• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.2
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• pp.56-64
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• 1998

Multi-layered perceptrons that are a nonlinear neural network model, have been widely used for various applications mainly thanks to good function approximation capability for nonlinear fuctions. However, for digital hardware implementation of the multi-layere perceptrons, the quantization scheme using "look-up tables (LUTs)" is commonly employed to handle nonlinear signmoid activation functions in the neworks, and thus requires large amount of storage to prevent unacceptable quantization errors. This paper is concerned with a new effective methodology for digital hardware implementation of multi-layered perceptrons, and proposes a "piecewise affine approximation" method in which input domain is divided into (small number of) sub-intervals and nonlinear sigmoid function is linearly approximated within each sub-interval. Using the proposed method, we develop an expression and an error backpropagation type learning algorithm for a multi-layered perceptron, and compare the performance with the quantization method through Monte Carlo simulations on XOR problems. Simulation results show that, in terms of learning convergece, the proposed method with a small number of sub-intervals significantly outperforms the quantization method with a very large storage requirement. We expect from these results that the proposed method can be utilized in digital system implementation to significantly reduce the storage requirement, quantization error, and learning time of the quantization method.quantization method.

• ETRI Journal
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• v.45 no.1
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• pp.119-130
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• 2023

We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

• Proceedings of the Korean Society for Emotion and Sensibility Conference
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• 1997.11a
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• pp.146-151
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• 1997

Recntly many devics print electronic images in a variety of ways. But the reproduced color, gamut mappung method and expanded nonlinear quantization are proposed. The color gamut mapping uses saturation mapping of HSI color space. Dithering operation for printing uses expanded nonlinear quantization which considers overlapping phenomena of neighboring printing dots. So the printed image is similar to the image of monitor and can produce high quality image in the low bit color devices.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.569-574
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• 1999

New methods for both color palette design and dithering based on human visual system (HVS) characteristics are proposed. Color quantization for palette design uses the relative visual sensitivity and spatial masking effect of HVS. The dithering operation for printing uses nonlinear quantization, which considers the overlapping phenomena among neighbor printing dots, and then a modified dot-diffusion algorithm is followed to compensate the degradation produced in the quantization process. The proposed techniques can produce high quality image in the low-bit color devices.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.3
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• pp.88-95
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• 1996

Recently, the use of color data is growing fast in the area of image processing. To represent full resolution image on a limited output device, image has to be quantized an dithered. So, many dithering techniques are foundd in the printing. In this paper, we propose nonlinear quantization to consider the overlapping phenomena of neighboring printing dots and modified dot diffusion algorithm to compensate the color degradation produced in the quantization process. In the modified dot-diffusion quantization errors to be diffused are adjusted to improve both image blur and color change produced in the dot diffusion. The printed image obtained by the proposed color dithering method has higher visual quality an less color degradation than the images by conventional printing method.

• Journal of the Korean Institute of Intelligent Systems
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• v.26 no.5
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• pp.375-382
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• 2016

In this paper, we presents a signatures verification by using the nonlinear quantization histogram of polar coordinate based on multi-dimensional adjacent pixel intensity difference. The multi-dimensional adjacent pixel intensity difference is calculated from an intensity difference between a pair of pixels in a horizontal, vertical, diagonal, and opposite diagonal directions centering around the reference pixel. The polar coordinate is converted from the rectangular coordinate by making a pair of horizontal and vertical difference, and diagonal and opposite diagonal difference, respectively. The nonlinear quantization histogram is also calculated from nonuniformly quantizing the polar coordinate value by using the Lloyd algorithm, which is the recursive method. The polar coordinate histogram of 4-directional intensity difference is applied not only for more considering the corelation between pixels but also for reducing the calculation load by decreasing the number of histogram. The nonlinear quantization is also applied not only to still more reflect an attribute of intensity variations between pixels but also to obtain the low level histogram. The proposed method has been applied to verified 90(3 persons * 30 signatures/person) images of 256*256 pixels based on a matching measures of city-block, Euclidean, ordinal value, and normalized cross-correlation coefficient. The experimental results show that the proposed method has a superior to the linear quantization histogram, and Euclidean distance is also the optimal matching measure.

• The Journal of the Acoustical Society of Korea
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• v.21 no.6
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• pp.522-530
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• 2002

This paper introduces a neural network (NN) -based nonlinear predictor for the LP (Linear Prediction) residual. To evaluate the effectiveness of the NN-based nonlinear predictor for LP-residual, we first compared the average prediction gain of the linear long-term predictor with that of the NN-based nonlinear long-term predictor. Then, the effects on the quantization noise of the nonlinear prediction residuals were investigated for the NN-based nonlinear predictor A new NN predictor takes into consideration not only prediction error but also quantization effects. To increase robustness against the quantization noise of the nonlinear prediction residual, a constrained back propagation learning algorithm, which satisfies a Kuhn-Tucker inequality condition is proposed. Experimental results indicate that the prediction gain of the proposed NN predictor was not seriously decreased even when the constrained optimization algorithm was employed.

• Journal of Broadcast Engineering
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• v.25 no.2
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• pp.157-165
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• 2020

In this paper. we propose an effective compensation scheme to the quantization error arisen from quantized learning in a machine learning on an embedded system. In the machine learning based on a gradient descent or nonlinear signal processing, the quantization error generates early vanishing of a gradient and occurs the degradation of learning performance. To compensate such quantization error, we derive an orthogonal compensation vector with respect to a maximum component of the gradient vector. Moreover, instead of the conventional constant learning rate, we propose the adaptive learning rate algorithm without any inner loop to select the step size, based on a nonlinear optimization technique. The simulation results show that the optimization solver based on the proposed quantized method represents sufficient learning performance.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.2
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• pp.133-138
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• 2015

This paper presents a performance improvement of gray level co-occurrence matrix(GLCM) based on the nonuniform quantization, which is generally used to analyze the texture of images. The nonuniform quantization is given by Lloyd algorithm of recursive technique by minimizing the mean square error. The nonlinear intensity levels by performing nonuniformly the quantization of image have been used to decrease the dimension of GLCM, that is applied to reduce the computation loads as a results of generating the GLCM and calculating the texture parameters by using GLCM. The proposed method has been applied to 30 images of $120{\times}120$ pixels with 256-gray level for analyzing the texture by calculating the 6 parameters, such as angular second moment, contrast, variance, entropy, correlation, inverse difference moment. The experimental results show that the proposed method has a superior computation time and memory to the conventional 256-level GLCM method without performing the quantization. Especially, 16-gray level by using the nonuniform quantization has the superior performance for analyzing textures to another levels of 48, 32, 12, and 8 levels.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.4
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• pp.529-535
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• 2013

This paper considers the problem of robust stability for uncertain discrete-time interval time-varying delayed descriptor systems using any combinations of quantization and overflow nonlinearities. First, delay-dependent linear matrix inequality (LMI) condition for discrete-time descriptor systems with time-varying delay and quantization/overflow nonlinearities is presented by proper Lyapunov function. Second, it is shown that the obtained condition can be extended into descriptor systems with uncertainties such as norm-bounded parameter uncertainties and polytopic uncertainties by some useful lemmas. The proposed results can be applied to both descriptor systems and non-descriptor systems. Finally, numerical examples are shown to illustrate the effectiveness and less conservativeness.