A globally linear model, as implied by conventional Principal Component Analysis (PCA), may be insufficient to represent multivariate data in many situations. It has been known for some time that a combination of several "local" PCA's can provide a suitable approach in such cases [1, 2] . An important question is then how to find an appropriate partitioning of the data space together with a proper choice of the local numbers of principal components (PC's). In this contribution we address both problems within a density estimation framework and propose a probabilistic approach which is based on a mixture of subspace-constrained Gaussians. Thereby the number of local PC's depends on a global resolution parameter, which represents the assumed noise level and determines the degree of smoothing imposed by the model. As a consequence the model leads to an automatic resolution-dependent adjustment of the optimal principal subspace dimensionalities, which may vary among the different mixture components. Furthermore it allows to provide the optimization with an annealing scheme, which solves the initialization problem and offers an incremental model refinement procedure. Experimental results on synthetic and high-dimensional realworld data illustrate the merits of the proposed approach.
In REF , the problem of finding an appropriate data partition for the application of the local PCA is investigated.
Local PCA Learning with Resolution-Dependent Mixtures of Gaussians
9th International Conference on Artificial Neural Networks: ICANN '99
9th International Conference on Artificial Neural Networks: ICANN '99
Computer Science