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Topography preserving Gaussian mixture models as cortical maps: applications of the generative topographic mapping and the elastic net
thesisposted on 2017-02-14, 00:51 authored by Cohen, Dror
In this thesis two topography preserving Gaussian Mixture Models are used to model cortical maps. Two major novel contributions are presented; the application of the Generative Topographic Mapping (GTM) to the formation of ocular dominance stripes and using the Elastic Net (EN) as a visual category representation. The applications are motivated by Marr's computational framework in that the contributions correspond to different levels of abstraction. Firstly, motivated by theoretical and experimental comparisons of the GTM and EN, the GTM is applied for the formation of ocular dominance stripes. Simulations are presented that demonstrate that the GTM can indeed produce realistic looking patterns in some instances, though careful parameter selection is required. In addition the GTM exhibits properties that the EN does not, such as twisting and 'hyper sensitivity'. Consequently it is proposed that further mathematical investigation may relate the neuronal interoprability of the GTM to that of the EN. In the second application the EN is used to model population of neurons in higher level processing that are postulated to code visual categories. Using the EN visualisations are presented that allow some novel insights. Motivated by the ability of the EN to capture 'high level' concepts a novel visual categorisation scheme is suggested. The proposed system is evaluated on the Caltech101 data set and shows good performance. A number of interesting future directions that pertain to both artificial and biological vision are suggested.