A Framework for Exploring Multidimensional Data with 3D Projections

Visualization of high-dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e. g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high-dimensional data to 3D visual spaces, based on a generalization of the Least-Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework`s applicability for both visual exploration of multidimensional abstract (non-spatial) data as well as the feature space of multi-variate spatial data.

An incremental space to visualize dynamic data sets

In Information Visualization, adding and removing data elements can strongly impact the underlying visual space. We have developed an inherently incremental technique (incBoard) that maintains a coherent disposition of elements from a dynamic multidimensional data set on a 2D grid as the set changes. Here, we introduce a novel layout that uses pairwise similarity from grid neighbors, as defined in incBoard, to reposition elements on the visual space, free from constraints imposed by the grid. The board continues to be updated and can be displayed alongside the new space. As similar items are placed together, while dissimilar neighbors are moved apart, it supports users in the identification of clusters and subsets of related elements. Densely populated areas identified in the incSpace can be efficiently explored with the corresponding incBoard visualization, which is not susceptible to occlusion. The solution remains inherently incremental and maintains a coherent disposition of elements, even for fully renewed sets. The algorithm considers relative positions for the initial placement of elements, and raw dissimilarity to fine tune the visualization. It has low computational cost, with complexity depending only on the size of the currently viewed subset, V. Thus, a data set of size N can be sequentially displayed in O(N) time, reaching O(N (2)) only if the complete set is simultaneously displayed.

Evolutionary fuzzy clustering of relational data

This paper is concerned with the computational efficiency of fuzzy clustering algorithms when the data set to be clustered is described by a proximity matrix only (relational data) and the number of clusters must be automatically estimated from such data. A fuzzy variant of an evolutionary algorithm for relational clustering is derived and compared against two systematic (pseudo-exhaustive) approaches that can also be used to automatically estimate the number of fuzzy clusters in relational data. An extensive collection of experiments involving 18 artificial and two real data sets is reported and analyzed. (C) 2011 Elsevier B.V. All rights reserved.

Investigation of a new GRASP-based clustering algorithm applied to biological data

A large amount of biological data has been produced in the last years. Important knowledge can be extracted from these data by the use of data analysis techniques. Clustering plays an important role in data analysis, by organizing similar objects from a dataset into meaningful groups. Several clustering algorithms have been proposed in the literature. However, each algorithm has its bias, being more adequate for particular datasets. This paper presents a mathematical formulation to support the creation of consistent clusters for biological data. Moreover. it shows a clustering algorithm to solve this formulation that uses GRASP (Greedy Randomized Adaptive Search Procedure). We compared the proposed algorithm with three known other algorithms. The proposed algorithm presented the best clustering results confirmed statistically. (C) 2009 Elsevier Ltd. All rights reserved.

Generalized external indexes for comparing data partitions with overlapping categories

There is a family of well-known external clustering validity indexes to measure the degree of compatibility or similarity between two hard partitions of a given data set, including partitions with different numbers of categories. A unified, fully equivalent set-theoretic formulation for an important class of such indexes was derived and extended to the fuzzy domain in a previous work by the author [Campello, R.J.G.B., 2007. A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Lett., 28, 833-841]. However, the proposed fuzzy set-theoretic formulation is not valid as a general approach for comparing two fuzzy partitions of data. Instead, it is an approach for comparing a fuzzy partition against a hard referential partition of the data into mutually disjoint categories. In this paper, generalized external indexes for comparing two data partitions with overlapping categories are introduced. These indexes can be used as general measures for comparing two partitions of the same data set into overlapping categories. An important issue that is seldom touched in the literature is also addressed in the paper, namely, how to compare two partitions of different subsamples of data. A number of pedagogical examples and three simulation experiments are presented and analyzed in details. A review of recent related work compiled from the literature is also provided. (c) 2010 Elsevier B.V. All rights reserved.

Multi-objective clustering ensemble for gene expression data analysis

In this paper, we present an algorithm for cluster analysis that integrates aspects from cluster ensemble and multi-objective clustering. The algorithm is based on a Pareto-based multi-objective genetic algorithm, with a special crossover operator, which uses clustering validation measures as objective functions. The algorithm proposed can deal with data sets presenting different types of clusters, without the need of expertise in cluster analysis. its result is a concise set of partitions representing alternative trade-offs among the objective functions. We compare the results obtained with our algorithm, in the context of gene expression data sets, to those achieved with multi-objective Clustering with automatic K-determination (MOCK). the algorithm most closely related to ours. (C) 2009 Elsevier B.V. All rights reserved.

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.

Template-based quadrilateral mesh generation from imaging data

This paper describes a novel template-based meshing approach for generating good quality quadrilateral meshes from 2D digital images. This approach builds upon an existing image-based mesh generation technique called Imeshp, which enables us to create a segmented triangle mesh from an image without the need for an image segmentation step. Our approach generates a quadrilateral mesh using an indirect scheme, which converts the segmented triangle mesh created by the initial steps of the Imesh technique into a quadrilateral one. The triangle-to-quadrilateral conversion makes use of template meshes of triangles. To ensure good element quality, the conversion step is followed by a smoothing step, which is based on a new optimization-based procedure. We show several examples of meshes generated by our approach, and present a thorough experimental evaluation of the quality of the meshes given as examples.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Buff XII regression models. (C) 2008 Published by Elsevier B.V.

A novel MAP-MRF approach for multispectral image contextual classification using combination of suboptimal iterative algorithms

In this paper we present a novel approach for multispectral image contextual classification by combining iterative combinatorial optimization algorithms. The pixel-wise decision rule is defined using a Bayesian approach to combine two MRF models: a Gaussian Markov Random Field (GMRF) for the observations (likelihood) and a Potts model for the a priori knowledge, to regularize the solution in the presence of noisy data. Hence, the classification problem is stated according to a Maximum a Posteriori (MAP) framework. In order to approximate the MAP solution we apply several combinatorial optimization methods using multiple simultaneous initializations, making the solution less sensitive to the initial conditions and reducing both computational cost and time in comparison to Simulated Annealing, often unfeasible in many real image processing applications. Markov Random Field model parameters are estimated by Maximum Pseudo-Likelihood (MPL) approach, avoiding manual adjustments in the choice of the regularization parameters. Asymptotic evaluations assess the accuracy of the proposed parameter estimation procedure. To test and evaluate the proposed classification method, we adopt metrics for quantitative performance assessment (Cohen`s Kappa coefficient), allowing a robust and accurate statistical analysis. The obtained results clearly show that combining sub-optimal contextual algorithms significantly improves the classification performance, indicating the effectiveness of the proposed methodology. (C) 2010 Elsevier B.V. All rights reserved.

Improving data perturbation testing techniques for Web services

The widespread use of service-oriented architectures (SOAs) and Web services in commercial software requires the adoption of development techniques to ensure the quality of Web services. Testing techniques and tools concern quality and play a critical role in accomplishing quality of SOA based systems. Existing techniques and tools for traditional systems are not appropriate to these new systems, making the development of Web services testing techniques and tools required. This article presents new testing techniques to automatically generate a set of test cases and data for Web services. The techniques presented here explore data perturbation of Web services messages upon data types, integrity and consistency. To support these techniques, a tool (GenAutoWS) was developed and applied to real problems. (C) 2010 Elsevier Inc. All rights reserved.

Structural matching of 2D electrophoresis gels using deformed graphs

2D electrophoresis is a well-known method for protein separation which is extremely useful in the field of proteomics. Each spot in the image represents a protein accumulation and the goal is to perform a differential analysis between pairs of images to study changes in protein content. It is thus necessary to register two images by finding spot correspondences. Although it may seem a simple task, generally, the manual processing of this kind of images is very cumbersome, especially when strong variations between corresponding sets of spots are expected (e.g. strong non-linear deformations and outliers). In order to solve this problem, this paper proposes a new quadratic assignment formulation together with a correspondence estimation algorithm based on graph matching which takes into account the structural information between the detected spots. Each image is represented by a graph and the task is to find a maximum common subgraph. Successful experimental results using real data are presented, including an extensive comparative performance evaluation with ground-truth data. (C) 2010 Elsevier B.V. All rights reserved.

Is the unfolding of the group discussion off-pattern? Improving coordination support in educational forums using mobile devices

A forum is a valuable tool to foster reflection in an in-depth discussion; however, it forces the course mediator to continually pay close attention in order to coordinate learners` activities. Moreover, monitoring a forum is time consuming given that it is impossible to know in advance when new messages are going to be posted. Additionally, a forum may be inactive for a long period and suddenly receive a burst of messages forcing forum mediators to frequently log on in order to know how the discussion is unfolding to intervene whenever it is necessary. Mediators also need to deal with a large amount of messages to identify off-pattern situations. This work presents a piece of action research that investigates how to improve coordination support in a forum using mobile devices for mitigating mediator`s difficulties in following the status of a forum. Based on summarized information extracted from message meta-data, mediators consult visual information summaries on PDAs and receive textual notifications in their mobile phone. This investigation revealed that mediators used the mobile-based coordination support to keep informed on what is taking place within the forum without the need to log on their desktop computer. (C) 2009 Elsevier Ltd. All rights reserved.