A unified model for probabilistic principal surfaces

摘要: Principal curves and surfaces are nonlinear generalizations of principal components subspaces, respectively. They can provide insightful summary high-dimensional data not typically attainable by classical linear methods. Solutions to several problems, such as proof existence convergence, faced the original curve formulation have been proposed in past few years. Nevertheless, these solutions generally extensible surfaces, mere computation which presents a formidable obstacle. Consequently, relatively studies available. We previously (2000) probabilistic surface (PPS) address number issues associated with current algorithms. PPS uses manifold oriented covariance noise model, based on generative topographical mapping (GTM), be viewed parametric Kohonen's self-organizing map. Building PPS, we introduce unified model that implements (0 1) varying clamping parameter /spl alpha/. Then, comprehensively evaluate empirical performance GTM, manifold-aligned GTM three popular benchmark sets. It is shown two different comparisons outperforms under identical settings. Convergence found computational overhead incurred decreases 40 percent or less for more complex manifolds. These results show generalized provides flexible effective way obtaining surfaces.