We propose a new self-organizing algorithm for a feedforward network inspired to an electrostatic problem that turns out to have intimate relations with information maximization.

We present two methods for nonuniformity correction of imaging array detectors based on neural networks; both exploit image properties to supply lack of calibrations and maximize the entropy of the output. The first method uses a self-organizing net that produces a linear correction of the raw data with coefficients that adapt continuously. The second method employs a kind of contrast equalization curve to match pixel distributions. Our work originates from silicon detectors, but the treatment is general enough to be applicable to many kinds of array detectors like those used in infrared imaging or in high-energy physics.

Unsupervised learning applied to an unstructured neural network can give approximate solutions to the traveling salesman problem. For 50 cities in the plane this algorithm performs like the elastic net of Durbin and Willshaw (1987) and it improves when increasing the number of cities to get better than simulated annealing for problems with more than 500 cities. In all the tests this algorithm requires a fraction of the time taken by simulated annealing.

A self-organizing feature map (Von der Malsburg 1973; Kohonen 1984) sorts n real numbers in O ( n ) time apparently violating the O ( n log n ) bound. Detailed analysis shows that the net takes advantage of the uniform distribution of the numbers and, in this case, sorting in O ( n ) is possible. There are, however, an exponentially small fraction of pathological distributions producing O ( n 2 ) sorting time. It is interesting to observe that standard learning produced a smart sorting algorithm.

We present a geometric interpretation of ordering in self-organizing feature maps. This view provides simpler proofs of Kohonen ordering theorem and of convergence to an ordered state in the one-dimensional case. At the same time it explains intuitively the origin of the problems in higher dimensional cases. Furthermore it provides a geometric view of the known characteristics of learning in self-organizing nets.