The Analysis of Variance.

Rainfall forecasting in space and time using a neural network

Earlier work by Driscoll and Healy has produced an efficient algorithm for
computing the Fourier transform of band-limited functions on the 2-sphere. In this article we present
a reformulation and variation of the original algorithm which results in a greatly improved inverse
transform, and consequent improved convolution algorithm for such functions. All require at most
O(N log2
 N) operations where N is the number of sample points. We also address implementation
considerations and give heuristics for allowing reliable and computationally efficient floating point
implementations of slightly modified algorithms. These claims are supported by extensive numerical
experiments from our implementation in C on DEC, HP, SGI and Linux Pentium platforms. These
results indicate that variations of the algorithm are both reliable and efficient for a large range of
useful problem sizes. Performance appears to be architecture-dependent. The article concludes
with a brief discussion of a few potential applications.

/pdf/ffts-for-the-2-sphere-improvements-and-variations-4mm7r7moxd.pdf

FFTs for the 2-Sphere-Improvements and Variations

Absrract-This paper investigates some fundamental issues concerning the capability of multilayer perceptrons with one hidden layer. The studies are focused on realizations of functions which map from a finite subset of E” into E“. Both real-valued and binary-valued functions are considered. In particular, a least upper bound is derived for the number of hidden neurons needed to realize an arbitrary function which maps from a finite subset of E“ into E“. A nontrivial lower bound is also obtained for realizations of injective functions. This result will be useful in studying pattern recognition and database retrieval. In addition, an upper hound is given for realizing binary-valued functions that are related to pattern classification problems.

/pdf/bounds-on-the-number-of-hidden-neurons-in-j76xhnbplh.pdf

Bounds on the Number of Hidden Neurons in

Spatially distributed rainfall patterns can now be detected using a variety of remote–sensing techniques ranging from weather radar to various satellite–based sensors. Conversion of the remote–sensed signal into rainfall rates, and hence into runoff for a given river basin, is a complex and difficult process using traditional approaches. Neural–network models hold the possibility of circumventing these difficulties by training the network to map rainfall patterns into various measures of runoff that may be of interest. To investigate the potential of this approach, a very simple 5 × 5 grid cell synthetic watershed is used to generate runoff from stochastically generated rainfall patterns. A back–propagation neural network is trained to predict the peak discharge and the time of peak resulting from a single rainfall pattern. Additionally, the neural network is trained to map a time series of three rainfall patterns into a continuum of discharges over future time by using a discrete Fourier series fit to the runoff hydrograph.

Neural-Network Models of Rainfall-Runoff Process

Recent results indicate that the number of hidden nodes (H) in a feedforward neural net depend only on the number of input training patterns (T). There appear to be conjectures that H is on the order of T-1 and of log/sub 2/T. A proof is given that the maximum number of separable regions (M) in the input space is a function of both H and input space dimension (d). The authors also show that H=M -1 and H=log/sub 2/M are special cases of that formulation. M defines a lower bound on T, the number of input patterns that may be used for training. Application to some experiments are investigated. >

On hidden nodes for neural nets

The application of adaptive filters in noise canceling often requires the relative placement of the two transducers at a distance that necessitates a larger order filter in order to obtain an adequate output signal-to-noise ratio. A new adaptive filter structure is introduced that permits a closer placement of the transducers and that allows the cancellation of noise in the presence of crosstalk. Algorithms are developed for the new transversal and lattice filter estimators. Simulations show considerable improvement in mean-square error over that obtained with standard noise canceling algorithms. >

A new adaptive noise cancellation scheme in the presence of crosstalk (speech signals)

https://www.heartrhythmjournal.com/article/S1547-5271(10)00012-3/pdf

The temporal variability of dominant frequency and complex fractionated atrial electrograms constrains the validity of sequential mapping in human atrial fibrillation

We propose the use of spectral analysis on certain noncommutative finite groups in digital signal processing and, in particular, image processing. We pay significant attention to groups constructed as wreath products of cyclic groups. Within this large class of groups, our approach recovers the discrete Fourier transform (DFT), the Haar wavelet transform, various multichannel pyramid filter banks, and other aspects of multiresolution analysis as special cases of a more general phenomenon. In addition, the group structure provides a rich algebraic structure that can be exploited for the analysis and manipulation of signals. Our approach relies on a synthesis of ideas found in the early work of Holmes (1987, 1990), Karpovsky and Trachtenberg (1985), and others on noncommutative filtering, as well as Diaconis's (1989) spectral analysis approach to understanding data.

A wreath product group approach to signal and image processing .I. Multiresolution analysis

The application of adaptive filters in noise cancel- ing often requires the relative placement of the two transducers at a distance that necessitates a large order filter in order to obtain an adequate output signal-to-noise ratio. A new adaptive filter structure is introduced that permits a closer placement of the transducers and that allows the cancellation of noise in the presence of crosstalk. Algorithms are developed for the new transversal and lattice filter estimators. Simulations show con- siderable improvement in mean-square error over that obtained with standard noise canceling algorithms.

G. Mirchandani

Papers

On hidden nodes for neural nets

A new adaptive noise cancellation scheme in the presence of crosstalk (speech signals)

The temporal variability of dominant frequency and complex fractionated atrial electrograms constrains the validity of sequential mapping in human atrial fibrillation

A wreath product group approach to signal and image processing .I. Multiresolution analysis

A New Adaptive Noise Cancellation Scheme in the Presence of Crosstalk