Complex spectral dimensionality on fractal structures

Complex spectral dimensionality on fractal structures

Fractal Dimension and Dimensionality Reduction

ABSTRACT In this paper we investigate the relationship between several dimensionality redu tion methods and the intrinsi dimensionality of the data in the redu ed spa e, as estimated by the fra tal dimension. We show that a su essful dimensionality redu tion/feature extra tion algorithm proje ts the data into a feature spa e with dimensionality lose to the intrinsi dimensionality of the data in...

Spectral Dimensionality Reduction

© 2004 Yoshua Bengio, Olivier Delalleau, Nicolas Le Roux, Jean-Francois Paiement, Pascal Vincent, Marie Ouimet. Tous droits réservés. All rights reserved. Reproduction partielle permise avec citation du document source, incluant la notice ©. Short sections may be quoted without explicit permission, if full credit, including © notice, is given to the source. Série Scientifique Scientific Series ...

Probabilistic Spectral Dimensionality Reduction

We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting probabilistic models are based on GRFs. The resulting model is a nonlinear generalization of principal component analysis. We show ...

Sevcik’s Fractal Based Dimensionality Reduction of Hyper-Spectral Remote Sensing Data

Recent advancements in Remote sensing has led the way for the development of Hyper spectral sensors. Hyper spectral remote sensing is a new technology that is currently being used by researchers and scientists with regard to the detection and identification of mineral, vegetation, man-made materials and other features. These sensors are far more superior as they collect information in a very na...