• The KIPS Transactions:PartB
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• v.9B no.5
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• pp.643-652
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• 2002

This paper proposes an efficient hybrid fixed-point (FP) algorithm for improving performances of the independent component analysis (ICA) based on neural networks. The proposed algorithm is the FP algorithm based on secant method and momentum for ICA. Secant method is applied to improve the separation performance by simplifying the computation process for estimating the root of objective function, which is to minimize the mutual informations of the independent components. The momentum is applied for high-speed convergence by restraining the oscillation if the process of converging to the optimal solution. It can simultaneously achieve a superior properties of the secant method and the momentum. The proposed algorithm has been applied to the composite fingerprints and the images generated by random mixing matrix in the 8 fingerprints of $256\times{256}$-pixel and the 10 images of $512\times{512}$-pixel, respectively. The simulation results show that the proposed algorithm has better performances of the separation speed and rate than those using the FP algorithm based on Newton and secant method. Especially, the secant FP algorithm can be solved the separating performances depending on initial points settings and the nonrealistic learning time for separating the large size images by using the Newton FP algorithm.

• East Asian mathematical journal
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• v.23 no.2
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• pp.261-270
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• 2007

We provide a local convergence analysis for Secant-like algorithm for solving nonsmooth variational inclusions in Banach spaces. An existence-convergence theorem and an improvement of the ratio of convergence of this algorithm are given under center-conditioned divided difference and Aubin's continuity concept. Our result compare favorably with related obtained in [16].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.131-135
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• 2005

This paper proposes an efficient face recognition using independent component analysis(ICA) derived from the fixed point(FP) algorithm based on secant method. The secant method can exclude the complex computation of differential process from the FP based on Newton method. The proposed ICA has been applied to recognize the 20 Yale face images of $324\times324$ pixels. The experimental results show that the proposed ICA is superior to PCA not only in the restoration performance of basis images but also in the recognition performance of the trained images and the test images. Then negative angle as similarity measures has better recognition ratio than city-block and Euclidean.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.336-341
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• 2004

This paper proposes an independent component analysis(ICA) of the fixed-point (FP) algorithm based on secant method and the kurtosis. The FP algorithm based on secant method is applied to improve the analysis speed and performance by simplifying the calculation process of the complex derivative in Newton method, the kurtosis is applied to cluster the components. The proposed ICA has been applied to the problems for separating the 6-mixed signals of 500 samples and 8-mixed images of $512{\times}512$ pixels, respectively. The experimental results show that the proposed ICA has always a fixed analysis sequence. The result can be solved the limit of conventional ICA based on secant method which has a variable sequence depending on the running of algorithm. Especially, the proposed ICA can be used for classifying and identifying the signals or the images.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.294-299
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• 2005

This paper presents the separation performance of the linearly mixed image signals with additive noises by using an independent component analyses(ICAs) of the fixed-point(FP) algorithm based on Newton and secant method, respectively. The Newton's FP-ICA uses the slope of objective function, and the secant's FP-ICA also uses the tangent line of objective function. The 2 kinds of ICA have been applied to the 2 dimensional 2-image with $512\times512$ pixels. Then Gaussian noise and Laplacian noise are added to the mixed images, respectively. The experimental results show that the Newton's FP-ICA has better the separation speed than secant FP-ICA and the secant's FP-ICA has also the better separation rate than Newton's FP-ICA. Especially, the Newton and secant method gives relatively larger improvement degree in separation speed and rate as the noise increases.

• Journal of Electrical Engineering and Technology
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• v.3 no.1
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• pp.52-59
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• 2008

This paper describes the secant method for solving the economic dispatch (ED) problem with generator constraints and transmission losses. The ED problem is an important optimization problem in the economic operation of a power system. The proposed algorithm involves selection of minimum and maximum incremental costs (lambda values) and then the evaluation of optimal lambda at required power demand is done by secant method. The proposed algorithm has been tested on a power system having 6, 15, and 40 generating units. Studies have been made on the proposed method to solve the ED problem by taking 120 and 200 units with generator constraints. Simulation results of the proposed approach were compared in terms of solution quality, convergence characteristics, and computation efficiency with conventional methods such as lambda iterative method, heuristic methods such as genetic algorithm, and meta-heuristic methods like particle swarm optimization. It is observed from different case studies that the proposed method provides qualitative solutions with less computational time compared to various methods available in the literature.

• The KIPS Transactions:PartB
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• v.11B no.4
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• pp.429-436
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• 2004

This paper proposes an independent component analyses(ICAs) of the fixed-point (FP) algorithm based on Newton and secant method by adding the kurtosis, respectively. The kurtosis is applied to cluster the analyzed components, and the FP algorithm is applied to get the fast analysis and superior performance irrelevant to learning parameters. The proposed ICAs have been applied to the problems for separating the 6-mixed signals of 500 samples and 10-mixed images of $512\times512$ pixels, respectively. The experimental results show that the proposed ICAs have always a fixed analysis sequence. The results can be solved the limit of conventional ICA without a kurtosis which has a variable sequence depending on the running of algorithm. Especially. the proposed ICA can be used for classifying and identifying the signals or the images. The results also show that the secant method has better the separation speed and performance than Newton method. And, the secant method gives relatively larger improvement degree as the problem size increases.

• The KIPS Transactions:PartB
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• v.11B no.7 s.96
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• pp.813-820
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• 2004

This paper proposes a digital image watermarking which is robust to geometric distortions using an independent component analysis(ICA) of fixed-point(FP) algorithm based on secant method. The FP algorithm of secant method is applied for better performance in a separation time and rate, and ICA is applied to reject the prior knowledges for original image, key, and watermark such as locations and size, etc. The proposed method embeds the watermark into the spatial domain of original image The proposed watermarking technique has been applied to lena, key, and two watermarks(text and Gaussian noise) respectively. The simulation results show that the proposed method has higher speed and better rate for extracting the original images than the FP algorithm of Newton method. And the proposed method has a watermarking which is robust to geometric distortions such as resizing, rotation, and cropping. Especially, the watermark of images with Gaussian noise has better extraction performance than the watermark with text since Gaussian noise has lower correlation coefficient than the text to the original and key images. The watermarking of ICA doesn't require the prior knowledge for the original images.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.6 no.2
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• pp.19-26
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• 1995

The design of broad-band, thin layer electromagnetic wave absorbers usually employs magnetic materials. The common absorber consists of a magnetic material layer bonded to a metal plate at the back. For such structure, a theoretical expression involving six parameters defines the allowable material shape and values of electromagnetic parameters that will produce zero reflection or more practically more than 99% absorption (20dB attenuation). The Secant Method was employed to compute the matching boundary values corresponding to 20dB attenuation. In addition, a search algorithm coupled with the Secant Method was developed to obtain allowable range of material parameters for the design of wave absorbers. These numerical methodes applicable to any six parameters effectively yielded accurate solutions in the least iterations.

• Journal of Korean Society of Forest Science
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• v.82 no.1
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• pp.34-43
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• 1993

In this paper, the characteristics of cable logging operations are discussed from a standpoint of mechanics. An example of standing skyline operations is used to illustrate the mechanical principles. Using force and moment boundary conditions, the maximum allowable payload was formulated as a function of slope profile, system geometry and operation options. This formulation includes fundamental equations for log drag and single segment mechanics. The catenary link model is the basic assumption in simulating cable segment stretches. In order to demonstrate the solution procedures of the formulation, a computer model was developed. The model uses Secant algorithm to determine the solution of the complex nonlinear equation set. Finally, the computer model was demonstrated using a hypothetical data set.