Analysis of high dimensional data is a common task. Often, small multiples are used to visualize 1 or 2 dimensions at a time, such as in a scatterplot matrix. Associating data points between different views can be difficult though, as the points are not fixed. Other times, dimensional reduction techniques are employed to summarize the whole dataset in one image, but individual dimensions are lost in this view. In this paper, we present a means of augmenting a dimensional reduction plot with isocontours to reintroduce the original dimensions. By applying this to each dimension in the original data, we create multiple views where the points are consistent, which facilitates their comparison. Our approach employs a combination of a novel, graph-based projection technique with a GPU accelerated implementation of moving least squares to interpolate space between the points. We also present evaluations of this approach both with a case study and with a user study.
Multidimensional data is one of the fundamental classes of data @cite_11 . As such, there is a large corpus of existing works on the visualization of multidimensional data @cite_37 @cite_3 @cite_5 @cite_17 . These include glyph-based approaches @cite_29 @cite_15 @cite_4 , pixel based techniques @cite_1 , or stacked plots @cite_42 , along with more geometric techniques such as scatterplots @cite_20 @cite_0 and parallel coordinates @cite_26 . Scatterplot matrices @cite_22 @cite_7 are particularly common, as they show the relationships between all dimensions simultaneously. However, they scale poorly with the number of dimensions as it takes @math views to represent all the dimensions, so each individual view will be quite small. Scagnostics can be used to single out plots of particular interest, but this would hide most of the dimensions, not to mention associations across plots would be even more difficult, nescessitating brushing and linking techniques.
@cite_37 @cite_11 @cite_4 @cite_26 @cite_22 @cite_7 @cite_29 @cite_42 @cite_1 @cite_3 @cite_0 @cite_5 @cite_15 @cite_20 @cite_17
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We introduce a method for organizing multivariate displays and for guiding interactive exploration through high-dimensional data. The method is based on nine characterizations of the 2D distributions of orthogonal pairwise projections on a set of points in multidimensional Euclidean space. These characterizations include such measures as density, skewness, shape, outliers, and texture. Statistical analysis of these measures leads to ways for 1) organizing 2D scatterplots of points for coherent viewing, 2) locating unusual (outlying) marginal 2D distributions of points for anomaly detection and 3) sorting multivariate displays based on high-dimensional data, such as trees, parallel coordinates, and glyphs Scatterplot matrices (SPLOMs), parallel coordinates, and glyphs can all be used to visualize the multiple continuous variables (i.e., dependent variables or measures) in multidimensional multivariate data. However, these techniques are not well suited to visualizing many categorical variables (i.e., independent variables or dimensions). To visualize multiple categorical variables, 'hierarchical axes' that 'stack dimensions' have been used in systems like Polaris and Tableau. However, this approach does not scale well beyond a small number of categorical variables. [8] extend the matrix paradigm of the SPLOM to simultaneously visualize several categorical and continuous variables, displaying many kinds of charts in the matrix depending on the kinds of variables involved. We propose a variant of their technique, called the Generalized Plot Matrix (GPLOM). The GPLOM restricts 's technique to only three kinds of charts (scatterplots for pairs of continuous variables, heatmaps for pairs of categorical variables, and barcharts for pairings of categorical and continuous variable), in an effort to make it easier to understand. At the same time, the GPLOM extends 's work by demonstrating interactive techniques suited to the matrix of charts. We discuss the visual design and interactive features of our GPLOM prototype, including a textual search feature allowing users to quickly locate values or variables by name. We also present a user study that compared performance with Tableau and our GPLOM prototype, that found that GPLOM is significantly faster in certain cases, and not significantly slower in other cases. We introduce a novel projection-based visualization method for high-dimensional data sets by combining concepts from MDS and the geometry of the hyperbolic spaces. This approach hyperbolic multi-dimensional scaling (H-MDS) is a synthesis of two important concepts for explorative data analysis and visualization: (i) multi-dimensional scaling uses proximity or pair distance data to generate a low-dimensional, spatial presentation of the data; (ii) previous work on the "hyperbolic tree browser" demonstrated the extraordinary advantages for an interactive display of graph-like data in the two-dimensional hyperbolic space (H2).In the new approach, H-MDS maps proximity data directly into the H2. This removes the restriction to "quasihierarchical", graph-based data--a major limitation of (ii). Since a suitable distance function can convert all kinds of data to proximity (or distance-based) data, this type of data can be considered the most general.We review important properties of the hyperbolic space and, in particular, the circular Poincare model of the H2. It enables effective human-computer interaction: by mouse dragging the "focus", the user can navigate in the data without loosing the context. In H2 the "fish-eye" behavior originates not simply by a non-linear view transformation but rather by extraordinary, non-Euclidean properties of the H2. Especially, the exponential growth of length and area of the underlying space makes the H2 a prime target for mapping hierarchical and (now also) high-dimensional data.Several high-dimensional mapping examples including synthetic and real-world data are presented. Since high-dimensional data produce "ring"-shaped displays, we present methods to enhance the display by modulating the dissimilarity contrast. This is demonstrated for an application for unstructured text: i.e., by using multiple film critiques from news:rec.art.movies.reviews and www.imdb.com, each movie is placed within the H2--creating a "space of movies" for interactive exploration. In this paper, we present a novel parallel coordinates design integrated with points (scattering points in parallel coordinates, SPPC), by taking advantage of both parallel coordinates and scatterplots. Different from most multiple views visualization frameworks involving parallel coordinates where each visualization type occupies an individual window, we convert two selected neighboring coordinate axes into a scatterplot directly. Multidimensional scaling is adopted to allow converting multiple axes into a single subplot. The transition between two visual types is designed in a seamless way. In our work, a series of interaction tools has been developed. Uniform brushing functionality is implemented to allow the user to perform data selection on both points and parallel coordinate polylines without explicitly switching tools. A GPU accelerated dimensional incremental multidimensional scaling (DIMDS) has been developed to significantly improve the system performance. Our case study shows that our scheme is more efficient than traditional multi-view methods in performing visual analysis tasks.