A new method for analyzing the intrinsic dimensionality (ID) of low-dimensional manifolds in high-dimensional feature spaces is presented. Compared to a previous approach by Fukunaga and Olsen (1971), the method has only linear instead of cubic time complexity with respect to the dimensionality of the input space. Moreover, it is less sensitive to noise than the former approach. Experiments include ID estimation of synthetic data for comparison and illustration as well as ID estimation of an image sequence.

In this contribution Dynamic Cell Structures (DCS network) are applied to classify local image structures at particular facial landmarks. The facial landmarks such as the corners of the eyes or intersections of the iris with the eyelid are computed in advance by a combined model and data driven sequential search strategy. To reduce the detection error after the processing of the sequential search strategy, the computed image positions are verified applying a DCS network. The DCS network is trained by supervised learning with feature vectors which encode spatially arranged edge and structural information at the keypoint position considered. The model driven localization as well as the data driven verification are based on steerable filters, which build a representation comparable with one provided by a receptive field in the human visual system. We apply a DCS based classifier because of its ability to grasp the topological structure of complex input spaces and because it has proved successful in a number of other classification tasks. In our experiments the average error resulting from false positive classifications is less than 1%.

Dynamic cell structures (DCS) represent a family of artificial neural architectures suited both for unsupervised and supervised learning. They belong to the recently (Martinetz 1994) introduced class of topology representing networks (TRN) that build perfectly topology preserving feature maps. DCS employ a modified Kohonen learning rule in conjunction with competitive Hebbian learning. The Kohonen type learning rule serves to adjust the synaptic weight vectors while Hebbian learning establishes a dynamic lateral connection structure between the units reflecting the topology of the feature manifold. In case of supervised learning, i.e., function approximation, each neural unit implements a radial basis function, and an additional layer of linear output units adjusts according to a delta-rule. DCS is the first RBF-based approximation scheme attempting to concurrently learn and utilize a perfectly topology preserving map for improved performance. Simulations on a selection of CMU-Benchmarks indicate that the DCS idea applied to the growing cell structure algorithm (Fritzke 1993c) leads to an efficient and elegant algorithm that can beat conventional models on similar tasks.

Dynamic Cell Structures (DCS) represent a family of artificial neural architectures suited both for unsupervised and supervised learning. They belong to the recently [Martinetz94] introduced class of Topology Representing Networks (TRN) which build perlectly topology pre(cid:173) serving feature maps. DCS empI'oy a modified Kohonen learning rule in conjunction with competitive Hebbian learning. The Kohonen type learning rule serves to adjust the synaptic weight vectors while Hebbian learning establishes a dynamic lateral connection structure between the units reflecting the topology of the feature manifold. In case of super(cid:173) vised learning, i.e. function approximation, each neural unit implements a Radial Basis Function, and an additional layer of linear output units adjusts according to a delta-rule. DCS is the first RBF-based approxima(cid:173) tion scheme attempting to concurrently learn and utilize a perfectly to(cid:173) pology preserving map for improved performance. Simulations on a selection of CMU-Benchmarks indicate that the DCS idea applied to the Growing Cell Structure algorithm [Fritzke93] leads to an efficient and elegant algorithm that can beat conventional models on similar tasks.