
Major Thesis of Joachim StaibInteractive Analysis and Visualization of Ambiguities of NonNegaitve Matrix FactorizationsChair for computer graphics and visualization
MotivationMatrix factorization techniques are valuable for analyzing and reducing huge amounts of data by representing them as a linear superposition of a small number of basis signals. When the input data is composed of only nonnegative values, nonnegative matrix factorization (NMF) techniques preserve this property in the factorization result. In general NMF is not unique, i.e. more than one factorization for a given data set exists. The goal of this work is to provide an interactive browser that allows the visual analysis of the nonconvex ambiguity space of all possible NMFs. Instead of changing the factorization algorithm to reflect different possibly fuzzy factorization requirements a human user actively involved in the process of finding a desired solution. DescriptionThe foundation of the browser is a sampling of the solution set for a given data set. For this a parameterization of this space is derived and a new sampling algorithm that can handle high dimensions is developed. The implemented browser works on image data. It enumerates various solutions and lets the user search for a factorization with desired properties. The browser provides the user with a tree oriented navigation structure where only important representatives of the solution set are shown. In combination with various visualizations of the sampled ambiguity space it becomes possible to quickly find a desired factorization for a given dataset. ResultsThe work deals with three main problems:
Outline of the approximation. (a) Beginning from a known starting point, the distance to the border of the valid space is searched. (b) Using the found border points a cuboid is fitted. (c) New points which serve as center points for future iterations are generated on the surface of the newly created cuboid. (d) Finally the space is approximated by a list of such cuboids.
Screenshot of the browser. The left panel contains an overview of the tree oriented search. Beginning with a sampling of the complete solution set (Complete) the third representative solution was used to start another sampling in its surrounding. Both samplings are presented as a list of filtered solutions. The right side shows different visualizations of the solution set.
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