Archana P. Sangole

Visualization of randomly ordered numeric data sets using spherical self-organizing feature maps

Abstract Scientific data visualization requires a variety of mathematical techniques to transform multivariate data sets into simple graphical objects, or glyphs, that provide scientists and engineers with a clearer understanding of the underlying system behaviour. The spherical self-organizing feature map (SOFM) described in this paper exploits an unsupervised clustering algorithm to map randomly organized N -dimensional data into a lower three-dimensional (3D) space for visual pattern analysis. Each node on the spherical lattice corresponds to a cluster of input vectors that lie in close spatial proximity within the original feature space, and neighbouring nodes on the lattice represent cluster centres with a high degree of vector similarity. Simple metrics are used to extract associations between the cluster units and the input vectors assigned to them. These are then graphically displayed on the spherical SOFM as either surface elevations or colourized facets. The resulting colourized graphical objects are displayed and manipulated within 3D immersive virtual reality (IVR) environments for interactive data analysis. The ability of the proposed algorithm to transform arbitrarily arranged numeric strings into unique, reproducible shapes is illustrated using chaotic data generated by the Lozi, Henon, Rossler, and Lorenz attractor functions under varying initial conditions. Implementation of the basic data visualization technique is further demonstrated using the more common Wisconsin breast cancer data and multi-spectral satellite data.

Representing high-dimensional data sets as closed surfaces

Scientific data visualization provides scientists and engineers with a deeper insight and greater understanding about physical phenomena through the use of graphical tools. Individuals are able to identify patterns embedded in data sets using visual cues such as color and shape, rather than directly searching through a vast volume of numbers. The visualization algorithm described in this paper utilizes a spherical self-organizing feature map (SOFM) to automatically cluster and develop a well-defined topology of arbitrary data vectors, based on a pre-defined measure of similarity, and generate a three-dimensional color-coded surface model that reflects cluster variations. Implementation of this self-organizing surface geometry for data visualization applications is illustrated by examining the graphical forms created for a small synthetic test data set and a large environmental data-base. The proposed methodology provides the researcher with a new tool to encode information into shape and easily transfer the geometric model to an immersive virtual reality (IVR) environment for interactive information analysis.

Mentoring Review and Reflections

This paper reviews mentoring definitions, mentor and protégée characteristics, and the process and outcomes of the mentoring process. In addition, the faculty provides some personal reflections about their mentoring process. Reflections of this nature may inspire us to consider further the adoption and investigation of formal and informal overt mentoring programs in our institutions in order to promote mentoring relationships that can foster personal and professional achievement and satisfaction.

Intelligent systems for interactive design and visualization

Intelligent systems for interactive design and visualization require technologies that reliably generate surface and solid models from acquired spatial data, user hand gestures and verbal instructions; and seamlessly integrate this information into the overall product design process. The deformable spherical self-organizing feature map (SOFM) is a versatile modeling tool that is able to create 3D shapes from numerous arbitrarily ordered N-dimensional data vectors. The data may be surface points on existing objects or multi-dimensional feature vectors obtained through experimental observation. The SOFM develops a topologically ordered lattice that provides information about magnitude and connectivity between neighboring vectors in the original data space. The shapes generated by the deformable SOFM can be displayed, reoriented, analyzed, and modified in an immersive virtual reality environment (IVR). This paper describes how the spherical SOFM can be used to reconstruct the shape of an existing object from measured coordinate points and be modified using shape transformation techniques for virtual 3D free-form design.

Scientific data visualization using three-dimensional self-organizing feature maps

The goal of scientific data visualization is to transform numeric or symbolic data into simple coherent patterns for enhanced human interpretation. It involves a combination of exploratory data analysis and data visualization techniques that create a new level of information providing a deeper look at the underlying structures present in high dimensional data. This paper discusses how a spherical self-organizing feature map (SOFM) enables multivariate numeric data to take a geometric form by mapping high dimensional data to a 3D, space, thereby providing a mechanism to explore large numeric databases for coherent patterns. The patterns present in the numeric data are given a shape based on similarity. The performance of the proposed visualization algorithm is tested using coordinate data from known geometry and multi-spectral satellite data.

Geometric Representations for High-Dimensional Data Using a Spherical SOFM

The self-organizing feature map (SOFM) is primarily used to map high-dimensional data into low-dimensional spaces for pattern classification applications. The pre-defined connections in the SOFM lattice and the weight adaptation algorithm enable topological associations to emerge within arbitrary numeric data. The degree of association or similarity between neighboring nodes on the lattice is largely influenced by mathematical and statistical measures between the data vectors assigned to the nodes. The relationship between neighboring nodes, or cluster units, can be visually interpreted by an observer if this information is displayed as colors and/or distortions on the SOFM lattice. This paper describes how a SOFM that starts as a tessellated unit sphere can develop a closed surface topology of arbitrary N -dimensional data vectors that reflects information content as defined by the mathematical or statistical measure. Transforming the numeric data into a closed geometric form enables the information embedded in large high-dimensional data sets to be easily transferred into an immersive 3D virtual reality environment for interactive scientific data visualization. The implementation of the proposed methodology is illustrated using both high-dimensional synthetic data and the more common Fishers Iris data.

FREEFORM SURFACE RECONSTRUCTION FROM SCATTERED POINTS USING A DEFORMABLE SPHERICAL MAP

Reconstruction of freeform surfaces from scattered coordinate data is a difficult problem encountered in many surface fitting and geometric modeling applications. Conventional tessellation and parametric surface fitting techniques are limited because they require prior knowledge about the connectivity between the sampled points. The method of surface reconstruction described in this paper exploits the learning capability of a self-organizing feature map (SOFM) to adaptively fit a deformable sphere to the unorganized 3D coordinate data. The learning algorithm automatically establishes the connectivity between the measured points by iteratively changing the topological relationships within the map. By incorporating additional constraints during the learning process it is possible to have the deformable map follow the shape of objects with surface holes and cavities. Several examples of freeform surfaces with varying levels of complexity are discussed in order to demonstrate the performance of the algorithm.

Shape Registration Using Deformable Self-Organizing Feature Maps

A novel approach to matching freeform surfaces for shape registration and object recognition is described in this paper. The proposed method builds a surface mesh of the underlying object geometry by iteratively deforming the nodal lattice of a spherical self-organizing feature map (SOFM) to “best” fit the measured 3D coordinate data. The final topology of the deformed mesh is, therefore, equivalent to the original lattice of the SOFM. Each node in the final mesh represents a cluster of coordinate points that lie in close spatial proximity in the input data space. In this way, closed surfaces with identical node topologies are created from different data sets. Information about node connectivity is then extracted from the ordered lattice and used to determine local surface features for correspondence matching. Based on the matched nodes, rigid body transformations between the original data sets can be determined. The shape registration algorithm enables comparisons to be made between different sized data sets or data acquired from similar freeform objects with arbitrary pose. The method is illustrated using measured coordinate data from three objects with complex freeform surface geometry.

Micro Geometry Flaws in the Exchange of Design Data Using STEP

A fundamental issue in concurrent engineering is sharing data among a vanety of commercially available computer-aided de sign, analysis, and manufacturing software tools. Geometry flaws often occur in the exchange of design data between dissimilar CAD systems and have multiplied with the ever-increasing complexity of product geometry. in recent years the international standard ISO 10303, STEP (Standard for the Exchange of Product model data), has achieved a success rate of 95-98% in the exchange of design data. This paper demonstrates that a significant portion of these errors are the result of the different degrees of precision used by com mercial CAD systems and are often apparent as minute gaps ranging from 0.00001-0.1 mm. The consequences are micro geometry gaps that are not visible to the designer but influence the creation of the final geometry at the receivers end. Research has found that these gaps can be directly linked to the incompatibility in the degrees of precision used by individual CAD systems to associate vertices and curves with related faces.

Shape Morphing and Reconstruction Using A Self-Organizing Feature Map

The shape reconstruction process has remained an active research area in archaeology, paleontology, forensics, cultural heritage restoration and art conservation. In all these cases, the reconstruction process is tedious and time consuming. Aside from collecting several randomly mixed fragments, the fragments also have to be glued together. A stable and efficient algorithm for computer aided reconstruction of fragmented models is introduced in this paper. This novel approach is based on the morphing technique using the deformable self organizing feature map (SOFM). The SOFM is a skeletal framework for modeling surfaces that dynamically change shape. The lattice of the SOFM is a spherical map that maintains the relative connectivity of the neighboring nodes as it transforms under external and internal forces. The digitized fragments are assigned weight vectors and morphed into the weight vectors of the original model. The technique is illustrated by reconstructing the geometry of a complete vase from the surface data acquired from several fragmented pieces.