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. LAMP's 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.

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analysis 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 is 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.

Abstract-In this paper, we present a novel approach for constructing bundled layouts of general graphs. As layout cues for bundles, we use medial axes, or skeletons, of edges which are similar in terms of position information. We combine edge clustering, distance fields, and 2D skeletonization to construct progressively bundled layouts for general graphs by iteratively attracting edges towards the centerlines of level sets of their distance fields. Apart from clustering, our entire pipeline is image-based with an efficient implementation in graphics hardware. Besides speed and implementation simplicity, our method allows explicit control of the emphasis on structure of the bundled layout, i.e. the creation of strongly branching (organic-like) or smooth bundles. We demonstrate our method on several large real-world graphs.Index Terms-Graph layouts, edge bundles, image-based information visualization.

The development of new methods and concepts to visualize massive amounts of data holds the promise to revolutionize the way scientific results are analyzed, especially when tasks such as classification and clustering are involved, as in the case of sensing and biosensing. In this paper we employ a suite of software tools, referred to as PEx-Sensors, through which projection techniques are used to analyze electrical impedance spectroscopy data in electronic tongues and related sensors. The possibility of treating high dimension datasets with PEx-Sensors is advantageous because the whole impedance vs. frequency curves obtained with various sensing units and for a variety of samples can be analyzed at once. It will be shown that non-linear projection techniques such as Sammon's Mapping or IDMAP provide higher distinction ability than linear methods for sensor arrays containing units capable of molecular recognition, apparently because these techniques are able to capture the cooperative response owing to specific interactions between the sensing unit material and the analyte. In addition to allowing for a higher sensitivity and selectivity, the use of PEx-Sensors permits the identification of the major contributors for the distinguishing ability of sensing units and of the optimized frequency range. The latter will be illustrated with sensing units made with layer-by-layer (LbL) films to detect phytic acid, whose capacitance data were visualized with Parallel Coordinates. Significantly, the implementation of PEx-Sensors was conceived so as to handle any type of sensor based on any type of principle of detection, representing therefore a generic platform for treating large amounts of data for sensors and biosensors.