Kernel-Based Equiprobabilistic Topographic Map Formation

1998 ◽  
Vol 10 (7) ◽  
pp. 1847-1871 ◽  
Author(s):  
Marc M. Van Hulle
Keyword(s):  
Density Estimation ◽  
Ad Hoc ◽  
Receptive Fields ◽  
Learning Rule ◽  
Basis Functions ◽  
Nonparametric Density Estimation ◽  
Topographic Map ◽  
Fixed Topology ◽  
Local Input ◽  
Learning Schemes

We introduce a new unsupervised competitive learning rule, the kernel-based maximum entropy learning rule (kMER), which performs equiprobabilistic topographic map formation in regular, fixed-topology lattices, for use with nonparametric density estimation as well as nonparametric regression analysis. The receptive fields of the formal neurons are overlapping radially symmetric kernels, compatible with radial basis functions (RBFs); but unlike other learning schemes, the radii of these kernels do not have to be chosen in an ad hoc manner: the radii are adapted to the local input density, together with the weight vectors that define the kernel centers, so as to produce maps of which the neurons have an equal probability to be active (equiprobabilistic maps). Both an “online” and a “batch” version of the learning rule are introduced, which are applied to nonparametric density estimation and regression, respectively. The application envisaged is blind source separation (BSS) from nonlinear, noisy mixtures.

Adaptive receptive fields for radial basis functions

Desalination ◽  
2001 ◽  
Vol 135 (1-3) ◽  
pp. 83-91 ◽  
Author(s):  
Mutaz M. Jafar ◽  
Ali Zilouchian
Keyword(s):  
Radial Basis Functions ◽  
Receptive Fields ◽  
Basis Functions ◽  
Radial Basis

scholarly journals Natural image sequences constrain dynamic receptive fields and imply a sparse code

2013 ◽  
Vol 1536 ◽  
pp. 53-67 ◽  
Author(s):  
Chris Häusler ◽  
Alex Susemihl ◽  
Martin P. Nawrot
Keyword(s):  
Receptive Fields ◽  
Image Sequences ◽  
Sparse Code ◽  
Natural Image ◽  
Dynamic Receptive Fields

The structure and symmetry of simple-cell receptive-field profiles in the cat’s visual cortex

1986 ◽  
Vol 228 (1253) ◽  
pp. 379-400 ◽  
Keyword(s):  
Visual Cortex ◽  
Receptive Field ◽  
Good Description ◽  
Quantitative Description ◽  
Receptive Fields ◽  
Basis Functions ◽  
Simple Cells ◽  
First Approximation ◽  
Cat Visual Cortex ◽  
Field Symmetry

Receptive fields of simple cells in the cat visual cortex have recently been discussed in relation to the ‘theory of communication' proposed by Gabor (1946). A number of investigators have suggested that the line-weighting functions, as measured orthogonal to the preferred orientation, may be best described as the product of a Gaussian envelope and a sinusoid (i.e. a Gabor function). Following Gabor’s theory of ‘basis’ functions, it has also been suggested that simple cells can be categorized into even-and odd-symmetric categories. Based on the receptive field profiles of 46 simple cells recorded from cat visual cortex, our analysis provides a quantitative description of both the receptive-field envelope and the receptive-field ‘symmetry’ of each of the 46 cells. The results support the notion that, to a first approximation, Gabor functions with three free parameters (envelope width, carrier frequency and carrier phase) provide a good description of the receptive-field profiles. However, our analysis does not support the notion that simple cells generally fit into even- and odd-symmetric categories.

scholarly journals Evidence for the intrinsically nonlinear nature of receptive fields in vision

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Marcelo Bertalmío ◽  
Alex Gomez-Villa ◽  
Adrián Martín ◽  
Javier Vazquez-Corral ◽  
David Kane ◽  
...  
Keyword(s):  
Receptive Field ◽  
Receptive Fields ◽  
Human Perception ◽  
Basis Functions ◽  
Linear Filters ◽  
Visual Neurons ◽  
Vision Science ◽  
Efficient Representation ◽  
Improved Performance ◽  
Nonlinear Nature

Abstract The responses of visual neurons, as well as visual perception phenomena in general, are highly nonlinear functions of the visual input, while most vision models are grounded on the notion of a linear receptive field (RF). The linear RF has a number of inherent problems: it changes with the input, it presupposes a set of basis functions for the visual system, and it conflicts with recent studies on dendritic computations. Here we propose to model the RF in a nonlinear manner, introducing the intrinsically nonlinear receptive field (INRF). Apart from being more physiologically plausible and embodying the efficient representation principle, the INRF has a key property of wide-ranging implications: for several vision science phenomena where a linear RF must vary with the input in order to predict responses, the INRF can remain constant under different stimuli. We also prove that Artificial Neural Networks with INRF modules instead of linear filters have a remarkably improved performance and better emulate basic human perception. Our results suggest a change of paradigm for vision science as well as for artificial intelligence.

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