. Subsequently, a comparison of stateoftheart methods outlines relations and shared research foci.
Jorge PocoMedina “Multidimensional Projection on Visualization:
"... Visual exploration of multidimensional datasets has become a common task in the last years. Information Visualization has many techniques which can handle this kind of data. For example, we have parallel coordinates, scatter plots, glyphs mapping, multidimensional projections, etc.. In this document ..."
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Visual exploration of multidimensional datasets has become a common task in the last years. Information Visualization has many techniques which can handle this kind of data. For example, we have parallel coordinates, scatter plots, glyphs mapping, multidimensional projections, etc.. In this document we report some theoretical aspects and classification of the multidimensional projection techniques, specially those ones which are applied on visualization. Furthermore we present two user cases where the multidimensional projections were successfully used. Former presents the combination of Parallel Coordinates (PC) and Multidimensional Projection (MP) to find patterns in two source of climate datasets (model output and model structure data). Here, the PC’s view is used to represent the model structure and the MP’s view represents the model outputs. Using linked views we can explore and find some interesting patterns showing the model output’s behavior based on the metadata. Latter uses the Multidimensional Projection technique in combination with a Topic Modeling Algorithm (TMA). Here the MP is used to do a postprocessing on the TMA’s output and get feedback from the user. The feedback is captured by allowing the user to interact with the projection view doing three kind of operations: merge, split and edit topics. These operators have mathematical foundations in order to not increase the error presented initially.