On Improved Projection Techniques to Support Visual Exploration of Multi-Dimensional Data Sets

Abstract

Projection (or dimensionality reduction) techniques have been used as a means to handling the growing dimensionality of data sets as well as providing a way to visualize information coded into point relationships. Their role is essential in data interpretation and simultaneous use of different projections and their visualizations improve data understanding and increase the level of confidence in the result. For that purpose, projections should be fast to allow multiple views of the same data set. In this work we present a novel fast technique for projecting multi-dimensional data sets into bidimensional (2D) spaces that preserves neighborhood relationships. Additionally, a new technique for improving 2D projections from multi-dimensional data is presented, that helps reduce the inherent loss of information yielded by dimensionality reduction. The results are stimulating and are presented in the form of comparative visualizations against known and new 2D projection techniques. Based on the projection improvement approach presented here, a new metric for quality of projection is also given, that matches well the visual perception of quality. We discuss the implication of using improved projections in visual exploration of large data sets and the role of interaction in visualization of projected subspaces.

Projection inspector: Assessment and synthesis of multidimensional projections

“…In our implementation we are using ffiffiffiffi ffi m p randomly chosen control points, where m is the number of instances in the data set. Control points are placed in the visual space using the Force Scheme method proposed in [41]. Fig.…”

Probing trace levels of prometryn solutions: from test samples in the lab toward real samples with tap water

“…The 2D plot is created by projecting them onto the plane with graphical markers represented by Y = {y 1 ,y 2 ,…,y n }, with the positions on the 2D plot being determined in an optimization procedure using an injective function f: X ? Y that minimizes |d( [19], where d(y i , y j ) is the distance function on the projected plane. The flexibility of this optimization approach arises from the availability of several cost (or error) functions used for placing the graphical markers on the 2D plot.…”

Information Visualization to Enhance Sensitivity and Selectivity in Biosensing

“…A projection technique is an injective function f: X ? Y which seeks to make |d(x i , [15]. Different formulations of the error function and different approaches to its minimization result in several possible choices for the mapping function f. The error function is as a measure of the information lost in the projection procedure.…”

“…It is based on a fast dimension reduction strategy referred to as Fastmap [18], which is employed to generate an initial placement of the data points that is improved with the Force Scheme [15], a strategy that mimics a placement approach based on simulating mass-spring models typically employed for drawing graph models [19]. The quality of the low-dimensional embedding achieved with a projection may depend on various factors, including properties of the data and behavior of the distance function, as well as user goals.…”