TAPCA: time adaptive self-organizing maps for adaptive principal components analysis

We propose a neural network called time adaptive principal components analysis (TAPCA) which is composed of a number of time adaptive self-organizing map (TASOM) networks. Each TASOM in the TAPCA network estimates one eigenvector of the correlation matrix of the input vectors entered so far, without having to calculate the correlation matrix. This estimation is done in an online fashion. The input distribution can be nonstationary, too. The eigenvectors appear in order of importance: the first TASOM calculates the eigenvector corresponding to the largest eigenvalue of the correlation matrix, and so on. The TAPCA network is tested in stationary environments, and is compared with the eigendecomposition (ED) method and generalized Hebbian algorithm (GHA) network. It performs better than both methods and needs fewer samples to converge. It is also tested in nonstationary environments, where it automatically tolerates translation, rotation, scaling, and a change in the shape of the distribution.

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