Arranging arbitrary data into structured layouts

Strong, Grant (2013) Arranging arbitrary data into structured layouts. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

Data. It can range from a single item to an exhaustive array of samples. It may be as simple as a binary label or as complex as a set of high dimensional vectors. It may be comparable by distance, by order, or not at all. In general, data is a term that encompasses a wide gamut. While specific data types vary in makeup and comparability, the common denominator is that it is always possible to take two elements of a data set and determine how dissimilar they are to some degree. The purpose of this thesis is to use that dissimilarity to arrange data into structured layouts in which each item occupies a unique cell. These layouts are meant to be simple, minimal, and free of occlusion. Three novel algorithms for this type of data arrangement are proposed. The first is an amalgamation of the Self-Organizing Map and the k-d tree. It builds a semi-structured layout that is later refined. It performs admirably but requires intermediary steps making it lack the speed necessary for scalability. The second algorithm, called the Self-Sorting Map, is new and is inspired by techniques from the field of dimension reduction. It approaches the problem from a sorting perspective and generates minimal, occlusion-free layouts from all types of data directly. It is fast, scalable, and parallel. The third algorithm transforms the problem from minimizing local dissimilarity, like the others, to maximizing global correlation. Entitled the Max Correlation Map, it is simpler and more robust than its counterparts. Throughout this thesis the three algorithms are analyzed and applied. Creative organizations of images, articles, and cities show the practical worth of organizing data into structured layouts.

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