Tomasz J. Cholewo

Sequential network construction for time series prediction

This paper introduces an application of the sequential network construction (SNC) method to select the size of several popular neural network predictor architectures for various benchmark training sets. The specific architectures considered are a FIR network and the partially recurrent Elman network and its extension, with context units also added for the output layer. We consider an enhancement of a FIR network in which only those weights having relevant time delays are utilized. Bias-variance trade-off in relation to the prediction risk estimation by means of nonlinear cross-validation (NCV) is discussed. The presented approach is applied to the Wolfer sunspot number data and a Mackey-Glass chaotic time series. Results show that the best predictions for the Wolfer data are computed using a FIR neural network while for Mackey-Glass data an Elman network yields superior results.

Printer model inversion by constrained optimization

This paper describes a novel method for finding colorant amounts for which a printer will produce a requested color appearance based on constrained optimization. An error function defines the gamut mapping method and black replacement method. The constraints limit the feasible solution region to the device gamut and prevent exceeding the maximum total area coverage. Colorant values corresponding to in-gamut colors are found with precision limited only by the accuracy of the device model. Out-of- gamut colors are mapped to colors within the boundary of the device gamut. This general approach, used in conjunction with different types of color difference equations, can perform a wide range of out-of-gamut mappings such as chroma clipping or for finding colors on gamut boundary having specified properties. We present an application of this method to the creation of PostScript color rendering dictionaries and ICC profiles.

Neural network tools for stellar light prediction

This paper presents a comparative study of state-of-the-art neurocomputing methods applied to several benchmark time series, including the white dwarf light curve. The goal is to determine which of the predictive models work best for data from natural sources. The emphasis is on using a unified methodology for selection of the best architectures among those used for comparison. The specific architectures considered are a Finite Impulse Response (FIR) network and three types of layered recurrent networks: Jordan, Elman, and extended Elman. An enhancement of a FIR network allowing selection of weights with relevant time delays only is also presented. Our approach is applied to two benchmark prediction problems: the Wolfer sunspot number data and a white dwarf light curve. Results show that the best predictions are obtained using a FIR neural network.

Black generation using lightness scaling

This paper describes a method for constructing a lookup table relating a 3D CMY coordinate system to CMYK colorant amounts in a way that maximizes the utilization of the printer gamut volume. The method is based on an assumption, satisfied by most printers, that adding a black colorant to any combination of CMY colorants does not result in a color with more chroma. Therefore the CMYK gamut can be obtained from the CMY gamut by expanding it towards lower lightness values. Use of black colorant on the gray axis is enforced by modifying the initial distribution of CMY points through an approximate black generation transform. Lightness values of a resulting set of points in CIELAB space are scaled to fill the four-color gamut volume. The output CMYK values corresponding to the modified CIELAB colors are found by inverting a printer model. This last step determines a specific black use rate which can depend on the region of the color space.

Exact Hessian calculation in feedforward FIR neural networks

FIR neural networks are feedforward neural networks with regular scalar synapses replaced by linear finite impulse response filters. This paper introduces the second order temporal backpropagation algorithm which enables the exact calculation of the second order error derivatives for a FIR neural network. This method is based on the error gradient calculation method first proposed by Wan (1993) and referred to as temporal backpropagation. A reduced FIR synapse model obtained by ignoring unnecessary time lags is proposed to reduce the number of network parameters.

Inverse mapping with neural network for control of nonlinear systems

This paper demonstrates some aspects of the method of inverse mapping control. In place of using the commonly known method of plant inverse dynamics learning, the control sequence is calculated using an inverse mapping approach. The discussion on enhancement of the inverse mapping algorithm and its convergence is also provided. The problem of controller retraining during its operation is also discussed.