Visualization of multidimensional data with collocated paired coordinates and general line coordinates

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Often multidimensional data are visualized by splitting n-D data to a set of low dimensional data. While it is useful it destroys integrity of n-D data, and leads to a shallow understanding complex n-D data. To mitigate this challenge a difficult perceptual task of assembling low-dimensional visualized pieces to the whole n-D vectors must be solved. Another way is a lossy dimension reduction by mapping n-D vectors to 2-D vectors (e.g., Principal Component Analysis). Such 2-D vectors carry only a part of information from n-D vectors, without a way to restore n-D vectors exactly from it. An alternative way for deeper understanding of n-D data is visual representations in 2-D that fully preserve n-D data. Methods of Parallel and Radial coordinates are such methods. Developing new methods that preserve dimensions is a long standing and challenging task that we address by proposing Paired Coordinates that is a new type of n-D data visual representation and by generalizing Parallel and Radial coordinates as a General Line coordinates. The important novelty of the concept of the Paired Coordinates is that it uses a single 2-D plot to represent n-D data as an oriented graph based on the idea of collocation of pairs of attributes. The advantage of the General Line Coordinates and Paired Coordinates is in providing a common framework that includes Parallel and Radial coordinates and generating a large number of new visual representations of multidimensional data without lossy dimension reduction.