Search results for: cartesian product.Mathematics Subject Classification[2000] :08A72

Authors: Nadia Masood Khan, Muhammad Salman Khan, Gul Muhammad Khan

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Cardiologists perform cardiac auscultation to detect abnormalities in heart sounds. Since accurate auscultation is a crucial first step in screening patients with heart diseases, there is a need to develop computer-aided detection/diagnosis (CAD) systems to assist cardiologists in interpreting heart sounds and provide second opinions. In this paper different algorithms are implemented for automated heart sound classification using unsegmented phonocardiogram (PCG) signals. Support vector machine (SVM), artificial neural network (ANN) and cartesian genetic programming evolved artificial neural network (CGPANN) without the application of any segmentation algorithm has been explored in this study. The signals are first pre-processed to remove any unwanted frequencies. Both time and frequency domain features are then extracted for training the different models. The different algorithms are tested in multiple scenarios and their strengths and weaknesses are discussed. Results indicate that SVM outperforms the rest with an accuracy of 73.64%.

Keywords: Pattern recognition, machine learning, computer aided diagnosis, heart sound classification, and feature extraction.

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Authors: Yiannis G. Smirlis

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The classification and the prediction of efficiencies in Data Envelopment Analysis (DEA) is an important issue, especially in large scale problems or when new units frequently enter the under-assessment set. In this paper, we contribute to the subject by proposing a grid structure based on interval segmentations of the range of values for the inputs and outputs. Such intervals combined, define hyper-rectangles that partition the space of the problem. This structure, exploited by Interval DEA models and a dominance relation, acts as a DEA pre-processor, enabling the classification and prediction of efficiency scores, without applying any DEA models.

Keywords: Data envelopment analysis, interval DEA, efficiency classification, efficiency prediction.

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Authors: Suzan Wedyan

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Associative classification (AC) is a data mining approach that combines association rule and classification to build classification models (classifiers). AC has attracted a significant attention from several researchers mainly because it derives accurate classifiers that contain simple yet effective rules. In the last decade, a number of associative classification algorithms have been proposed such as Classification based Association (CBA), Classification based on Multiple Association Rules (CMAR), Class based Associative Classification (CACA), and Classification based on Predicted Association Rule (CPAR). This paper surveys major AC algorithms and compares the steps and methods performed in each algorithm including: rule learning, rule sorting, rule pruning, classifier building, and class prediction.

Keywords: Associative Classification, Classification, Data Mining, Learning, Rule Ranking, Rule Pruning, Prediction.

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Authors: Yih-Ferng Peng

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In this paper, the local grid refinement is focused by using a nested grid technique. The Cartesian grid numerical method is developed for simulating unsteady, viscous, incompressible flows with complex immersed boundaries. A finite volume method is used in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a nested grid solver are imposition of interface conditions on the inter-block and accurate discretization of the governing equation in cells that are with the inter-block as a control surface. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the spatial accuracy of the underlying solver. The present nested grid method has been tested by two numerical examples to examine its performance in the two dimensional problems. The numerical examples include flow past a circular cylinder symmetrically installed in a Channel and flow past two circular cylinders with different diameters. From the numerical experiments, the ability of the solver to simulate flows with complicated immersed boundaries is demonstrated and the nested grid approach can efficiently speed up the numerical solutions.

Keywords: local grid refinement, Cartesian grid, nested grid, fractional-step method.

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Authors: Makram Ben Jeddou

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ABC classification is widely used by managers for inventory control. The classical ABC classification is based on Pareto principle and according to the criterion of the annual use value only. Single criterion classification is often insufficient for a closely inventory control. Multi-criteria inventory classification models have been proposed by researchers in order to consider other important criteria. From these models, we will consider a specific model in order to make a sensitive analysis on the composite score calculated for each item. In fact, this score, based on a normalized average between a good and a bad optimized index, can affect the ABC-item classification. We will focus on items differently assigned to classes and then propose a classification compromise.

Keywords: ABC classification, Multi criteria inventory classification models, ZF-model.

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Authors: Vesile Evrim, Aliyu Awwal

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Today, there is a large number of political transcripts available on the Web to be mined and used for statistical analysis, and product recommendations. As the online political resources are used for various purposes, automatically determining the political orientation on these transcripts becomes crucial. The methodologies used by machine learning algorithms to do an automatic classification are based on different features that are classified under categories such as Linguistic, Personality etc. Considering the ideological differences between Liberals and Conservatives, in this paper, the effect of Personality traits on political orientation classification is studied. The experiments in this study were based on the correlation between LIWC features and the BIG Five Personality traits. Several experiments were conducted using Convote U.S. Congressional- Speech dataset with seven benchmark classification algorithms. The different methodologies were applied on several LIWC feature sets that constituted by 8 to 64 varying number of features that are correlated to five personality traits. As results of experiments, Neuroticism trait was obtained to be the most differentiating personality trait for classification of political orientation. At the same time, it was observed that the personality trait based classification methodology gives better and comparable results with the related work.

Keywords: Politics, personality traits, LIWC, machine learning.

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Authors: Abdenour Bounsiar, Edith Grall, Pierre Beauseroy

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In this paper we are interested in classification problems with a performance constraint on error probability. In such problems if the constraint cannot be satisfied, then a rejection option is introduced. For binary labelled classification, a number of SVM based methods with rejection option have been proposed over the past few years. All of these methods use two thresholds on the SVM output. However, in previous works, we have shown on synthetic data that using thresholds on the output of the optimal SVM may lead to poor results for classification tasks with performance constraint. In this paper a new method for supervised classification with rejection option is proposed. It consists in two different classifiers jointly optimized to minimize the rejection probability subject to a given constraint on error rate. This method uses a new kernel based linear learning machine that we have recently presented. This learning machine is characterized by its simplicity and high training speed which makes the simultaneous optimization of the two classifiers computationally reasonable. The proposed classification method with rejection option is compared to a SVM based rejection method proposed in recent literature. Experiments show the superiority of the proposed method.

Keywords: rejection, Chow's rule, error-reject tradeoff, SupportVector Machine.

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Authors: M. Ben Othmen, M. Sayadi, F. Fnaiech

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Wavelet transform provides several important characteristics which can be used in a texture analysis and classification. In this work, an efficient texture classification method, which combines concepts from wavelet and co-occurrence matrices, is presented. An Euclidian distance classifier is used to evaluate the various methods of classification. A comparative study is essential to determine the ideal method. Using this conjecture, we developed a novel feature set for texture classification and demonstrate its effectiveness

Keywords: Classification, Wavelet, Co-occurrence, Euclidian Distance, Classifier, Texture.

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Authors: A. Javed, K. Djidjeli, J. T. Xing, S. J. Cox

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A method for simulating flow around the solid bodies has been presented using hybrid meshfree and mesh-based schemes. The presented scheme optimizes the computational efficiency by combining the advantages of both meshfree and mesh-based methods. In this approach, a cloud of meshfree nodes has been used in the domain around the solid body. These meshfree nodes have the ability to efficiently adapt to complex geometrical shapes. In the rest of the domain, conventional Cartesian grid has been used beyond the meshfree cloud. Complex geometrical shapes can therefore be dealt efficiently by using meshfree nodal cloud and computational efficiency is maintained through the use of conventional mesh-based scheme on Cartesian grid in the larger part of the domain. Spatial discretization of meshfree nodes has been achieved through local radial basis functions in finite difference mode (RBF-FD). Conventional finite difference scheme has been used in the Cartesian ‘meshed’ domain. Accuracy tests of the hybrid scheme have been conducted to establish the order of accuracy. Numerical tests have been performed by simulating two dimensional steady and unsteady incompressible flows around cylindrical object. Steady flow cases have been run at Reynolds numbers of 10, 20 and 40 and unsteady flow problems have been studied at Reynolds numbers of 100 and 200. Flow Parameters including lift, drag, vortex shedding, and vorticity contours are calculated. Numerical results have been found to be in good agreement with computational and experimental results available in the literature.

Keywords: CFD, Meshfree particle methods, Hybrid grid, Incompressible Navier Strokes equations, RBF-FD.

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Authors: Kiyohiro Yamazaki

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The purpose of this paper is to examine the hypothesis explaining the mechanism in the case, where the product is deleted or reduced the fundamental function of the product through the product concept changes in the digital camera industry. This paper points out not owning the fundamental technology might cause the change of the product concept. Casio could create new competitive factor so that this paper discusses a possibility of the mechanism of changing the product concept.

Keywords: Casio, digital camera, mechanism, product concept, product development process.

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Authors: Karim Abouelmehdi, Loubna Dali, Elmoutaoukkil Abdelmajid, Hoda Elsayed Eladnani Fatiha, Benihssane Abderahim

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The security of cloud services is the concern of cloud service providers. In this paper, we will mention different classifications of cloud attacks referred by specialized organizations. Each agency has its classification of well-defined properties. The purpose is to present a high-level classification of current research in cloud computing security. This classification is organized around attack strategies and corresponding defenses.

Keywords: Cloud computing, security, classification, risk.

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Authors: C. Perez, O. Reinoso, N. Garcia, J. M. Sabater, L. Gracia

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For high-speed control of robots, a good knowledge of system modelling is necessary to obtain the desired bandwidth. In this paper, we present a cartesian robot with a pan/tilt unit in end-effector (5 dof). This robot is implemented with powerful direct drive AC induction machines. The dynamic model, parameter identification and model validation of the robot are studied (including actuators). This work considers the cartesian robot coupled and non linear (contrary to normal considerations for this type of robots). The mechanical and control architecture proposed in this paper is efficient for industrial and research application in which high speed, well known model and very high accuracy are required.

Keywords: Robot modelling, parameter identification and validation, AC servo-motors.

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Authors: Shao Bo Cheng, Yong-Jin Han, Se Young Park, Seong-Bae Park

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Consumer-to-Consumer (C2C) E-commerce has been growing at a very high speed in recent years. Since identical or nearly-same kinds of products compete one another by relying on keyword search in C2C E-commerce, some sellers describe their products with spam keywords that are popular but are not related to their products. Though such products get more chances to be retrieved and selected by consumers than those without spam keywords, the spam keywords mislead the consumers and waste their time. This problem has been reported in many commercial services like ebay and taobao, but there have been little research to solve this problem. As a solution to this problem, this paper proposes a method to classify whether keywords of a product are spam or not. The proposed method assumes that a keyword for a given product is more reliable if the keyword is observed commonly in specifications of products which are the same or the same kind as the given product. This is because that a hierarchical category of a product in general determined precisely by a seller of the product and so is the specification of the product. Since higher layers of the hierarchical category represent more general kinds of products, a reliable degree is differently determined according to the layers. Hence, reliable degrees from different layers of a hierarchical category become features for keywords and they are used together with features only from specifications for classification of the keywords. Support Vector Machines are adopted as a basic classifier using the features, since it is powerful, and widely used in many classification tasks. In the experiments, the proposed method is evaluated with a golden standard dataset from Yi-han-wang, a Chinese C2C E-commerce, and is compared with a baseline method that does not consider the hierarchical category. The experimental results show that the proposed method outperforms the baseline in F1-measure, which proves that spam keywords are effectively identified by a hierarchical category in C2C E-commerce.

Keywords: Spam Keyword, E-commerce, keyword features, spam filtering.

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Authors: Debabrata Mandal

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Cubic ideals, cubic bi-ideals and cubic quasi-ideals of a Γ-semiring are introduced and various properties of these ideals are investigated. Among all other results, some characterizations of regular Γ-semirings are achieved.

Keywords: Γ-semiring, cubic ideal, normal cubic ideal, cubic bi-ideal, cubic quasi-ideal, cartesian product, regular, intra-regular.

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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: Y. A. Adla, R. Soubra, M. Kasab, M. O. Diab, A. Chkeir

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Over the past several years, researchers have shown a great interest in assessing the mobility of elderly people to measure their functional status. Usually, such an assessment is done by conducting tests that require the subject to walk a certain distance, turn around, and finally sit back down. Consequently, this study aims to provide an at home monitoring system to assess the patient’s status continuously. Thus, we proposed a technique to automatically detect when a subject sits down while walking at home. In this study, we utilized a Doppler radar system to capture the motion of the subjects. More than 20 features were extracted from the radar signals out of which 11 were chosen based on their Intraclass Correlation Coefficient (ICC > 0.75). Accordingly, the sequential floating forward selection wrapper was applied to further narrow down the final feature vector. Finally, five features were introduced to the Linear Discriminant Analysis classifier and an accuracy of 93.75% was achieved as well as a precision and recall of 95% and 90% respectively.

Keywords: Doppler radar system, stand-to-sit phase, TUG test, machine learning, classification

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Authors: Mohamed E. Salem Abozaed

Abstract:

Detection and classification of power quality (PQ) disturbances is an important consideration to electrical utilities and many industrial customers so that diagnosis and mitigation of such disturbance can be implemented quickly. S-transform algorithm and continuous wavelet transforms (CWT) are time-frequency algorithms, and both of them are powerful in detection and classification of PQ disturbances. This paper presents detection and classification of PQ disturbances using S-transform and CWT algorithms. The results of detection and classification, provides that S-transform is more accurate in detection and classification for most PQ disturbance than CWT algorithm, where as CWT algorithm more powerful in detection in some disturbances like notching

Keywords: CWT, Disturbances classification, Disturbances detection, Power quality, S-transform.

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Authors: M. Vogiatzis, K. Perakis

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Spatial-explicit and up-to-date land use/land cover information is fundamental for spatial planning, land management, sustainable development, and sound decision-making. In the last decade, many satellite-derived land cover products at different spatial, spectral, and temporal resolutions have been developed, such as the European Copernicus Land Cover product. However, more efficient and detailed information for land use/land cover is required at the regional or local scale. A typical Mediterranean basin with a complex landscape comprised of various forest types, crops, artificial surfaces, and wetlands was selected to test and develop our approach. In this study, we investigate the improvement of Copernicus Land Cover product (CLC2018) using Landsat 8 and Sentinel-2 pixel-based classification based on all available existing geospatial data (Forest Maps, LPIS, Natura2000 habitats, cadastral parcels, etc.). We examined and compared the performance of the Random Forest classifier for land use/land cover mapping. In total, 10 land use/land cover categories were recognized in Landsat 8 and 11 in Sentinel-2A. A comparison of the overall classification accuracies for 2018 shows that Landsat 8 classification accuracy was slightly higher than Sentinel-2A (82,99% vs. 80,30%). We concluded that the main land use/land cover types of CLC2018, even within a heterogeneous area, can be successfully mapped and updated according to CLC nomenclature. Future research should be oriented toward integrating spatiotemporal information from seasonal bands and spectral indexes in the classification process.

Keywords: land use/land cover, random forest, Landsat-8 OLI, Sentinel-2A MSI, Corine land cover

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Authors: Jun Wan, Zehua Chen, Yingwu Chen, Zhidong Bai

Abstract:

Classification is an interesting problem in functional data analysis (FDA), because many science and application problems end up with classification problems, such as recognition, prediction, control, decision making, management, etc. As the high dimension and high correlation in functional data (FD), it is a key problem to extract features from FD whereas keeping its global characters, which relates to the classification efficiency and precision to heavens. In this paper, a novel automatic method which combined Genetic Algorithm (GA) and classification algorithm to extract classification features is proposed. In this method, the optimal features and classification model are approached via evolutional study step by step. It is proved by theory analysis and experiment test that this method has advantages in improving classification efficiency, precision and robustness whereas using less features and the dimension of extracted classification features can be controlled.

Keywords: Classification, functional data, feature extraction, genetic algorithm, wavelet.

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Authors: Milan Hladik

Abstract:

The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

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Authors: Minh Vuong Pham, Frédéric Plourde, Son Doan Kim

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A strip domain decomposition parallel algorithm for fast direct Poisson solver is presented on a 3D Cartesian staggered grid. The parallel algorithm follows the principles of sequential algorithm for fast direct Poisson solver. Both Dirichlet and Neumann boundary conditions are addressed. Several test cases are likewise addressed in order to shed light on accuracy and efficiency in the strip domain parallelization algorithm. Actually the current implementation shows a very high efficiency when dealing with a large grid mesh up to 3.6 * 10⁹ under massive parallel approach, which explicitly demonstrates that the proposed algorithm is ready for massive parallel computing.

Keywords: Strip-decomposition, parallelization, fast directpoisson solver.

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Authors: Daniel I. Morariu, Lucian N. Vintan, Volker Tresp

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Text categorization is the problem of classifying text documents into a set of predefined classes. In this paper, we investigated three approaches to build a meta-classifier in order to increase the classification accuracy. The basic idea is to learn a metaclassifier to optimally select the best component classifier for each data point. The experimental results show that combining classifiers can significantly improve the accuracy of classification and that our meta-classification strategy gives better results than each individual classifier. For 7083 Reuters text documents we obtained a classification accuracies up to 92.04%.

Keywords: Meta-classification, Learning with Kernels, Support Vector Machine, and Performance Evaluation.

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Authors: Xun Ge, Jingju Qian

Abstract:

To investigate some relations between higher mathe¬matics scores in Chinese graduate student entrance examination and calculus (resp. linear algebra, probability statistics) scores in subject's completion examination of Chinese university, we select 20 students as a sample, take higher mathematics score as a decision attribute and take calculus score, linear algebra score, probability statistics score as condition attributes. In this paper, we are based on rough-set theory (Rough-set theory is a logic-mathematical method proposed by Z. Pawlak. In recent years, this theory has been widely implemented in the many fields of natural science and societal science.) to investigate importance of condition attributes with respective to decision attribute and strength of condition attributes supporting decision attribute. Results of this investigation will be helpful for university students to raise higher mathematics scores in Chinese graduate student entrance examination.

Keywords: Rough set, higher mathematics scores, decision attribute, condition attribute.

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Authors: Fabio Fabris, Alex A. Freitas

Abstract:

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: Sinee Sankrusme

Abstract:

Boon Rawd Brewery is a beer company based in Thailand that has an exemplary image, both as a good employer and a well-managed company with a strong record of social responsibility. The most famous of the company’s products is Singha beer. To study the company’s marketing strategy, a case study analysis was conducted together with qualitative research methods. The study analyzed the marketing strategy of Boon Rawd Brewery before the liberalization of the liquor market in 2000. The company’s marketing strategies consisted of the following: product line strategy, product development strategy, block channel strategy, media strategy, trade strategy, and consumer incentive strategy. Additionally, the company employed marketing mix strategy based on the 4Ps: product, price, promotion and place (of distribution).

Keywords: Beer, Boon Rawd Brewery Company, Marketing Strategy.

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Authors: M.A. Lazim, M.T.Abu Osman

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This paper deals with the application of a fuzzy set in measuring teachers- beliefs about mathematics. The vagueness of beliefs was transformed into standard mathematical values using a fuzzy preferences model. The study employed a fuzzy approach questionnaire which consists of six attributes for measuring mathematics teachers- beliefs about mathematics. The fuzzy conjoint analysis approach based on fuzzy set theory was used to analyze the data from twenty three mathematics teachers from four secondary schools in Terengganu, Malaysia. Teachers- beliefs were recorded in form of degrees of similarity and its levels of agreement. The attribute 'Drills and practice is one of the best ways of learning mathematics' scored the highest degree of similarity at 0. 79860 with level of 'strongly agree'. The results showed that the teachers- beliefs about mathematics were varied. This is shown by different levels of agreement and degrees of similarity of the measured attributes.

Keywords: belief, membership function, degree of similarity, conjoint analysis

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Authors: Alexandros Leontitsis, Archana P. Sangole

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This article presents a short discussion on optimum neighborhood size selection in a spherical selforganizing feature map (SOFM). A majority of the literature on the SOFMs have addressed the issue of selecting optimal learning parameters in the case of Cartesian topology SOFMs. However, the use of a Spherical SOFM suggested that the learning aspects of Cartesian topology SOFM are not directly translated. This article presents an approach on how to estimate the neighborhood size of a spherical SOFM based on the data. It adopts the L-curve criterion, previously suggested for choosing the regularization parameter on problems of linear equations where their right-hand-side is contaminated with noise. Simulation results are presented on two artificial 4D data sets of the coupled Hénon-Ikeda map.

Keywords: Parameter estimation, self-organizing feature maps, spherical topology.

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Authors: Maythapolnun Athimethphat, Boontarika Lerteerawong

Abstract:

There are several approaches for handling multiclass classification. Aside from one-against-one (OAO) and one-against-all (OAA), hierarchical classification technique is also commonly used. A binary classification tree is a hierarchical classification structure that breaks down a k-class problem into binary sub-problems, each solved by a binary classifier. In each node, a set of classes is divided into two subsets. A good class partition should be able to group similar classes together. Many algorithms measure similarity in term of distance between class centroids. Classes are grouped together by a clustering algorithm when distances between their centroids are small. In this paper, we present a binary classification tree with tuned observation-based clustering (BCT-TOB) that finds a class partition by performing clustering on observations instead of class centroids. A merging step is introduced to merge any insignificant class split. The experiment shows that performance of BCT-TOB is comparable to other algorithms.

Keywords: multiclass classification, hierarchical classification, binary classification tree, clustering, observation-based clustering

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Authors: Kai-Siou Wu, Justie Su-Tzu Juan

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In a graph G, a cycle is Hamiltonian cycle if it contain all vertices of G. Two Hamiltonian cycles C_1 = ⟨u_0, u_1, u_2, ..., u_{n−1}, u_0⟩ and C_2 = ⟨v_0, v_1, v_2, ..., v_{n−1}, v_0⟩ in G are independent if u_0 = v_0, u_i = ̸ v_i for all 1 ≤ i ≤ n−1. In G, a set of Hamiltonian cycles C = {C_1, C_2, ..., C_k} is mutually independent if any two Hamiltonian cycles of C are independent. The mutually independent Hamiltonicity IHC(G), = k means there exist a maximum integer k such that there exists k-mutually independent Hamiltonian cycles start from any vertex of G. In this paper, we prove that IHC(C_n × C_n) = 4, for n ≥ 3.

Keywords: Hamiltonian, independent, cycle, Cartesian product, mutually independent Hamiltonicity

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Authors: Kam-moon Liu, Kwok-chi Chim, Kwok-wai Chung, Daniel Wing-cheong Ho

Abstract:

Students often adopt routine practicing as learning strategy for mathematics. The reason is they are often bound and trained to solving conventional-typed questions in Mathematics in high school. This will be problematic if students further consolidate this practice in university. Therefore, the Department of Mathematics emphasized and integrated the Discovery-enriched approach in the undergraduate curriculum. This paper presents the details of implementing the Discovery-enriched Curriculum by providing adequate platform for project-learning, expertise for guidance and internship opportunities for students majoring in Mathematics. The Department also provided project-learning opportunities to mathematics courses targeted for students majoring in other science or engineering disciplines. The outcome is promising: the research ability and problem solving skills of students are enhanced.

Keywords: Discovery-enriched curriculum, higher education, mathematics education, project learning.

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