Search results for: hierarchical Hidden Markov Model

Authors: Jaroslav Polec, Viliam Hirner, Michal Martinovič, Kvetoslava Kotuliaková

Abstract:

In this paper we present a novel error model for packet loss and subsequent error description. The proposed model simulates the error performance of wireless communication link. The model is designed as two independent Markov chains, where the first one is used for packet generation and the second one generates correctly and incorrectly transmitted bits for received packets from the first chain. The statistical analyses of real communication on the wireless link are used for determination of model-s parameters. Using the obtained parameters and the implementation of the generator, we collected generated traffic. The obtained results generated by proposed model are compared with the real data collection.

Keywords: Wireless channel, error model, Markov chain, Elliot model, Gilbert model, generator, IEEE 802.11.

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Authors: Shaukat Wasi, Zubair A. Shaikh, Sajid Qasmi, Hussain Sachwani, Rehman Lalani, Aamir Chagani

Abstract:

Automatic Extraction of Event information from social text stream (emails, social network sites, blogs etc) is a vital requirement for many applications like Event Planning and Management systems and security applications. The key information components needed from Event related text are Event title, location, participants, date and time. Emails have very unique distinctions over other social text streams from the perspective of layout and format and conversation style and are the most commonly used communication channel for broadcasting and planning events. Therefore we have chosen emails as our dataset. In our work, we have employed two statistical NLP methods, named as Finite State Machines (FSM) and Hidden Markov Model (HMM) for the extraction of event related contextual information. An application has been developed providing a comparison among the two methods over the event extraction task. It comprises of two modules, one for each method, and works for both bulk as well as direct user input. The results are evaluated using Precision, Recall and F-Score. Experiments show that both methods produce high performance and accuracy, however HMM was good enough over Title extraction and FSM proved to be better for Venue, Date, and time.

Keywords: Emails, Event Extraction, Event Detection, Finite state machines, Hidden Markov Model.

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Authors: Zhanli Zhang, Wei Chen, Xin Jiang, Lili Ma, Shaoting Tang, Zhiming Zheng

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A new class of percolation model in complex networks, in which nodes are characterized by hidden variables reflecting the properties of nodes and the occupied probability of each link is determined by the hidden variables of the end nodes, is studied in this paper. By the mean field theory, the analytical expressions for the phase of percolation transition is deduced. It is determined by the distribution of the hidden variables for the nodes and the occupied probability between pairs of them. Moreover, the analytical expressions obtained are checked by means of numerical simulations on a particular model. Besides, the general model can be applied to describe and control practical diffusion models, such as disease diffusion model, scientists cooperation networks, and so on.

Keywords: complex networks, percolation transition, hidden variable, occupied probability.

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Authors: Mahmoud Elmezain, Ayoub Al-Hamadi, Jörg Appenrodt, Bernd Michaelis

Abstract:

Gesture recognition is a challenging task for extracting meaningful gesture from continuous hand motion. In this paper, we propose an automatic system that recognizes isolated gesture, in addition meaningful gesture from continuous hand motion for Arabic numbers from 0 to 9 in real-time based on Hidden Markov Models (HMM). In order to handle isolated gesture, HMM using Ergodic, Left-Right (LR) and Left-Right Banded (LRB) topologies is applied over the discrete vector feature that is extracted from stereo color image sequences. These topologies are considered to different number of states ranging from 3 to 10. A new system is developed to recognize the meaningful gesture based on zero-codeword detection with static velocity motion for continuous gesture. Therefore, the LRB topology in conjunction with Baum-Welch (BW) algorithm for training and forward algorithm with Viterbi path for testing presents the best performance. Experimental results show that the proposed system can successfully recognize isolated and meaningful gesture and achieve average rate recognition 98.6% and 94.29% respectively.

Keywords: Computer Vision & Image Processing, Gesture Recognition, Pattern Recognition, Application

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Authors: N. Sopipan, A. Intarasit, K. Chuarkham

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 In this paper, we forecast the volatility of Baht/USDs using Markov Regime Switching GARCH (MRS-GARCH) models. These models allow volatility to have different dynamics according to unobserved regime variables. The main purpose of this paper is to find out whether MRS-GARCH models are an improvement on the GARCH type models in terms of modeling and forecasting Baht/USD volatility. The MRS-GARCH is the best performance model for Baht/USD volatility in short term but the GARCH model is best perform for long term.

Keywords: Volatility, Markov Regime Switching, Forecasting.

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Authors: Dali Zhang, Baoqun Yin, Hongsheng Xi

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In this paper, we propose a single sample path based algorithm with state aggregation to optimize the average rewards of singularly perturbed Markov reward processes (SPMRPs) with a large scale state spaces. It is assumed that such a reward process depend on a set of parameters. Differing from the other kinds of Markov chain, SPMRPs have their own hierarchical structure. Based on this special structure, our algorithm can alleviate the load in the optimization for performance. Moreover, our method can be applied on line because of its evolution with the sample path simulated. Compared with the original algorithm applied on these problems of general MRPs, a new gradient formula for average reward performance metric in SPMRPs is brought in, which will be proved in Appendix, and then based on these gradients, the schedule of the iteration algorithm is presented, which is based on a single sample path, and eventually a special case in which parameters only dominate the disturbance matrices will be analyzed, and a precise comparison with be displayed between our algorithm with the old ones which is aim to solve these problems in general Markov reward processes. When applied in SPMRPs, our method will approach a fast pace in these cases. Furthermore, to illustrate the practical value of SPMRPs, a simple example in multiple programming in computer systems will be listed and simulated. Corresponding to some practical model, physical meanings of SPMRPs in networks of queues will be clarified.

Keywords: Singularly perturbed Markov processes, Gradient of average reward, Differential reward, State aggregation, Perturbed close network.

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Authors: Pavol Tanuska, Pavel Vazan, Michal Kebisek, Dominika Jurovata

Abstract:

The paper gives the results of the project that was oriented on the usage of knowledge discoveries from production systems for needs of the hierarchical process control. One of the main project goals was the proposal of knowledge discovery model for process control. Specifics data mining methods and techniques was used for defined problems of the process control. The gained knowledge was used on the real production system thus the proposed solution has been verified. The paper documents how is possible to apply the new discovery knowledge to use in the real hierarchical process control. There are specified the opportunities for application of the proposed knowledge discovery model for hierarchical process control.

Keywords: Hierarchical process control, knowledge discovery from databases, neural network.

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Authors: Mahmoud Elmezain, Samar El-shinawy

Abstract:

Many approaches to pattern recognition are founded on probability theory, and can be broadly characterized as either generative or discriminative according to whether or not the distribution of the image features. Generative and discriminative models have very different characteristics, as well as complementary strengths and weaknesses. In this paper, we study these models to recognize the patterns of alphabet characters (A-Z) and numbers (0-9). To handle isolated pattern, generative model as Hidden Markov Model (HMM) and discriminative models like Conditional Random Field (CRF), Hidden Conditional Random Field (HCRF) and Latent-Dynamic Conditional Random Field (LDCRF) with different number of window size are applied on extracted pattern features. The gesture recognition rate is improved initially as the window size increase, but degrades as window size increase further. Experimental results show that the LDCRF is the best in terms of results than CRF, HCRF and HMM at window size equal 4. Additionally, our results show that; an overall recognition rates are 91.52%, 95.28%, 96.94% and 98.05% for CRF, HCRF, HMM and LDCRF respectively.

Keywords: Statistical Pattern Recognition, Generative Model, Discriminative Model, Human Computer Interaction.

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Authors: Sumith Matharage, Damminda Alahakoon

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Textual data plays an important role in the modern world. The possibilities of applying data mining techniques to uncover hidden information present in large volumes of text collections is immense. The Growing Self Organizing Map (GSOM) is a highly successful member of the Self Organising Map family and has been used as a clustering and visualisation tool across wide range of disciplines to discover hidden patterns present in the data. A comprehensive analysis of the GSOM’s capabilities as a text clustering and visualisation tool has so far not been published. These functionalities, namely map visualisation capabilities, automatic cluster identification and hierarchical clustering capabilities are presented in this paper and are further demonstrated with experiments on a benchmark text corpus.

Keywords: Text Clustering, Growing Self Organizing Map, Automatic Cluster Identification, Hierarchical Clustering.

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Authors: Yilun Shang

Abstract:

We study a long-range percolation model in the hierarchical lattice ΩN of order N where probability of connection between two nodes separated by distance k is of the form min{αβ−k, 1}, α ≥ 0 and β > 0. The parameter α is the percolation parameter, while β describes the long-range nature of the model. The ΩN is an example of so called ultrametric space, which has remarkable qualitative difference between Euclidean-type lattices. In this paper, we characterize the sizes of large clusters for this model along the line of some prior work. The proof involves a stationary embedding of ΩN into Z. The phase diagram of this long-range percolation is well understood.

Keywords: percolation, component, hierarchical lattice, phase transition.

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Authors: Shilpi Lavania, Deepak Nagaria

Abstract:

A mixed method for model order reduction is presented in this paper. The denominator polynomial is derived by matching both Markov parameters and time moments, whereas numerator polynomial derivation and error minimization is done using Genetic Algorithm. The efficiency of the proposed method can be investigated in terms of closeness of the response of reduced order model with respect to that of higher order original model and a comparison of the integral square error as well.

Keywords: Model Order Reduction (MOR), control theory, Markov parameters, time moments, genetic algorithm, Single Input Single Output (SISO).

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Authors: Helyane B. Borges, Julio Cesar Nievola

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Hierarchical classification is a problem with applications in many areas as protein function prediction where the dates are hierarchically structured. Therefore, it is necessary the development of algorithms able to induce hierarchical classification models. This paper presents experimenters using the algorithm for hierarchical classification called Multi-label Hierarchical Classification using a Competitive Neural Network (MHC-CNN). It was tested in ten datasets the Gene Ontology (GO) Cellular Component Domain. The results are compared with the Clus-HMC and Clus-HSC using the hF-Measure.

Keywords: Hierarchical Classification, Competitive Neural Network, Global Classifier.

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Authors: Abdallah Al Sabbagh

Abstract:

Next Generation Wireless Network (NGWN) is expected to be a heterogeneous network which integrates all different Radio Access Technologies (RATs) through a common platform. A major challenge is how to allocate users to the most suitable RAT for them. An optimized solution can lead to maximize the efficient use of radio resources, achieve better performance for service providers and provide Quality of Service (QoS) with low costs to users. Currently, Radio Resource Management (RRM) is implemented efficiently for the RAT that it was developed. However, it is not suitable for a heterogeneous network. Common RRM (CRRM) was proposed to manage radio resource utilization in the heterogeneous network. This paper presents a user level Markov model for a three co-located RAT networks. The load-balancing based and service based CRRM algorithms have been studied using the presented Markov model. A comparison for the performance of load-balancing based and service based CRRM algorithms is studied in terms of traffic distribution, new call blocking probability, vertical handover (VHO) call dropping probability and throughput.

Keywords: Heterogeneous Wireless Network, Markov chain model, load-balancing based and service based algorithm, CRRM algorithms, Beyond 3G network.

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Authors: Essam S. Altubaishi

Abstract:

The motivation for adaptive modulation and coding is to adjust the method of transmission to ensure that the maximum efficiency is achieved over the link at all times. The receiver estimates the channel quality and reports it back to the transmitter. The transmitter then maps the reported quality into a link mode. This mapping however, is not a one-to-one mapping. In this paper we investigate a method for selecting the proper modulation scheme. This method can dynamically adapt the mapping of the Signal-to- Noise Ratio (SNR) into a link mode. It enables the use of the right modulation scheme irrespective of changes in the channel conditions by incorporating errors in the received data. We propose a Markov model for this method, and use it to derive the average switching thresholds and the average throughput. We show that the average throughput of this method outperforms the conventional threshold method.

Keywords: Adaptive modulation and coding, CDMA, Markov model.

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Authors: Diego Ordonez, Carlos Dafonte, Minia Manteiga, Bernardino Arcayy

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This work presents a neural network model for the clustering analysis of data based on Self Organizing Maps (SOM). The model evolves during the training stage towards a hierarchical structure according to the input requirements. The hierarchical structure symbolizes a specialization tool that provides refinements of the classification process. The structure behaves like a single map with different resolutions depending on the region to analyze. The benefits and performance of the algorithm are discussed in application to the Iris dataset, a classical example for pattern recognition.

Keywords: Neural networks, Self-organizing feature maps, Hierarchicalsystems, Pattern clustering methods.

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Authors: Dongdong Zhang, Deran Zhang

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In this paper, a Markovian risk model with two-type claims is considered. In such a risk model, the occurrences of the two type claims are described by two point processes {Ni(t), t ¸ 0}, i = 1, 2, where {Ni(t), t ¸ 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t ¸ 0} . The ruin probability ª(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability ª(u) is obtained and the bounds for the convergence rate of the ruin probability ª(u) are given by using key-renewal theorem.

Keywords: Risk model, ruin probability, Markov jump process, integral equation.

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Authors: A. Bayaga

Abstract:

This research provides a technical account of estimating Transition Probability using Time-homogeneous Markov Jump Process applying by South African HIV/AIDS data from the Statistics South Africa. It employs Maximum Likelihood Estimator (MLE) model to explore the possible influence of Transition Probability of mortality cases in which case the data was based on actual Statistics South Africa. This was conducted via an integrated demographic and epidemiological model of South African HIV/AIDS epidemic. The model was fitted to age-specific HIV prevalence data and recorded death data using MLE model. Though the previous model results suggest HIV in South Africa has declined and AIDS mortality rates have declined since 2002 – 2013, in contrast, our results differ evidently with the generally accepted HIV models (Spectrum/EPP and ASSA2008) in South Africa. However, there is the need for supplementary research to be conducted to enhance the demographic parameters in the model and as well apply it to each of the nine (9) provinces of South Africa.

Keywords: AIDS mortality rates, Epidemiological model, Time-homogeneous Markov Jump Process, Transition Probability, Statistics South Africa.

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Authors: Sheena Christabel Pravin, M. Palanivelan

Abstract:

Speech disfluencies are common in spontaneous speech. The primary purpose of this study was to distinguish linguistic disfluencies from stuttering disfluencies in bilingual Tamil–English (TE) speaking children. The secondary purpose was to determine whether their disfluencies are mediated by native language dominance and/or on an early onset of developmental stuttering at childhood. A detailed study was carried out to identify the prosodic and acoustic features that uniquely represent the disfluent regions of speech. This paper focuses on statistical modeling of repetitions, prolongations, pauses and interjections in the speech corpus encompassing bilingual spontaneous utterances from school going children – English and Tamil. Two classifiers including Hidden Markov Models (HMM) and the Multilayer Perceptron (MLP), which is a class of feed-forward artificial neural network, were compared in the classification of disfluencies. The results of the classifiers document the patterns of disfluency in spontaneous speech samples of school-aged children to distinguish between Children Who Stutter (CWS) and Children with Language Impairment CLI). The ability of the models in classifying the disfluencies was measured in terms of F-measure, Recall, and Precision.

Keywords: Bilingual, children who stutter, children with language impairment, Hidden Markov Models, multi-layer perceptron, linguistic disfluencies, stuttering disfluencies.

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Authors: Jong Woo Kim, Go Bong Choi, Sang Hwan Son, Dae Shik Kim, Jung Chul Suh, Jong Min Lee

Abstract:

The Markov decision process (MDP) based methodology is implemented in order to establish the optimal schedule which minimizes the cost. Formulation of MDP problem is presented using the information about the current state of pipe, improvement cost, failure cost and pipe deterioration model. The objective function and detailed algorithm of dynamic programming (DP) are modified due to the difficulty of implementing the conventional DP approaches. The optimal schedule derived from suggested model is compared to several policies via Monte Carlo simulation. Validity of the solution and improvement in computational time are proved.

Keywords: Markov decision processes, Dynamic Programming, Monte Carlo simulation, Periodic replacement, Weibull distribution.

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Authors: Ing-Jr Ding

Abstract:

This paper presents a technical speaker adaptation method called WMLLR, which is based on maximum likelihood linear regression (MLLR). In MLLR, a linear regression-based transform which adapted the HMM mean vectors was calculated to maximize the likelihood of adaptation data. In this paper, the prior knowledge of the initial model is adequately incorporated into the adaptation. A series of speaker adaptation experiments are carried out at a 30 famous city names database to investigate the efficiency of the proposed method. Experimental results show that the WMLLR method outperforms the conventional MLLR method, especially when only few utterances from a new speaker are available for adaptation.

Keywords: hidden Markov model, maximum likelihood linearregression, speech recognition, speaker adaptation.

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Authors: Leila Jafari, Viliam Makis, Akram Khaleghei G.B.

Abstract:

In this paper, we present a maintenance model of a two-unit series system with economic dependence. Unit#1 which is considered to be more expensive and more important, is subject to condition monitoring (CM) at equidistant, discrete time epochs and unit#2, which is not subject to CM has a general lifetime distribution. The multivariate observation vectors obtained through condition monitoring carry partial information about the hidden state of unit#1, which can be in a healthy or a warning state while operating. Only the failure state is assumed to be observable for both units. The objective is to find an optimal opportunistic maintenance policy minimizing the long-run expected average cost per unit time. The problem is formulated and solved in the partially observable semi-Markov decision process framework. An effective computational algorithm for finding the optimal policy and the minimum average cost is developed, illustrated by a numerical example.

Keywords: Condition-Based Maintenance, Semi-Markov Decision Process, Multivariate Bayesian Control Chart, Partially Observable System, Two-unit System.

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Authors: Eunji Choi, Borang Park, Youngjae Choi, Jinwoo Moon

Abstract:

In this study, a predictive model for estimating the metabolism (MET) of human body was developed for the optimal control of indoor thermal environment. Human body images for indoor activities and human body joint coordinated values were collected as data sets, which are used in predictive model. A deep learning algorithm was used in an initial model, and its number of hidden layers and hidden neurons were optimized. Lastly, the model prediction performance was analyzed after the model being trained through collected data. In conclusion, the possibility of MET prediction was confirmed, and the direction of the future study was proposed as developing various data and the predictive model.

Keywords: Deep learning, indoor quality, metabolism, predictive model.

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Authors: F. C. Calnegru

Abstract:

This article presents a computationally tractable probabilistic model for the relation between the complex wavelet coefficients of two images of the same scene. The two images are acquisitioned at distinct moments of times, or from distinct viewpoints, or by distinct sensors. By means of the introduced probabilistic model, we argue that the similarity between the two images is controlled not by the values of the wavelet coefficients, which can be altered by many factors, but by the nature of the wavelet coefficients, that we model with the help of hidden state variables. We integrate this probabilistic framework in the construction of a new image registration algorithm. This algorithm has sub-pixel accuracy and is robust to noise and to other variations like local illumination changes. We present the performance of our algorithm on various image types.

Keywords: Complex wavelet transform, image registration, modeling using hidden state variables, probabilistic similaritymeasure.

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Authors: Mohamad Mahdavi

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Most of the real queuing systems include special properties and constraints, which can not be analyzed directly by using the results of solved classical queuing models. Lack of Markov chains features, unexponential patterns and service constraints, are the mentioned conditions. This paper represents an applied general algorithm for analysis and optimizing the queuing systems. The algorithm stages are described through a real case study. It is consisted of an almost completed non-Markov system with limited number of customers and capacities as well as lots of common exception of real queuing networks. Simulation is used for optimizing this system. So introduced stages over the following article include primary modeling, determining queuing system kinds, index defining, statistical analysis and goodness of fit test, validation of model and optimizing methods of system with simulation.

Keywords: Estimation, queuing system, simulation model, probability distribution, non-Markov chain.

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Authors: Fabio Fabris, Alex A. Freitas

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Hierarchical classification is a special type of classification task where the class labels are organised into a hierarchy, with more generic class labels being ancestors of more specific ones. Meta-learning for classification-algorithm recommendation consists of recommending to the user a classification algorithm, from a pool of candidate algorithms, for a dataset, based on the past performance of the candidate algorithms in other datasets. Meta-learning is normally used in conventional, non-hierarchical classification. By contrast, this paper proposes a meta-learning approach for more challenging task of hierarchical classification, and evaluates it in a large number of bioinformatics datasets. Hierarchical classification is especially relevant for bioinformatics problems, as protein and gene functions tend to be organised into a hierarchy of class labels. This work proposes meta-learning approach for recommending the best hierarchical classification algorithm to a hierarchical classification dataset. This work’s contributions are: 1) proposing an algorithm for splitting hierarchical datasets into new datasets to increase the number of meta-instances, 2) proposing meta-features for hierarchical classification, and 3) interpreting decision-tree meta-models for hierarchical classification algorithm recommendation.

Keywords: Algorithm recommendation, meta-learning, bioinformatics, hierarchical classification.

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Authors: Ahmed K. Hasan, A. A. Zaidan, Anas Majeed, B. B. Zaidan, Rosli Salleh, Omar Zakaria, Ali Zuheir

Abstract:

Wireless mesh networks based on IEEE 802.11 technology are a scalable and efficient solution for next generation wireless networking to provide wide-area wideband internet access to a significant number of users. The deployment of these wireless mesh networks may be within different authorities and without any planning, they are potentially overlapped partially or completely in the same service area. The aim of the proposed model is design a new model to Enhancement Throughput of Unplanned Wireless Mesh Networks Deployment Using Partitioning Hierarchical Cluster (PHC), the unplanned deployment of WMNs are determinates there performance. We use throughput optimization approach to model the unplanned WMNs deployment problem based on partitioning hierarchical cluster (PHC) based architecture, in this paper the researcher used bridge node by allowing interworking traffic between these WMNs as solution for performance degradation.

Keywords: Wireless Mesh Networks, 802.11s Internetworking, partitioning Hierarchical Cluste.

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Authors: M. Sinecen, M. Makinacı

Abstract:

The purpose of this paper is to assess the value of neural networks for classification of cancer and noncancer prostate cells. Gauss Markov Random Fields, Fourier entropy and wavelet average deviation features are calculated from 80 noncancer and 80 cancer prostate cell nuclei. For classification, artificial neural network techniques which are multilayer perceptron, radial basis function and learning vector quantization are used. Two methods are utilized for multilayer perceptron. First method has single hidden layer and between 3-15 nodes, second method has two hidden layer and each layer has between 3-15 nodes. Overall classification rate of 86.88% is achieved.

Keywords: Artificial neural networks, texture classification, cancer diagnosis.

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Authors: Suparman

Abstract:

Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

Keywords: Piecewise, Bayesian, reversible jump MCMC, segmentation.

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Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis.

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Authors: Dipti Patra, Mridula J

Abstract:

In this paper, we propose a new image segmentation approach for colour textured images. The proposed method for image segmentation consists of two stages. In the first stage, textural features using gray level co-occurrence matrix(GLCM) are computed for regions of interest (ROI) considered for each class. ROI acts as ground truth for the classes. Ohta model (I1, I2, I3) is the colour model used for segmentation. Statistical mean feature at certain inter pixel distance (IPD) of I2 component was considered to be the optimized textural feature for further segmentation. In the second stage, the feature matrix obtained is assumed to be the degraded version of the image labels and modeled as Markov Random Field (MRF) model to model the unknown image labels. The labels are estimated through maximum a posteriori (MAP) estimation criterion using ICM algorithm. The performance of the proposed approach is compared with that of the existing schemes, JSEG and another scheme which uses GLCM and MRF in RGB colour space. The proposed method is found to be outperforming the existing ones in terms of segmentation accuracy with acceptable rate of convergence. The results are validated with synthetic and real textured images.

Keywords: Texture Image Segmentation, Gray Level Cooccurrence Matrix, Markov Random Field Model, Ohta colour space, ICM algorithm.

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