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.

Use of Information Visualization Methods Eliminating Cross Talk in Multiple Sensing Units Investigated for a Light-Addressable Potentiometric Sensor

The integration of nanostructured films containing biomolecules and silicon-based technologies is a promising direction for reaching miniaturized biosensors that exhibit high sensitivity and selectivity. A challenge, however, is to avoid cross talk among sensing units in an array with multiple sensors located on a small area. In this letter, we describe an array of 16 sensing units, of a light-addressable potentiometric sensor (LAPS), which was made with layer-by-Layer (LbL) films of a poly(amidomine) dendrimer (PAMAM) and single-walled carbon nanotubes (SWNTs), coated with a layer of the enzyme penicillinase. A visual inspection of the data from constant-current measurements with liquid samples containing distinct concentrations of penicillin, glucose, or a buffer indicated a possible cross talk between units that contained penicillinase and those that did not. With the use of multidimensional data projection techniques, normally employed in information Visualization methods, we managed to distinguish the results from the modified LAPS, even in cases where the units were adjacent to each other. Furthermore, the plots generated with the interactive document map (IDMAP) projection technique enabled the distinction of the different concentrations of penicillin, from 5 mmol L(-1) down to 0.5 mmol L(-1). Data visualization also confirmed the enhanced performance of the sensing units containing carbon nanotubes, consistent with the analysis of results for LAPS sensors. The use of visual analytics, as with projection methods, may be essential to handle a large amount of data generated in multiple sensor arrays to achieve high performance in miniaturized systems.

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.

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.