Magnification Control in Winner Relaxing Neural Gas

An important goal in neural map learning, which can conveniently be accomplished by magnification control, is to achieve information optimal coding in the sense of information theory. In the present contribution we consider the winner relaxing approach for the neural gas network. Originally, winner relaxing learning is a slight modification of the self-organizing map learning rule that allows for adjustment of the magnification behavior by an a priori chosen control parameter. We transfer this approach to the neural gas algorithm. The magnification exponent can be calculated analytically for arbitrary dimension from a continuum theory, and the entropy of the resulting map is studied numerically conf irming the theoretical prediction. The influence of a diagonal term, which can be added without impacting the magnification, is studied numerically. This approach to maps of maximal mutual information is interesting for applications as the winner relaxing term only adds computational cost of same order and is easy to implement. In particular, it is not necessary to estimate the generally unknown data probability density as in other magnification control approaches.Comment: 14pages, 2 figure

Magnification Control in Self-Organizing Maps and Neural Gas

We consider different ways to control the magnification in self-organizing maps (SOM) and neural gas (NG). Starting from early approaches of magnification control in vector quantization, we then concentrate on different approaches for SOM and NG. We show that three structurally similar approaches can be applied to both algorithms: localized learning, concave-convex learning, and winner relaxing learning. Thereby, the approach of concave-convex learning in SOM is extended to a more general description, whereas the concave-convex learning for NG is new. In general, the control mechanisms generate only slightly different behavior comparing both neural algorithms. However, we emphasize that the NG results are valid for any data dimension, whereas in the SOM case the results hold only for the one-dimensional case.Comment: 24 pages, 4 figure

A Generative Model of Natural Texture Surrogates

Natural images can be viewed as patchworks of different textures, where the local image statistics is roughly stationary within a small neighborhood but otherwise varies from region to region. In order to model this variability, we first applied the parametric texture algorithm of Portilla and Simoncelli to image patches of 64X64 pixels in a large database of natural images such that each image patch is then described by 655 texture parameters which specify certain statistics, such as variances and covariances of wavelet coefficients or coefficient magnitudes within that patch. To model the statistics of these texture parameters, we then developed suitable nonlinear transformations of the parameters that allowed us to fit their joint statistics with a multivariate Gaussian distribution. We find that the first 200 principal components contain more than 99% of the variance and are sufficient to generate textures that are perceptually extremely close to those generated with all 655 components. We demonstrate the usefulness of the model in several ways: (1) We sample ensembles of texture patches that can be directly compared to samples of patches from the natural image database and can to a high degree reproduce their perceptual appearance. (2) We further developed an image compression algorithm which generates surprisingly accurate images at bit rates as low as 0.14 bits/pixel. Finally, (3) We demonstrate how our approach can be used for an efficient and objective evaluation of samples generated with probabilistic models of natural images.Comment: 34 pages, 9 figure

Prototype selection for parameter estimation in complex models

Parameter estimation in astrophysics often requires the use of complex physical models. In this paper we study the problem of estimating the parameters that describe star formation history (SFH) in galaxies. Here, high-dimensional spectral data from galaxies are appropriately modeled as linear combinations of physical components, called simple stellar populations (SSPs), plus some nonlinear distortions. Theoretical data for each SSP is produced for a fixed parameter vector via computer modeling. Though the parameters that define each SSP are continuous, optimizing the signal model over a large set of SSPs on a fine parameter grid is computationally infeasible and inefficient. The goal of this study is to estimate the set of parameters that describes the SFH of each galaxy. These target parameters, such as the average ages and chemical compositions of the galaxy's stellar populations, are derived from the SSP parameters and the component weights in the signal model. Here, we introduce a principled approach of choosing a small basis of SSP prototypes for SFH parameter estimation. The basic idea is to quantize the vector space and effective support of the model components. In addition to greater computational efficiency, we achieve better estimates of the SFH target parameters. In simulations, our proposed quantization method obtains a substantial improvement in estimating the target parameters over the common method of employing a parameter grid. Sparse coding techniques are not appropriate for this problem without proper constraints, while constrained sparse coding methods perform poorly for parameter estimation because their objective is signal reconstruction, not estimation of the target parameters.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS500 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Reflectance Hashing for Material Recognition

We introduce a novel method for using reflectance to identify materials. Reflectance offers a unique signature of the material but is challenging to measure and use for recognizing materials due to its high-dimensionality. In this work, one-shot reflectance is captured using a unique optical camera measuring {\it reflectance disks} where the pixel coordinates correspond to surface viewing angles. The reflectance has class-specific stucture and angular gradients computed in this reflectance space reveal the material class. These reflectance disks encode discriminative information for efficient and accurate material recognition. We introduce a framework called reflectance hashing that models the reflectance disks with dictionary learning and binary hashing. We demonstrate the effectiveness of reflectance hashing for material recognition with a number of real-world materials