Parallel coordinate plots (PCPs) are among the most useful techniques for the visualization and exploration of high-dimensional data spaces. They are especially useful for the representation of correlations among the dimensions, which identify relationships and interdependencies between variables. However, within these high-dimensional spaces, PCPs face difficulties in displaying the correlation between combinations of dimensions and generally require additional display space as the number of dimensions increases. In this paper, we present a new technique for high-dimensional data visualization in which a set of low-dimensional PCPs are interactively constructed by sampling user-selected subsets of the high-dimensional data space. In our technique, we first construct a graph visualization of sets of well-correlated dimensions. Users observe this graph and are able to interactively select the dimensions by sampling from its cliques, thereby dynamically specifying the most relevant lower dimensional data to be used for the construction of focused PCPs. Our interactive sampling overcomes the shortcomings of the PCPs by enabling the visualization of the most meaningful dimensions (i.e., the most relevant information) from high-dimensional spaces. We demonstrate the effectiveness of our technique through two case studies, where we show that the proposed interactive low-dimensional space constructions were pivotal for visualizing the high-dimensional data and discovering new patterns.
As mentioned previously, PCPs @cite_31 display high-dimensional datasets as polylines intersecting with parallel axes. The improvement of PCPs is a very active research topic and one of the well-known challenges in this domain is that of polyline cluttering, i.e., a reduction of line crossings and overlaps for visual comprehensibility. Several techniques have attempted to improve the comprehensibility of the results obtained by PCPs by applying clustering or sampling of the polylines @cite_23 @cite_25 @cite_0 @cite_5 . In addition, the effectiveness of PCPs are highly dependent on the order of the dimensions and various dimension ordering techniques have recently been proposed to address this issue @cite_14 @cite_35 @cite_42 @cite_10 . The last major challenge is the difficulty in representing all correlations in one display space, especially when a particular dimension is strongly correlated with many other dimensions. In these circumstances, PCPs can represent only a subset of all possible relationships between the dimensions.
@cite_35 @cite_14 @cite_42 @cite_0 @cite_23 @cite_5 @cite_31 @cite_10 @cite_25
2291534001 2093219811 2163925089 2145646037 2034694694 2066560342 2166947480
We introduce the parallel coordinates matrix (PCM) as the counterpart to the scatterplot matrix (SPLOM). Using a graph-theoretic approach, we determine a list of axis orderings such that all pairwise relations can be displayed without redundancy while each parallel-coordinates plot can be used independently to visualize all variables of the dataset. Therefore, existing axis-ordering algorithms, rendering techniques, and interaction methods can easily be applied to the individual parallel-coordinates plots. We demonstrate the value of the PCM in two case studies and show how it can serve as an overview visualization for parallel coordinates. Finally, we apply existing focus-and-context techniques in an interactive setup to support a detailed analysis of multivariate data. High-dimensional data visualization is receiving increasing interest because of the growing abundance of highdimensional datasets. To understand such datasets, visualization of the structures present in the data, such as clusters, can be an invaluable tool. Structures may be present in the full high-dimensional space, as well as in its subspaces. Two widely used methods to visualize high-dimensional data are the scatter plot matrix (SPM) and the parallel coordinate plot (PCP). SPM allows a quick overview of the structures present in pairwise combinations of dimensions. On the other hand, PCP has the potential to visualize not only bi-dimensional structures but also higher dimensional ones. A problem with SPM is that it suffers from crowding and clutter which makes interpretation hard. Approaches to reduce clutter are available in the literature, based on changing the order of the dimensions. However, usually this reordering has a high computational complexity. For effective visualization of high-dimensional structures, also PCP requires a proper ordering of the dimensions. In this paper, we propose methods for reordering dimensions in PCP in such a way that high-dimensional structures (if present) become easier to perceive. We also present a method for dimension reordering in SPM which yields results that are comparable to those of existing approaches, but at a much lower computational cost. Our approach is based on finding relevant subspaces for clustering using a quality criterion and cluster information. The quality computation and cluster detection are done in image space, using connected morphological operators. We demonstrate the potential of our approach for synthetic and astronomical datasets, and show that our method compares favorably with a number of existing approaches. Visual clutter denotes a disordered collection of graphical entities in information visualization. Clutter can obscure the structure present in the data. Even in a small dataset, clutter can make it hard for the viewer to find patterns, relationships and structure. In this paper, we define visual clutter as any aspect of the visualization that interferes with the viewer's understanding of the data, and present the concept of clutter-based dimension reordering. Dimension order is an attribute that can significantly affect a visualization's expressiveness. By varying the dimension order in a display, it is possible to reduce clutter without reducing information content or modifying the data in any way. Clutter reduction is a display-dependent task. In this paper, we follow a three-step procedure for four different visualization techniques. For each display technique, first, we determine what constitutes clutter in terms of display properties; then we design a metric to measure visual clutter in this display; finally we search for an order that minimizes the clutter in a display Our ability to accumulate large, complex (multivariate) data sets has far exceeded our ability to effectively process them in searching for patterns, anomalies and other interesting features. Conventional multivariate visualization techniques generally do not scale well with respect to the size of the data set. The focus of this paper is on the interactive visualization of large multivariate data sets based on a number of novel extensions to the parallel coordinates display technique. We develop a multi-resolution view of the data via hierarchical clustering, and use a variation of parallel coordinates to convey aggregation information for the resulting clusters. Users can then navigate the resulting structure until the desired focus region and level of detail is reached, using our suite of navigational and filtering tools. We describe the design and implementation of our hierarchical parallel coordinates system which is based on extending the XmdvTool system. Lastly, we show examples of the tools and techniques applied to large (hundreds of thousands of records) multivariate data sets. A methodology for visualizing analytic and synthetic geometry in RN is presented. It is based on a system of parallel coordinates which induces a non-projective mapping between N-Dimensional and 2-Dimensional sets. Hypersurfaces are represented by their planar images which have some geometrical properties analogous to the properties of the hypersurface that they represent. A point ← → line duality when N = 2 generalizes to lines and hyperplanes enabling the representation of polyhedra in RN. The representation of a class of convex and non-convex hypersurfaces is discussed together with an algorithm for constructing and displaying any interior point. The display shows some local properties of the hypersurface and provides information on the point's proximity to the boundary. Applications to Air Traffic Control, Robotics, Computer Vision, Computational Geometry, Statistics, Instrumentation and other areas are discussed. The navigation of high-dimensional data spaces remains challenging, making multivariate data exploration difficult. To be effective and appealing for mainstream application, navigation should use paradigms and metaphors that users are already familiar with. One such intuitive navigation paradigm is interactive route planning on a connected network. We have employed such an interface and have paired it with a prominent high-dimensional visualization paradigm showing the N-D data in undistorted raw form: parallel coordinates. In our network interface, the dimensions form nodes that are connected by a network of edges representing the strength of association between dimensions. A user then interactively specifies nodes edges to visit, and the system computes an optimal route, which can be further edited and manipulated. In our interface, this route is captured by a parallel coordinate data display in which the dimension ordering is configured by the specified route. Our framework serves both as a data exploration environment and as an interactive presentation platform to demonstrate, explain, and justify any identified relationships to others. We demonstrate our interface within a business scenario and other applications. In order to gain insight into multivariate data, complex structures must be analysed and understood. Parallel coordinates is an excellent tool for visualizing this type of data but has its limitations. This paper deals with one of its main limitations - how to visualize a large number of data items without hiding the inherent structure they constitute. We solve this problem by constructing clusters and using high precision textures to represent them. We also use transfer functions that operate on the high precision textures in order to highlight different aspects of the cluster characteristics. Providing predefined transfer functions as well as the support to draw customized transfer functions makes it possible to extract different aspects of the data. We also show how feature animation can be used as guidance when simultaneously analysing several clusters. This technique makes it possible to visually represent statistical information about clusters and thus guides the user, making the analysis process more efficient.