Search results for: Gaussian Filtering
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 537

Search results for: Gaussian Filtering

477 Information Filtering using Index Word Selection based on the Topics

Authors: Takeru YOKOI, Hidekazu YANAGIMOTO, Sigeru OMATU

Abstract:

We have proposed an information filtering system using index word selection from a document set based on the topics included in a set of documents. This method narrows down the particularly characteristic words in a document set and the topics are obtained by Sparse Non-negative Matrix Factorization. In information filtering, a document is often represented with the vector in which the elements correspond to the weight of the index words, and the dimension of the vector becomes larger as the number of documents is increased. Therefore, it is possible that useless words as index words for the information filtering are included. In order to address the problem, the dimension needs to be reduced. Our proposal reduces the dimension by selecting index words based on the topics included in a document set. We have applied the Sparse Non-negative Matrix Factorization to the document set to obtain these topics. The filtering is carried out based on a centroid of the learning document set. The centroid is regarded as the user-s interest. In addition, the centroid is represented with a document vector whose elements consist of the weight of the selected index words. Using the English test collection MEDLINE, thus, we confirm the effectiveness of our proposal. Hence, our proposed selection can confirm the improvement of the recommendation accuracy from the other previous methods when selecting the appropriate number of index words. In addition, we discussed the selected index words by our proposal and we found our proposal was able to select the index words covered some minor topics included in the document set.

Keywords: Information Filtering, Sparse NMF, Index wordSelection, User Profile, Chi-squared Measure

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476 Gaussian Density and HOG with Content Based Image Retrieval System – A New Approach

Authors: N. Shanmugapriya, R. Nallusamy

Abstract:

Content-based image retrieval (CBIR) uses the contents of images to characterize and contact the images. This paper focus on retrieving the image by separating images into its three color mechanism R, G and B and for that Discrete Wavelet Transformation is applied. Then Wavelet based Generalized Gaussian Density (GGD) is practical which is used for modeling the coefficients from the wavelet transforms. After that it is agreed to Histogram of Oriented Gradient (HOG) for extracting its characteristic vectors with Relevant Feedback technique is used. The performance of this approach is calculated by exactness and it confirms that this method is wellorganized for image retrieval.

Keywords: Content-Based Image Retrieval (CBIR), Relevant Feedback, Histogram of Oriented Gradient (HOG), Generalized Gaussian Density (GGD).

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475 An Efficient Gaussian Noise Removal Image Enhancement Technique for Gray Scale Images

Authors: V. Murugan, R. Balasubramanian

Abstract:

Image enhancement is a challenging issue in many applications. In the last two decades, there are various filters developed. This paper proposes a novel method which removes Gaussian noise from the gray scale images. The proposed technique is compared with Enhanced Fuzzy Peer Group Filter (EFPGF) for various noise levels. Experimental results proved that the proposed filter achieves better Peak-Signal-to-Noise-Ratio PSNR than the existing techniques. The proposed technique achieves 1.736dB gain in PSNR than the EFPGF technique.

Keywords: Gaussian noise, adaptive bilateral filter, fuzzy peer group filter, switching bilateral filter, PSNR

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474 An Improved Quality Adaptive Rate Filtering Technique Based on the Level Crossing Sampling

Authors: Saeed Mian Qaisar, Laurent Fesquet, Marc Renaudin

Abstract:

Mostly the systems are dealing with time varying signals. The Power efficiency can be achieved by adapting the system activity according to the input signal variations. In this context an adaptive rate filtering technique, based on the level crossing sampling is devised. It adapts the sampling frequency and the filter order by following the input signal local variations. Thus, it correlates the processing activity with the signal variations. Interpolation is required in the proposed technique. A drastic reduction in the interpolation error is achieved by employing the symmetry during the interpolation process. Processing error of the proposed technique is calculated. The computational complexity of the proposed filtering technique is deduced and compared to the classical one. Results promise a significant gain of the computational efficiency and hence of the power consumption.

Keywords: Level Crossing Sampling, Activity Selection, Rate Filtering, Computational Complexity, Interpolation Error.

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473 DWM-CDD: Dynamic Weighted Majority Concept Drift Detection for Spam Mail Filtering

Authors: Leili Nosrati, Alireza Nemaney Pour

Abstract:

Although e-mail is the most efficient and popular communication method, unwanted and mass unsolicited e-mails, also called spam mail, endanger the existence of the mail system. This paper proposes a new algorithm called Dynamic Weighted Majority Concept Drift Detection (DWM-CDD) for content-based filtering. The design purposes of DWM-CDD are first to accurate the performance of the previously proposed algorithms, and second to speed up the time to construct the model. The results show that DWM-CDD can detect both sudden and gradual changes quickly and accurately. Moreover, the time needed for model construction is less than previously proposed algorithms.

Keywords: Concept drift, Content-based filtering, E-mail, Spammail.

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472 Propagation of a Generalized Beam in ABCD System

Authors: Halil Tanyer Eyyuboğu

Abstract:

For a generalized Hermite sinosiodal / hyperbolic Gaussian beam passing through an ABCD system with a finite aperture, the propagation properties are derived using the Collins integral. The results are obtained in the form of intensity graphs indicating that previously demonstrated rules of reciprocity are applicable, while the existence of the aperture accelerates this transformation.

Keywords: Optical communications, Hermite-Gaussian beams, ABCD system.

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471 Minimal Residual Method for Adaptive Filtering with Finite Termination

Authors: Noor Atinah Ahmad, Shazia Javed

Abstract:

We present a discussion of three adaptive filtering algorithms well known for their one-step termination property, in terms of their relationship with the minimal residual method. These algorithms are the normalized least mean square (NLMS), Affine Projection algorithm (APA) and the recursive least squares algorithm (RLS). The NLMS is shown to be a result of the orthogonality condition imposed on the instantaneous approximation of the Wiener equation, while APA and RLS algorithm result from orthogonality condition in multi-dimensional minimal residual formulation. Further analysis of the minimal residual formulation for the RLS leads to a triangular system which also possesses the one-step termination property (in exact arithmetic)

Keywords: Adaptive filtering, minimal residual method, projection method.

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470 Computing SAGB-Gröbner Basis of Ideals of Invariant Rings by Using Gaussian Elimination

Authors: Sajjad Rahmany, Abdolali Basiri

Abstract:

The link between Gröbner basis and linear algebra was described by Lazard [4,5] where he realized the Gr┬¿obner basis computation could be archived by applying Gaussian elimination over Macaulay-s matrix . In this paper, we indicate how same technique may be used to SAGBI- Gröbner basis computations in invariant rings.

Keywords: Gröbner basis, SAGBI- Gröbner basis, reduction, Invariant ring, permutation groups.

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469 Intra Prediction using Weighted Average of Pixel Values According to Prediction Direction

Authors: Kibaek Kim, Dongjin Jung, Jinik Jang, Jechang Jeong

Abstract:

In this paper, we proposed a method to reduce quantization error. In order to reduce quantization error, low pass filtering is applied on neighboring samples of current block in H.264/AVC. However, it has a weak point that low pass filtering is performed regardless of prediction direction. Since it doesn-t consider prediction direction, it may not reduce quantization error effectively. Proposed method considers prediction direction for low pass filtering and uses a threshold condition for reducing flag bit. We compare our experimental result with conventional method in H.264/AVC and we can achieve the average bit-rate reduction of 1.534% by applying the proposed method. Bit-rate reduction between 0.580% and 3.567% are shown for experimental results.

Keywords: Coding efficiency, H.264/AVC, Intra prediction, Low pass filter

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468 Fractional Masks Based On Generalized Fractional Differential Operator for Image Denoising

Authors: Hamid A. Jalab, Rabha W. Ibrahim

Abstract:

This paper introduces an image denoising algorithm based on generalized Srivastava-Owa fractional differential operator for removing Gaussian noise in digital images. The structures of nxn fractional masks are constructed by this algorithm. Experiments show that, the capability of the denoising algorithm by fractional differential-based approach appears efficient to smooth the Gaussian noisy images for different noisy levels. The denoising performance is measured by using peak signal to noise ratio (PSNR) for the denoising images. The results showed an improved performance (higher PSNR values) when compared with standard Gaussian smoothing filter.

Keywords: Fractional calculus, fractional differential operator, fractional mask, fractional filter.

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467 From Maskee to Audible Noise in Perceptual Speech Enhancement

Authors: Asmaa Amehraye, Dominique Pastor, Ahmed Tamtaoui, Driss Aboutajdine

Abstract:

A new analysis of perceptual speech enhancement is presented. It focuses on the fact that if only noise above the masking threshold is filtered, then noise below the masking threshold, but above the absolute threshold of hearing, can become audible after the masker filtering. This particular drawback of some perceptual filters, hereafter called the maskee-to-audible-noise (MAN) phenomenon, favours the emergence of isolated tonals that increase musical noise. Two filtering techniques that avoid or correct the MAN phenomenon are proposed to effectively suppress background noise without introducing much distortion. Experimental results, including objective and subjective measurements, show that these techniques improve the enhanced speech quality and the gain they bring emphasizes the importance of the MAN phenomenon.

Keywords: Perceptual speech filtering, maskee to audible noise, distorsion, musical noise.

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466 Removing Ocular Artifacts from EEG Signals using Adaptive Filtering and ARMAX Modeling

Authors: Parisa Shooshtari, Gelareh Mohamadi, Behnam Molaee Ardekani, Mohammad Bagher Shamsollahi

Abstract:

EEG signal is one of the oldest measures of brain activity that has been used vastly for clinical diagnoses and biomedical researches. However, EEG signals are highly contaminated with various artifacts, both from the subject and from equipment interferences. Among these various kinds of artifacts, ocular noise is the most important one. Since many applications such as BCI require online and real-time processing of EEG signal, it is ideal if the removal of artifacts is performed in an online fashion. Recently, some methods for online ocular artifact removing have been proposed. One of these methods is ARMAX modeling of EEG signal. This method assumes that the recorded EEG signal is a combination of EOG artifacts and the background EEG. Then the background EEG is estimated via estimation of ARMAX parameters. The other recently proposed method is based on adaptive filtering. This method uses EOG signal as the reference input and subtracts EOG artifacts from recorded EEG signals. In this paper we investigate the efficiency of each method for removing of EOG artifacts. A comparison is made between these two methods. Our undertaken conclusion from this comparison is that adaptive filtering method has better results compared with the results achieved by ARMAX modeling.

Keywords: Ocular Artifacts, EEG, Adaptive Filtering, ARMAX

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465 A Recommender System Fusing Collaborative Filtering and User’s Review Mining

Authors: Seulbi Choi, Hyunchul Ahn

Abstract:

Collaborative filtering (CF) algorithm has been popularly used for recommender systems in both academic and practical applications. It basically generates recommendation results using users’ numeric ratings. However, the additional use of the information other than user ratings may lead to better accuracy of CF. Considering that a lot of people are likely to share their honest opinion on the items they purchased recently due to the advent of the Web 2.0, user's review can be regarded as the new informative source for identifying user's preference with accuracy. Under this background, this study presents a hybrid recommender system that fuses CF and user's review mining. Our system adopts conventional memory-based CF, but it is designed to use both user’s numeric ratings and his/her text reviews on the items when calculating similarities between users.

Keywords: Recommender system, collaborative filtering, text mining, review mining.

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464 A Fuzzy Predictive Filter for Sinusoidal Signals with Time-Varying Frequencies

Authors: X. Z. Gao, S. J. Ovaska, X. Wang

Abstract:

Prediction of sinusoidal signals with time-varying frequencies has been an important research topic in power electronics systems. To solve this problem, we propose a new fuzzy predictive filtering scheme, which is based on a Finite Impulse Response (FIR) filter bank. Fuzzy logic is introduced here to provide appropriate interpolation of individual filter outputs. Therefore, instead of regular 'hard' switching, our method has the advantageous 'soft' switching among different filters. Simulation comparisons between the fuzzy predictive filtering and conventional filter bank-based approach are made to demonstrate that the new scheme can achieve an enhanced prediction performance for slowly changing sinusoidal input signals.

Keywords: Predictive filtering, fuzzy logic, sinusoidal signals, time-varying frequencies.

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463 Adaptive Filtering in Subbands for Supervised Source Separation

Authors: Bruna Luisa Ramos Prado Vasques, Mariane Rembold Petraglia, Antonio Petraglia

Abstract:

This paper investigates MIMO (Multiple-Input Multiple-Output) adaptive filtering techniques for the application of supervised source separation in the context of convolutive mixtures. From the observation that there is correlation among the signals of the different mixtures, an improvement in the NSAF (Normalized Subband Adaptive Filter) algorithm is proposed in order to accelerate its convergence rate. Simulation results with mixtures of speech signals in reverberant environments show the superior performance of the proposed algorithm with respect to the performances of the NLMS (Normalized Least-Mean-Square) and conventional NSAF, considering both the convergence speed and SIR (Signal-to-Interference Ratio) after convergence.

Keywords: Adaptive filtering, multirate processing, normalized subband adaptive filter, source separation.

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462 A Hybrid Recommender System based on Collaborative Filtering and Cloud Model

Authors: Chein-Shung Hwang, Ruei-Siang Fong

Abstract:

User-based Collaborative filtering (CF), one of the most prevailing and efficient recommendation techniques, provides personalized recommendations to users based on the opinions of other users. Although the CF technique has been successfully applied in various applications, it suffers from serious sparsity problems. The cloud-model approach addresses the sparsity problems by constructing the user-s global preference represented by a cloud eigenvector. The user-based CF approach works well with dense datasets while the cloud-model CF approach has a greater performance when the dataset is sparse. In this paper, we present a hybrid approach that integrates the predictions from both the user-based CF and the cloud-model CF approaches. The experimental results show that the proposed hybrid approach can ameliorate the sparsity problem and provide an improved prediction quality.

Keywords: Cloud model, Collaborative filtering, Hybridrecommender system

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461 Gaussian Process Model Identification Using Artificial Bee Colony Algorithm and Its Application to Modeling of Power Systems

Authors: Tomohiro Hachino, Hitoshi Takata, Shigeru Nakayama, Ichiro Iimura, Seiji Fukushima, Yasutaka Igarashi

Abstract:

This paper presents a nonparametric identification of continuous-time nonlinear systems by using a Gaussian process (GP) model. The GP prior model is trained by artificial bee colony algorithm. The nonlinear function of the objective system is estimated as the predictive mean function of the GP, and the confidence measure of the estimated nonlinear function is given by the predictive covariance of the GP. The proposed identification method is applied to modeling of a simplified electric power system. Simulation results are shown to demonstrate the effectiveness of the proposed method.

Keywords: Artificial bee colony algorithm, Gaussian process model, identification, nonlinear system, electric power system.

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460 Adaptive Gaussian Mixture Model for Skin Color Segmentation

Authors: Reza Hassanpour, Asadollah Shahbahrami, Stephan Wong

Abstract:

Skin color based tracking techniques often assume a static skin color model obtained either from an offline set of library images or the first few frames of a video stream. These models can show a weak performance in presence of changing lighting or imaging conditions. We propose an adaptive skin color model based on the Gaussian mixture model to handle the changing conditions. Initial estimation of the number and weights of skin color clusters are obtained using a modified form of the general Expectation maximization algorithm, The model adapts to changes in imaging conditions and refines the model parameters dynamically using spatial and temporal constraints. Experimental results show that the method can be used in effectively tracking of hand and face regions.

Keywords: Face detection, Segmentation, Tracking, Gaussian Mixture Model, Adaptation.

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459 E-Learning Recommender System Based on Collaborative Filtering and Ontology

Authors: John Tarus, Zhendong Niu, Bakhti Khadidja

Abstract:

In recent years, e-learning recommender systems has attracted great attention as a solution towards addressing the problem of information overload in e-learning environments and providing relevant recommendations to online learners. E-learning recommenders continue to play an increasing educational role in aiding learners to find appropriate learning materials to support the achievement of their learning goals. Although general recommender systems have recorded significant success in solving the problem of information overload in e-commerce domains and providing accurate recommendations, e-learning recommender systems on the other hand still face some issues arising from differences in learner characteristics such as learning style, skill level and study level. Conventional recommendation techniques such as collaborative filtering and content-based deal with only two types of entities namely users and items with their ratings. These conventional recommender systems do not take into account the learner characteristics in their recommendation process. Therefore, conventional recommendation techniques cannot make accurate and personalized recommendations in e-learning environment. In this paper, we propose a recommendation technique combining collaborative filtering and ontology to recommend personalized learning materials to online learners. Ontology is used to incorporate the learner characteristics into the recommendation process alongside the ratings while collaborate filtering predicts ratings and generate recommendations. Furthermore, ontological knowledge is used by the recommender system at the initial stages in the absence of ratings to alleviate the cold-start problem. Evaluation results show that our proposed recommendation technique outperforms collaborative filtering on its own in terms of personalization and recommendation accuracy.

Keywords: Collaborative filtering, e-learning, ontology, recommender system.

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458 Optimal Data Compression and Filtering: The Case of Infinite Signal Sets

Authors: Anatoli Torokhti, Phil Howlett

Abstract:

We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.

Keywords: stochastic signals, optimization problems in signal processing.

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457 A Robust Wavelet-Based Watermarking Algorithm Using Edge Detection

Authors: John N. Ellinas

Abstract:

In this paper, a robust watermarking algorithm using the wavelet transform and edge detection is presented. The efficiency of an image watermarking technique depends on the preservation of visually significant information. This is attained by embedding the watermark transparently with the maximum possible strength. The watermark embedding process is carried over the subband coefficients that lie on edges, where distortions are less noticeable, with a subband level dependent strength. Also, the watermark is embedded to selected coefficients around edges, using a different scale factor for watermark strength, that are captured by a morphological dilation operation. The experimental evaluation of the proposed method shows very good results in terms of robustness and transparency to various attacks such as median filtering, Gaussian noise, JPEG compression and geometrical transformations.

Keywords: Watermarking, wavelet transform, edge detection.

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456 Human Action Recognition Using Variational Bayesian HMM with Dirichlet Process Mixture of Gaussian Wishart Emission Model

Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.

Keywords: Human action recognition, Bayesian HMM, Dirichlet process mixture model, Gaussian-Wishart emission model, Variational Bayesian inference, Prior distribution and approximate posterior distribution, KTH dataset.

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455 3D Face Recognition Using Modified PCA Methods

Authors: Omid Gervei, Ahmad Ayatollahi, Navid Gervei

Abstract:

In this paper we present an approach for 3D face recognition based on extracting principal components of range images by utilizing modified PCA methods namely 2DPCA and bidirectional 2DPCA also known as (2D) 2 PCA.A preprocessing stage was implemented on the images to smooth them using median and Gaussian filtering. In the normalization stage we locate the nose tip to lay it at the center of images then crop each image to a standard size of 100*100. In the face recognition stage we extract the principal component of each image using both 2DPCA and (2D) 2 PCA. Finally, we use Euclidean distance to measure the minimum distance between a given test image to the training images in the database. We also compare the result of using both methods. The best result achieved by experiments on a public face database shows that 83.3 percent is the rate of face recognition for a random facial expression.

Keywords: 3D face recognition, 2DPCA, (2D) 2 PCA, Rangeimage

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454 Parallel Discrete Fourier Transform for Fast FIR Filtering Based on Overlapped-save Block Structure

Authors: Ying-Wen Bai, Ju-Maw Chen

Abstract:

To successfully provide a fast FIR filter with FTT algorithms, overlapped-save algorithms can be used to lower the computational complexity and achieve the desired real-time processing. As the length of the input block increases in order to improve the efficiency, a larger volume of zero padding will greatly increase the computation length of the FFT. In this paper, we use the overlapped block digital filtering to construct a parallel structure. As long as the down-sampling (or up-sampling) factor is an exact multiple lengths of the impulse response of a FIR filter, we can process the input block by using a parallel structure and thus achieve a low-complex fast FIR filter with overlapped-save algorithms. With a long filter length, the performance and the throughput of the digital filtering system will also be greatly enhanced.

Keywords: FIR Filter, Overlapped-save Algorithm, ParallelStructure

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453 Optimal and Generalized Multiple Descriptions Image Coding Transform in the Wavelet Domain

Authors: Bahi brahim, El hassane Ibn Elhaj, Driss Aboutajdine

Abstract:

In this paper we propose a Multiple Description Image Coding(MDIC) scheme to generate two compressed and balanced rates descriptions in the wavelet domain (Daubechies biorthogonal (9, 7) wavelet) using pairwise correlating transform optimal and application method for Generalized Multiple Description Coding (GMDC) to image coding in the wavelet domain. The GMDC produces statistically correlated streams such that lost streams can be estimated from the received data. Our performance test shown that the proposed method gives more improvement and good quality of the reconstructed image when the wavelet coefficients are normalized by Gaussian Scale Mixture (GSM) model then the Gaussian one ,.

Keywords: Multiple description coding (MDC), gaussian scale mixture (GSM) model, joint source-channel coding, pairwise correlating transform, GMDCT.

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452 On the Efficiency and Robustness of Commingle Wiener and Lévy Driven Processes for Vasciek Model

Authors: Rasaki O. Olanrewaju

Abstract:

The driven processes of Wiener and Lévy are known self-standing Gaussian-Markov processes for fitting non-linear dynamical Vasciek model. In this paper, a coincidental Gaussian density stationarity condition and autocorrelation function of the two driven processes were established. This led to the conflation of Wiener and Lévy processes so as to investigate the efficiency of estimates incorporated into the one-dimensional Vasciek model that was estimated via the Maximum Likelihood (ML) technique. The conditional laws of drift, diffusion and stationarity process was ascertained for the individual Wiener and Lévy processes as well as the commingle of the two processes for a fixed effect and Autoregressive like Vasciek model when subjected to financial series; exchange rate of Naira-CFA Franc. In addition, the model performance error of the sub-merged driven process was miniature compared to the self-standing driven process of Wiener and Lévy.

Keywords: Wiener process, Lévy process, Vasciek model, drift, diffusion, Gaussian density stationary.

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451 Environmental Interference Cancellation of Speech with the Radial Basis Function Networks: An Experimental Comparison

Authors: Nima Hatami

Abstract:

In this paper, we use Radial Basis Function Networks (RBFN) for solving the problem of environmental interference cancellation of speech signal. We show that the Second Order Thin- Plate Spline (SOTPS) kernel cancels the interferences effectively. For make comparison, we test our experiments on two conventional most used RBFN kernels: the Gaussian and First order TPS (FOTPS) basis functions. The speech signals used here were taken from the OGI Multi-Language Telephone Speech Corpus database and were corrupted with six type of environmental noise from NOISEX-92 database. Experimental results show that the SOTPS kernel can considerably outperform the Gaussian and FOTPS functions on speech interference cancellation problem.

Keywords: Environmental interference, interference cancellation of speech, Radial Basis Function networks, Gaussian and TPS kernels.

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450 Cyclostationary Gaussian Linearization for Analyzing Nonlinear System Response under Sinusoidal Signal and White Noise Excitation

Authors: R. J. Chang

Abstract:

A cyclostationary Gaussian linearization method is formulated for investigating the time average response of nonlinear system under sinusoidal signal and white noise excitation. The quantitative measure of cyclostationary mean, variance, spectrum of mean amplitude, and mean power spectral density of noise are analyzed. The qualitative response behavior of stochastic jump and bifurcation are investigated. The validity of the present approach in predicting the quantitative and qualitative statistical responses is supported by utilizing Monte Carlo simulations. The present analysis without imposing restrictive analytical conditions can be directly derived by solving non-linear algebraic equations. The analytical solution gives reliable quantitative and qualitative prediction of mean and noise response for the Duffing system subjected to both sinusoidal signal and white noise excitation.

Keywords: Cyclostationary, Duffing system, Gaussian linearization, sinusoidal signal and white noise.

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449 On One Mathematical Model for Filtration of Weakly Compressible Chemical Compound in the Porous Heterogeneous 3D Medium. Part I: Model Construction with the Aid of the Ollendorff Approach

Authors: Sharif E. Guseynov, Jekaterina V. Aleksejeva, Janis S. Rimshans

Abstract:

A filtering problem of almost incompressible liquid chemical compound in the porous inhomogeneous 3D domain is studied. In this work general approaches to the solution of twodimensional filtering problems in ananisotropic, inhomogeneous and multilayered medium are developed, and on the basis of the obtained results mathematical models are constructed (according to Ollendorff method) for studying the certain engineering and technical problem of filtering the almost incompressible liquid chemical compound in the porous inhomogeneous 3D domain. For some of the formulated mathematical problems with additional requirements for the structure of the porous inhomogeneous medium, namely, its isotropy, spatial periodicity of its permeability coefficient, solution algorithms are proposed. Continuation of the current work titled ”On one mathematical model for filtration of weakly compressible chemical compound in the porous heterogeneous 3D medium. Part II: Determination of the reference directions of anisotropy and permeabilities on these directions” will be prepared in the shortest terms by the authors.

Keywords: Porous media, filtering, permeability, elliptic PDE.

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448 Enhancing Predictive Accuracy in Pharmaceutical Sales Through an Ensemble Kernel Gaussian Process Regression Approach

Authors: Shahin Mirshekari, Mohammadreza Moradi, Hossein Jafari, Mehdi Jafari, Mohammad Ensaf

Abstract:

This research employs Gaussian Process Regression (GPR) with an ensemble kernel, integrating Exponential Squared, Revised Matérn, and Rational Quadratic kernels to analyze pharmaceutical sales data. Bayesian optimization was used to identify optimal kernel weights: 0.76 for Exponential Squared, 0.21 for Revised Matérn, and 0.13 for Rational Quadratic. The ensemble kernel demonstrated superior performance in predictive accuracy, achieving an R² score near 1.0, and significantly lower values in MSE, MAE, and RMSE. These findings highlight the efficacy of ensemble kernels in GPR for predictive analytics in complex pharmaceutical sales datasets.

Keywords: Gaussian Process Regression, Ensemble Kernels, Bayesian Optimization, Pharmaceutical Sales Analysis, Time Series Forecasting, Data Analysis.

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