Principal component neural networks: theory and applications
Principal component neural networks: theory and applications
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
A view of the EM algorithm that justifies incremental, sparse, and other variants
Learning in graphical models
Mixtures of probabilistic principal component analyzers
Neural Computation
Estimating the Intrinsic Dimension of Data with a Fractal-Based Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Manifold-adaptive dimension estimation
Proceedings of the 24th international conference on Machine learning
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
IEEE Transactions on Signal Processing
Self-organizing maps, vector quantization, and mixture modeling
IEEE Transactions on Neural Networks
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This paper introduces an unsupervised batch algorithm for learning the underlying regional linear manifolds and estimating their dimensionalities using a data set in a topographic map. For this purpose, a unified free energy functional is designed and an expectation-maximization procedure is developed to minimize it. Regional dimensionality estimation controls the extent of the linear manifolds. This property makes the model appropriate for representing the datasets with varying regional intrinsic dimensions, compared to the resembling techniques without dimensionality learning capability. Experimental results show the good performance of the model on synthesized and real-world applications.