Parallel Coordinate System Research Articles

Graphical data mining and knowledge discovery for computational estimation in AI alloys

The advances in manufacturing technology and proliferation of information from research laboratories have posed the problem of information explosion. To understand any system's behaviour it would be significant if the process can be visualised as a mapping from inputs to outputs. In materials research also, the generation of hypothesis about various materials properties and the compositions leading to such properties can be better understood by multivariate visualisation and machine learning techniques. Attempts have been made to develop a novel method for multivariate visualisation using parallel coordinate systems. Using two popular methods, clustering and the k-nearest neighbour technique, solves the materials classification problem. The prototype will allow the user to interactively discover the hidden patterns by semi-automatic generation of hypothesis and testing. As a case study the developed prototype has been tested on an aluminium alloy database.

Magnetic Resonance Imaging–Based Breast Volumetry in Breast Surgery: A Transfer from Neurosurgery

Sir: Quantitative breast volume assessment may optimize the results in breast surgery. Methods such as the anthropomorphic method, using thermoplastic sheets, counting displaced water, and three-dimensional photography have been described.1 We thought that magnetic resonance tomography, which is an accepted diagnostic and volumetric tool for the female breast, might serve also as a breast volumetry measure.2,3 Calculating volumes of specific organs or tissues is possible because of the different densities of various tissues.4 Current image-guided neuronavigation in neurosurgical procedures provides helpful surgical guidance for planning and performing the procedure by referencing the coordinate system of the brain to a parallel coordinate system based on three-dimensional image data of the patient on the console of the computer workstation. The medical images become point-to-point maps of the corresponding actual locations of the brain.5 Current neurosurgical systems include a tool with which to calculate the volume of the previously marked lesion. We hypothesized that magnetic resonance imaging data sets of the breast could be processed like cranial magnetic resonance imaging data for magnetic resonance imaging–based breast volumetry. In a pilot approach, we studied a 42-year-old woman who had undergone bilateral breast augmentation with 270-cc silicone implants on both sides 8 years previously. Magnetic resonance imaging examinations had been performed with a 1.5-T magnetic resonance scanner (MRT Gyroscan Intera 1.5 T; Philips, Hamburg, Germany) with the patient in the prone position. The implant was intact on the magnetic resonance imaging scans. Given the known size of the intact implant from the implant pass, another blinded examiner performed the volume analysis of the breast using Brainlab I Plan 2.6 navigation software. The process of marking the borders of the breast implant within the patient's breast is simple and straightforward (<2 minutes) (Fig. 1). The amount of the overlying breast tissue is easily measured and calculated by the software as well (Fig. 2). The magnetic resonance imaging–based volumetry of the implants was 273 cc for the right side and 275 cc for the left side, with 270-cc built-in implants based on the implant pass. Thus, the magnetic resonance imaging breast volumetry was within a 2 percent error of the size of the original breast implant. Also, the volume of the total breast with the implant could be calculated in the same setting, which was 570 cc on the right side and 559 cc on the left side.Fig. 1.: Using Brainlab I Plan 2.6 navigation software, the mammary implants are marked on axial slices by surrounding them with a digital pen guided by the computer mouse. This process can be performed simply and quickly. An included volume analysis tool calculates the volume of the marked tissue, like the left-sided breast implant in this screen shot. The calculated volume was 275 cc, with 270 cc given in the implant pass.Fig. 2.: The entire female breast can be visualized and the volume can be analyzed. Because axial, sagittal, and coronal slices can be processed, a naturalistic image of the breast is available. Analyzed breast volumes were 570 cc on the right side and 559 cc on the left side.The advantage of magnetic resonance imaging–based breast volumetry is the fact that often magnetic resonance imaging data are available to rule out implant rupture,2 to quantify capsular contracture, and for breast cancer screeninig.3 The use of magnetic resonance imaging–based volumetry is intriguing because the navigation software is often available in the hospitals were neurosurgical units are on call. We thought to transfer the current neurosurgical practice for magnetic resonance imaging–based breast volumetry. We found our pilot results encouraging, with a variation of less than 2 percent, in contrast to the real implant size in two measurements with blinded operators. However, large-scale prospective trials are warranted to elucidate the value of preoperative magnetic resonance imaging–based breast volumetry. DISCLOSURE None of the authors has any commercial associations that might pose or create a conflict of interest with information on products presented in this article. Christian Herold, M.D. Karsten Knobloch, M.D., Ph.D. Department of Plastic, Hand, and Reconstructive Surgery; Hannover Medical School Lennart H. Stieglitz, M.D. Amir Samii, M.D., Ph.D. International Neuroscience Institute Peter M. Vogt, M.D., Ph.D. Department of Plastic, Hand, and Reconstructive Surgery; Hannover Medical School; Hannover, Germany

3D parallel coordinate systems—A new data visualization method in the context of microscopy‐based multicolor tissue cytometry

Presentation of multiple interactions is of vital importance in the new field of cytomics. Quantitative analysis of multi- and polychromatic stained cells in tissue will serve as a basis for medical diagnosis and prediction of disease in forthcoming years. A major problem associated with huge interdependent data sets is visualization. Therefore, alternative and easy-to-handle strategies for data visualization as well as data meta-evaluation (population analysis, cross-correlation, co-expression analysis) were developed. To facilitate human comprehension of complex data, 3D parallel coordinate systems have been developed and used in automated microscopy-based multicolor tissue cytometry (MMTC). Frozen sections of human skin were stained using the combination anti-CD45-PE, anti-CD14-APC, and SytoxGreen as well as the appropriate single and double negative controls. Stained sections were analyzed using automated confocal laser microscopy and semiquantitative MMTC-analysis with TissueQuest 2.0. The 3D parallel coordinate plots are generated from semiquantitative immunofluorescent data of single cells. The 2D and 3D parallel coordinate plots were produced by further processing using the Matlab environment (Mathworks, USA). Current techniques in data visualization primarily utilize scattergrams, where two parameters are plotted against each other on linear or logarithmic scales. However, data evaluation on cartesian x/y-scattergrams is, in general, only of limited value in multiparameter analysis. Dot plots suffer from serious problems, and in particular, do not meet the requirements of polychromatic high-context tissue cytometry of millions of cells. The 3D parallel coordinate plot replaces the vast amount of scattergrams that are usually needed for the cross-correlation analysis. As a result, the scientist is able to perform the data meta-evaluation by using one single plot. On the basis of 2D parallel coordinate systems, a density isosurface is created for representing the event population in an intuitive way. The proposed method opens new possibilities to represent and explore multidimensional data in the perspective of cytomics and other life sciences, e.g., DNA chip array technology. Current protocols in immunofluorescence permit simultaneous staining of up to 17 markers. Showing the cross-correlation between these markers requires 136 scattergrams, which is a prohibitively high number. The improved data visualization method allows the observation of such complex patterns in only one 3D plot and could take advantage of the latest developments in 3D imaging.

Process design optimisation using embedded hybrid visualisation and data analysis techniques within a genetic algorithm optimisation framework

Process optimisation is a difficult task due to the non-linear, non-convex and often discontinuous nature of the mathematical models used. Although significant advances in deterministic methods have been made, stochastic procedures, specifically genetic algorithms, provide an attractive technology for solving these optimisation problems. However, genetic algorithms are not naturally suited to highly constrained problems. We propose a targeted genetic algorithm for process optimisation which is suitable for highly constrained problems. The genetic operators, crossover and mutation, are defined based on information gained about the feasible region and the behaviour of the objective function through the use of a data analysis procedure. The data analysis is based on a visual representation, the parallel co-ordinate system. A pattern matching algorithm, the Scan Circle Algorithm [K. Wang, A. Salhi, E.S. Fraga, Cluster identification using a parallel co-ordinate system for knowledge discovery and nonlinear optimization, in: J. Grievink, J. van Schijndel (Eds.), Proceedings of the 12th European Symposium on Computer-Aided Process Engineering, Computer-Aided Chemical Engineering, vol. 10, Elsevier, Amsterdam, 2002, pp. 1003–1008], is extended through the use of Learning Vector Quantization [T. Kohonen, Self-Organizing Maps, Springer-Verlag, Heidelberg, 1995] to identify, automatically, key features of the objective function and the search space. These features are used to target the genetic operators. Results from the application of the new targeted genetic algorithm to an oil stabilisation problem are presented, demonstrating the effective, efficient and robust nature of the implementation. The use of visualisation as the core of the data analysis step also provides a useful tool for explaining the results obtained by the optimisation procedure.

Visualization and data mining of high-dimensional data

Visualization provides insight through images and can be considered as a collection of application specific mappings: ProblemDomain→VisualRange. For the visualization of multivariate problems a multidimensional system of parallel coordinates (abbreviated as ∥-coords) is constructed which induces a one-to-one mapping between subsets of N-space and subsets of 2-space. The result is a rigorous methodology for doing and seeing N-dimensional geometry. Starting with an the overview of the mathematical foundations, it is seen that the display of high-dimensional datasets and search for multivariate relations among the variables is transformed into a 2-D pattern recognition problem. This is the basis for the application to Visual Data Mining which is illustrated with real dataset of Very Large Scale Integration (VLSI—“chip”) production. Then a recent geometric classifier is presented and applied to three real datasets. The results compared to those of 23 other classifiers have the least error. The algorithm has quadratic computational complexity in the size and number of parameters, provides comprehensible and explicit rules, does dimensionality selection—where the minimal set of original variables required to state the rule is found—and orders these variables so as to optimize the clarity of separation between the designated set and its complement. Finally, a simple visual economic model of a real country is constructed and analyzed in order to illustrate the special strength of ∥-coords in modeling multivariate relations by means of hypersurfaces.

Exploratory Analysis using Parallel Coordinate Systems: Data Visualization in N-Dimensions

We introduce an exploratory technique that is used to visualize higher order geometries in an easily recognizable two-dimensional representation: parallel coordinate systems. In this research, parallel coordinate systems visual analysis is used to assess competitive pricing behavior. Results show that this simple exploratory technique identified the same main and cross-elasticities identified by an MCI model. This research illustrates the value and simplicity of adding parallel coordinate systems visual analysis to the manager's exploratory analysis tool kit. Implications are discussed.

Cluster identification with parallel coordinates

In this paper, the visualization of multi-dimensional data with the parallel coordinate representation is studied. A particular problem of interest is the identification of lines to which clusters of points are close in an n-dimensional space. By using the duality between the Cartesian and the parallel coordinate systems, a scan-line approach in the parallel coordinate system is established and implemented to aid the identification of such lines.

Parallel Volume Coordinates for Hyperdimensional Computer Graphics

A new coordinate system for hyperdimensional computer graphics called parallel volume coordinates is developed. Parallel axis, parallel plane, and parallel volume coordinates are compared using the representations of points, lines, hyperplanes, and hypervolumes. Coordinate dimension is distinguished from parametric dimension. A unique correspondence property for each of the three parallel coordinate systems is characterized, illustrated, and proved.

Multidimensional Lines. I: Representation

Based on a system of parallel coordinates, a methodology for visualizing multivariate relations (i.e., subsets of $R^N $) by mapping them uniquely into indexed subsets of $R^2 $ was introduced earlier. Here, the foundations for the representation mapping in general are given, and the representation of lines in $R^N $ by $N - 1$ planar points indexed by a pair of distinct integers from $\{ 0,1,2, \cdots ,N \}$ in $R^2 $ is obtained. This yields construction and display algorithms for the representation of lines, points on lines, changes of parameterization, and line transformations.

Convexity algorithms in parallel coordinates

With a system of parallel coordinates , objects in R N can be represented with planar “ graphs ” (i.e., planar diagrams) for arbitrary N [21]. In R 2 , embedded in the projective plane, parallel coordinates induce a point ← → line duality. This yields a new duality between bounded and unbounded convex sets and hstars ( a generalization of hyperbolas ), as well as a duality between convex union (convex merge) and intersection. From these results, algorithms for constructing the intersection and convex merge of convex polygons in O ( n ) time and the convex hull on the plane in O (log n ) for real-time and O ( n log n ) worst-case construction, where n is the total number of points, are derived. By virtue of the duality, these algorithms also apply to polygons whose edges are a certain class of convex curves. These planar constructions are studied prior to exploring generalizations to N -dimensions. The needed results on parallel coordinates are given first.

Mobility analysis of planar four-bar mechanisms through the parallel coordinate system

This paper presents a new method for the mobility analysis of planar mechanisms. The method utilizes a geometrical representation known as “parallel coordinates.” It is a transformation that maps the Euclidean space R N to N parallel coordinates in the projective plane. Points in R 2 are transformed to line segments in the parallel coordinate plane, and circles in R 2 are transformed to hyperbolae. Also, in this investigation, special techniques required for mobility analysis are developed. First, the intersection of circles is performed graphically through the parallel coordinate system. The parallel coordinate plane is then appended to relate this intersection data to the angular coordinates of the various members of the linkage. The ranges of these angular coordinates are the results of the mobility analysis.

射影写像による透視図の合成法― (2)

On a plane, properly arranging a pair of plan and elevation of a solid figure, projecting those figures respectively on proper two lines from two points and furthermore projecting those images from other two, points, perspective drawing of the original solid figure can be constructed by intersection of corresponding projector. This paper presents the theory of this new method of obtaining perspective drawing and its applications and elucidates the relation of two parallel coordinate systems which keep images on line constant and between the arrangement of plan and elevation and the center of projection, and also shows that this method is an extension of Einschneideverfahren in parallel axonometric drawing and that it is easy to obtain perspective drawing without any technical knowledge if the arrangement of plan and elevation and the center of projection is previously given.

Transformation of the wave equation solution between parallel displaced cylindrical coordinate systems

With regard to the revolution condition the solution of the wave equation in cylindrical coordinates can be considered as a linear combination of numerable infinite partial solutions. By means of the addition theorems for Bessel functions each of these partial solutions is transformed into a parallel displaced cylindrical coordinate system where it is represented again as a linear combination of partial solutions of the wave equation. The transformation matrices are formulated and combine the vectors of amplitudes of these linear combinations in both parallel displaced cylindrical coordinate systems.

The Thomas Precession

This paper is intended to give a simple physical understanding of the kinematic effect referred to as the Wigner rotation or, when applied to an orbiting object, the Thomas precession. Since this is a kinematic effect it applies not only to particles with spin but to all physical bodies in which a direction can be defined. To aid in avoiding the usual pitfalls in working with these problems, a review is made of several different approaches to the problem of an infinitesimally extended accelerating physical object. The central problem is in taking successive Lorentz transformations between parallel coordinate systems and clearly distinguishing between physical rotations of the object and coordinate rotations. When accounting for the energy associated with the Thomas precession a simple physical explanation is given rather than the misleading description popularly presented.