Luis Gustavo Nonato

Least Square Projection: A Fast High-Precision Multidimensional Projection Technique and Its Application to Document Mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses 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 high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

On improved projection techniques to support visual exploration of multidimensional data sets

Projection (or dimensionality reduction) techniques have been used as a means to handling the growing dimensionality of data sets as well as providing a way to visualize information coded into point relationships. Their role is essential in data interpretation and simultaneous use of different projections and their visualizations improve data understanding and increase the level of confidence in the result. For that purpose, projections should be fast to allow multiple views of the same data set. In this work we present a novel fast technique for projecting multi-dimensional data sets into bidimensional (2D) spaces that preserves neighborhood relationships. Additionally, a new technique for improving 2D projections from multi-dimensional data is presented, that helps reduce the inherent loss of information yielded by dimensionality reduction. The results are stimulating and are presented in the form of comparative visualizations against known and new 2D projection techniques. Based on the projection improvement approach presented here, a new metric for quality of projection is also given, that matches well the visual perception of quality. We discuss the implication of using improved projections in visual exploration of large data sets and the role of interaction in visualization of projected subspaces.

Local Affine Multidimensional Projection

Multidimensional projection techniques have experienced many improvements lately, mainly regarding computational times and accuracy. However, existing methods do not yet provide flexible enough mechanisms for visualization-oriented fully interactive applications. This work presents a new multidimensional projection technique designed to be more flexible and versatile than other methods. This novel approach, called Local Affine Multidimensional Projection (LAMP), relies on orthogonal mapping theory to build accurate local transformations that can be dynamically modified according to user knowledge. The accuracy, flexibility and computational efficiency of LAMP is confirmed by a comprehensive set of comparisons. LAMPs versatility is exploited in an application which seeks to correlate data that, in principle, has no connection as well as in visual exploration of textual documents.

A benchmark for surface reconstruction

We present a benchmark for the evaluation and comparison of algorithms which reconstruct a surface from point cloud data. Although a substantial amount of effort has been dedicated to the problem of surface reconstruction, a comprehensive means of evaluating this class of algorithms is noticeably absent. We propose a simple pipeline for measuring surface reconstruction algorithms, consisting of three main phases: surface modeling, sampling, and evaluation. We use implicit surfaces for modeling shapes which are capable of representing details of varying size and sharp features. From these implicit surfaces, we produce point clouds by synthetically generating range scans which resemble realistic scan data produced by an optical triangulation scanner. We validate our synthetic sampling scheme by comparing against scan data produced by a commercial optical laser scanner, where we scan a 3D-printed version of the original surface. Last, we perform evaluation by comparing the output reconstructed surface to a dense uniformly distributed sampling of the implicit surface. We decompose our benchmark into two distinct sets of experiments. The first set of experiments measures reconstruction against point clouds of complex shapes sampled under a wide variety of conditions. Although these experiments are quite useful for comparison, they lack a fine-grain analysis. To complement this, the second set of experiments measures specific properties of surface reconstruction, in terms of sampling characteristics and surface features. Together, these experiments depict a detailed examination of the state of surface reconstruction algorithms.

Two-Phase Mapping for Projecting Massive Data Sets

Most multidimensional projection techniques rely on distance (dissimilarity) information between data instances to embed high-dimensional 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 Part-Linear Multidimensional Projection (PLMP), has been tailored to handle multivariate data represented in Cartesian high-dimensional 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 high-dimensional space, we can make PLMP a truly streaming data projection technique, a trait absent in previous methods.

Semantic Wordification of Document Collections

Word clouds have become one of the most widely accepted visual resources for document analysis and visualization, motivating the development of several methods for building layouts of keywords extracted from textual data. Existing methods are effective to demonstrate content, but are not capable of preserving semantic relationships among keywords while still linking the word cloud to the underlying document groups that generated them. Such representation is highly desirable for exploratory analysis of document collections. In this paper we present a novel approach to build document clouds, named ProjCloud that aim at solving both semantical layouts and linking with document sets. ProjCloud generates a semantically consistent layout from a set of documents. Through a multidimensional projection, it is possible to visualize the neighborhood relationship between highly related documents and their corresponding word clouds simultaneously. Additionally, we propose a new algorithm for building word clouds inside polygons, which employs spectral sorting to maintain the semantic relationship among words. The effectiveness and flexibility of our methodology is confirmed when comparisons are made to existing methods. The technique automatically constructs projection based layouts the user may choose to examine in the form of the point clouds or corresponding word clouds, allowing a high degree of control over the exploratory process.

Piecewise laplacian-based projection for interactive data exploration and organization

Multidimensional projection has emerged as an important visualization tool in applications involving the visual analysis of high‐dimensional data. However, high precision projection methods are either computationally expensive or not flexible enough to enable feedback from user interaction into the projection process. A built‐in mechanism that dynamically adapts the projection based on direct user intervention would make the technique more useful for a larger range of applications and data sets. In this paper we propose the Piecewise Laplacian‐based 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 alter the projection map dynamically, a capability unique of this technique. We exploit the flexibility provided by PLP in two interactive projection‐based applications, one designed to organize pictures visually and another to build music playlists. These applications illustrate the usefulness of PLP in handling high‐dimensional data in a flexible and highly visual way. We also compare PLP with the currently most promising projections in terms of precision and speed, showing that it performs very well also according to these quality criteria.

Interactive Vector Field Feature Identification

We introduce a flexible technique for interactive exploration of vector field data through classification derived from user-specified feature templates. Our method is founded on the observation that, while similar features within the vector field may be spatially disparate, they share similar neighborhood characteristics. Users generate feature-based visualizations by interactively highlighting well-accepted and domain specific representative feature points. Feature exploration begins with the computation of attributes that describe the neighborhood of each sample within the input vector field. Compilation of these attributes forms a representation of the vector field samples in the attribute space. We project the attribute points onto the canonical 2D plane to enable interactive exploration of the vector field using a painting interface. The projection encodes the similarities between vector field points within the distances computed between their associated attribute points. The proposed method is performed at interactive rates for enhanced user experience and is completely flexible as showcased by the simultaneous identification of diverse feature types.

Laplacian Coordinates for Seeded Image Segmentation

Seed-based image segmentation methods have gained much attention lately, mainly due to their good performance in segmenting complex images with little user interaction. Such popularity leveraged the development of many new variations of seed-based image segmentation techniques, which vary greatly regarding mathematical formulation and complexity. Most existing methods in fact rely on complex mathematical formulations that typically do not guarantee unique solution for the segmentation problem while still being prone to be trapped in local minima. In this work we present a novel framework for seed-based image segmentation that is mathematically simple, easy to implement, and guaranteed to produce a unique solution. Moreover, the formulation holds an anisotropic behavior, that is, pixels sharing similar attributes are kept closer to each other while big jumps are naturally imposed on the boundary between image regions, thus ensuring better fitting on object boundaries. We show that the proposed framework outperform state-of-the-art techniques in terms of quantitative quality metrics as well as qualitative visual results.

Topology Verification for Isosurface Extraction

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.