Algorithms for nonnegative independent component analysis.

We consider the task of solving the independent component analysis (ICA) problem x=As given observations x, with a constraint of nonnegativity of the source random vector s. We refer to this as nonnegative independent component analysis and we consider methods for solving this task. For independent sources with nonzero probability density function (pdf) p(s) down to s=0 it is sufficient to find the orthonormal rotation y=Wz of prewhitened sources z=Vx, which minimizes the mean squared error of the reconstruction of z from the rectified version y/sup +/ of y. We suggest some algorithms which perform this, both based on a nonlinear principal component analysis (PCA) approach and on a geodesic search method driven by differential geometry considerations. We demonstrate the operation of these algorithms on an image separation problem, which shows in particular the fast convergence of the rotation and geodesic methods and apply the approach to a musical audio analysis task.

Denoising and segmentation of the second heart sound using matching pursuit.

We propose a denoising and segmentation technique for the second heart sound (S2). To denoise, Matching Pursuit (MP) was applied using a set of non-linear chirp signals as atoms. We show that the proposed method can be used to segment the phonocardiogram of the second heart sound into its two clinically meaningful components: the aortic (A2) and pulmonary (P2) components.

Information processing in negative feedback neural networks.

Information theory suggests that extraction of the principal sub-space from data is useful when the input to a neural network is corrupted with additive noise. A number of neural network algorithms exist which can find this principal sub-space, many of which also extract the principal components of the input. However, when there is noise on both input and output of a network, simply extracting the principal sub-space (or components) is not sufficient to optimize information capacity. An approximate solution to maximizing information capacity would be to extract the principal sub-space of components with variances above a certain threshold, and then ensure that these are uncorrelated and that they have equal variance at the output. A neural network is described which uses negative feedback connections to achieve this uncorrelated, equal-variance solution.

Do cortical maps adapt to optimize information density?

Topographic maps are found in many biological and artificial neural systems. In biological systems, some parts of these can form a significantly expanded representation of their sensory input, such as the representation of the fovea in the visual cortex. We propose that a cortical feature map should be organized to optimize the efficiency of information transmission through it. This leads to a principle of uniform cortical information density across the map as the desired optimum. An expanded representation in the cortex for a particular sensory area (i.e. a high magnification factor) means that a greater information density is concentrated in that sensory area, leading to finer discrimination thresholds. Improvement may ultimately be limited by the construction of the sensors themselves. This approach gives a good fit to threshold versus cortical area data of Recanzone et al on owl monkeys trained on a tactile frequency-discrimination task.