| Elastic Principal Graphs and Manifolds for Data Visualization |
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Location: Room 124 SCSIS Senate House
Host/Speaker: A.N. Gorban, University of Leicester
Date and Time:
Tuesday, 21 March 2006, 16:45 - 17:45
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Principal manifolds can serve as a useful tool in many practical applications. These manifolds are defined as lines or surfaces passing through ``the middle'' of data distribution. We propose an algorithm for fast construction of grid approximations of principal manifolds with given topology. The algorithm is based on a similarity between principal manifolds and elastic membranes and plates. The functional to be minimized in this method becomes quadratic at the step of the vertices position refinement. This makes the algorithm effective, especially for parallel implementations. One more feature of the method is that the same algorithmic kernel is applied for constructing principal manifolds of different dimensions and topologies. We demonstrate how the flexibility of the approach leads to numerous adaptive strategies like principal graph constructing, etc. The principal cubic complexes are constructed with a specially developed device, the topological grammars. The algorithm is implemented as a C++ package, Elmap, and as part of a stand-alone data visualization tool, VidaExpert, which is available on the web (see http://www.math.le.ac.uk/people/ag153/). Several examples of application of the algorithm, with performance characteristics, are provided.
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