A Data-Driven Approach for Mapping Multivariate Data to Color

A Data-Driven Approach for Mapping Multivariate Data to Color Shenghui Cheng, Wei Xu, Wen Zhong and Klaus Mueller Visual Analytics and Imaging (VAI) Lab, Computer Science Department, Stony Brook University and Brookhaven National Lab ABSTRACT A wide variety of color schemes have been devised for mapping scalar data to color. Some use the data value to index a color scale. Others assign colors to different, usually blended disjoint materials, to handle areas where materials overlap. A number of methods can map low-dimensional data to color, however, these methods do not scale to higher dimensional data. Likewise, schemes that take a more artistic approach through color mixing and the like also face limits when it comes to the number of variables they can encode. We address the challenge of mapping multivariate data to color and avoid these limitations at the same time. It is a data driven method, which first gauges the similarity of the attributes and then arranges them according to the periphery of a convex 2D color space, such as HSL. The color of a multivariate data sample is then obtained via generalized barycentric coordinate (GBC) interpolation. 1 INTRODUCTION Mapping data to color has a rich history and several well-tested color schemes have emerged [1]. In this paper, we are interested in colorizing multivariate data. Here we wish to go beyond the bivariate and trivariate cases, where the two or three variables can be assigned to two or three primary colors through bilinear or barycentric interpolation respectively [3]. Our method is an automatic and data-driven method for visually encoding similarities of variables and data items. 2 OUR MULTIVARIATE COLOR MAPPING SCHEME Our color scheme is a data-driven method based on the relations of data. We first conducted the analysis to extract the similarities or distances among data items and variables. GBC plot is a typical way to visualize the relations among data items and variables, but it loses accuracy. Thus we make use of the improved GBC plot described by Cheng et al [2]. It first maps the variables at the GBC plot periphery (the vertices of the GBC – we choose a circular representation) and then map the data points into it. Since this layout scheme is an optimized approach, it is able to preserve the similarity of variables, the similarity of data points, and the similarity of data points to variables. We illustrate our work with 300 data samples obtained at irregularly placed sensors in a city. Measured are heavy pollutant chemicals, such as “As”, “Cd”, “Cr”, “Cu”, “Hg”, “Ni”, “Pb”, and “Zn”. Fig. 1 shows a visualization of these data with our interface. Color Space After laying out the data, we seek to map the data to a proper color space. Here we wish to choose a color space that can preserve the various similarities described above. Considering the circular shape of the GBC plot, we choose the HSL color space (alternatively, an implementation with the HCL space is in progress). The HSL has a double cone topology and turns into a circle if the lightness L is fixed. This circle can be integrated into the GBC layout. Hence, the HSL color space provides a straightforward geometry for mapping. Using the GBC mapping scheme for the layout, the variables can then be positioned at the circle’s boundary and consequently the samples are laid out in the circle’s center. As such, the layout will result in the sample’s Hue H and Saturation S. The GBC plot directly maps to the center slice of the HSL color space and given this direct mapping it is straightforward to obtain the H and S values for the geospatial Fig. 1. The interface of our approach. The white arrow points to a small red-colored region (black dot). The color legend shows its position in the color map and the bar charts show its attributes’ values. The scatter plots show the same position in different individual maps. (b) (c) (d) (a) * {shecheng, wxu, wezzhong, mueller}@cs.stonybrook.edu map colors. For the lightness, we typically choose L=0.65 for now (Fig. 2 (a)), but we also allow users to adjust it to enhance some features. The GBC layout of the attributes preserves the original similarities in the data and this feature is still maintained in the HS space. By using the GBC plot and the HS space, we can map similar colors to similar attributes, and vice versa. Likewise, similar points map to similar locations in the GBC plot’s interior (and the HS map) and thus will end up having similar colors. Due to the similarity-based, contextual layout of data items and variables, the GBC plot enables users to appreciate what the dominant pollutants are. It is important to realize that the HSL slice-based plot maps samples by the percentage of pollutants they have, and not by absolute value. Conversely, for drawing the colored spatial map we can map the sample weight to intensity. After assigning colors to samples, w

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