Search results for: Learning aids.

Authors: Luisa Mesquita Oliveira Ribeiro, Alexei Manso Correa Machado

Abstract:

Handwritten signature is a unique form for recognizing an individual, used to discern documents, carry out investigations in the criminal, legal, banking areas and other applications. Signature verification is based on large amounts of biometric data, as they are simple and easy to acquire, among other characteristics. Given this scenario, signature forgery is a worldwide recurring problem and fast and precise techniques are needed to prevent crimes of this nature from occurring. This article carried out a study on the efficiency of the Capsule Network in analyzing and recognizing signatures. The chosen architecture achieved an accuracy of 98.11% and 80.15% for the CEDAR and GPDS databases, respectively.

Keywords: Biometrics, deep learning, handwriting, signature forgery.

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Authors: Magdalena Pejas

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This article concerns the presentation of an integrated method for detection of steganographic content embedded by new unknown programs. The method is based on data mining and aggregated hypothesis testing. The article contains the theoretical basics used to deploy the proposed detection system and the description of improvement proposed for the basic system idea. Further main results of experiments and implementation details are collected and described. Finally example results of the tests are presented.

Keywords: Steganography, steganalysis, data embedding, data mining, feature extraction, knowledge base, system learning, hypothesis testing, error estimation, black box program, file structure.

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Authors: Andrey V. Timofeev

Abstract:

The paper presents new results concerning selection of optimal information fusion formula for ensembles of C-OTDR channels. The goal of information fusion is to create an integral classificator designed for effective classification of seismoacoustic target events. The LPBoost (LP-β and LP-B variants), the Multiple Kernel Learning, and Weighing of Inversely as Lipschitz Constants (WILC) approaches were compared. The WILC is a brand new approach to optimal fusion of Lipschitz Classifiers Ensembles. Results of practical usage are presented.

Keywords: Lipschitz Classifier, Classifiers Ensembles, LPBoost, C-OTDR systems, ν-OTDR systems.

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Authors: Andrew Laghos

Abstract:

Computers are increasingly being used as educational tools in elementary/primary schools worldwide. A specific application of such computer use, is that of multimedia games, where the aim is to combine pedagogy and entertainment. This study reports on a case-study whereby an educational multimedia game has been developed for use by elementary school children. The stages of the application-s design, implementation and evaluation are presented. Strengths of the game are identified and discussed, and its weaknesses are identified, allowing for suggestions for future redesigns. The results show that the use of games can engage children in the learning process for longer periods of time with the added benefit of the entertainment factor.

Keywords: Education, entertainment, games, school

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Authors: Mario Mastriani

Abstract:

This work deals with unsupervised image deblurring. We present a new deblurring procedure on images provided by lowresolution synthetic aperture radar (SAR) or simply by multimedia in presence of multiplicative (speckle) or additive noise, respectively. The method we propose is defined as a two-step process. First, we use an original technique for noise reduction in wavelet domain. Then, the learning of a Kohonen self-organizing map (SOM) is performed directly on the denoised image to take out it the blur. This technique has been successfully applied to real SAR images, and the simulation results are presented to demonstrate the effectiveness of the proposed algorithms.

Keywords: Blur, Kohonen self-organizing map, noise, speckle, synthetic aperture radar.

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Authors: Mohammad K. Abedin, Mohammad Shahjahan, Zeenat Sultana, Tawfique Jahan, Jesmin Akter

Abstract:

To strengthen social and behavior change communication (SBCC) capacity of Ministry of Health and Family Welfare (MoHFW) of the Government of Bangladesh, BCCP/BKMI developed two eLearning courses providing opportunities for professional development of SBCC Program Managers who have no access to training or refreshers training. The two eLearning courses – Message and Material Development (MMD) and Monitoring and Evaluation (MandE) of SBCC programs – went online in September 2015, where all users could register their participation so results could be monitored. Methodology: To assess the uses of these courses a randomly selected sample was collected to run a pre and post-test analyses and a phone survey were conducted. Systematic random sampling was used to select a sample of 75 MandE and 25 MMD course participants from a sampling frame of 179 and 51 respectively. Results: As of September 2016, more than 179 learners have completed the MandE course, and 49 learners have completed the MMD course. The users of these courses are program managers, university faculty members, and students. Encouraging results were revealed from the analysis of pre and post-test scores and a phone survey three months after course completion. Test scores suggested a substantial increase in knowledge. The pre-test scores findings suggested that about 19% learners scored high on the MandE. The post-test scores finding indicated a high score (92%) of the sample across 4 modules of MandE. For MMD course in pre-test scoring, 30% of the learners scored high, and 100% scored high at the post-test. It was found that all the learners in the phone survey have discussed the courses. Most of the sharing occurred with colleagues and friends, usually through face to face (70%) interaction. The learners reported that they did recommend the two courses to concerned people. About 67% MandE and 76% MMD learners stated that the concepts that they had to learn during the course were put into practice in their work settings. The respondents for both MandE and MMD courses have provided a valuable set of suggestions that would further strengthen the courses. Conclusions: The study showed that the initiative offered ample opportunities to build capacity in various ways in which the eLearning courses were used. It also highlighted the importance of scaling up these efforts to further strengthen the outcomes.

Keywords: E-learning course, message and material development, monitoring and evaluation, social and behavior change communication.

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Authors: Kefaya Qaddoum

Abstract:

The aim of this study is to predict breast cancer and to construct a supportive model that will stimulate a more reliable prediction as a factor that is fundamental for public health. In this study, we utilize general regression neural networks (GRNN) to replace the normal predictions with prediction periods to achieve a reasonable percentage of confidence. The mechanism employed here utilises a machine learning system called conformal prediction (CP), in order to assign consistent confidence measures to predictions, which are combined with GRNN. We apply the resulting algorithm to the problem of breast cancer diagnosis. The results show that the prediction constructed by this method is reasonable and could be useful in practice.

Keywords: Neural network, conformal prediction, cancer classification, regression.

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Authors: Sylvia Encheva

Abstract:

Students in high education are presented with new terms and concepts in nearly every lecture they attend. Many of them prefer Web-based self-tests for evaluation of their concepts understanding since they can use those tests independently of tutors- working hours and thus avoid the necessity of being in a particular place at a particular time. There is a large number of multiple-choice tests in almost every subject designed to contribute to higher level learning or discover misconceptions. Every single test provides immediate feedback to a student about the outcome of that test. In some cases a supporting system displays an overall score in case a test is taken several times by a student. What we still find missing is how to secure delivering of personalized feedback to a user while taking into consideration the user-s progress. The present work is motivated to throw some light on that question.

Keywords: Clustering, rough sets, many valued logic, predictions

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Authors: S. Vural, H. Yamauchi

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Current systems for face recognition techniques often use either SVM or Adaboost techniques for face detection part and use PCA for face recognition part. In this paper, we offer a novel method for not only a powerful face detection system based on Six-segment-filters (SSR) and Adaboost learning algorithms but also for a face recognition system. A new exclusive face detection algorithm has been developed and connected with the recognition algorithm. As a result of it, we obtained an overall high-system performance compared with current systems. The proposed algorithm was tested on CMU, FERET, UNIBE, MIT face databases and significant performance has obtained.

Keywords: Adaboost, Face Detection, Face recognition, SVM, Gabor filters, PCA-ICA.

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Authors: Ahmet Faruk Akyuz, Hasan Sakir Bilge

Abstract:

Depth estimation using stereo images is a challenging problem in computer vision. Many different studies have been carried out to solve this problem. With advancing machine learning, tackling this problem is often done with neural network-based solutions. The images used in these studies are mostly in the visible spectrum. However, the need to use the Infrared (IR) spectrum for depth estimation has emerged because it gives better results than visible spectra in some conditions. At this point, we recommend using thermal-thermal (IR) image pairs for depth estimation. In this study, we used two well-known networks (PSMNet, FADNet) with minor modifications to demonstrate the viability of this idea.

Keywords: thermal stereo matching, depth estimation, deep neural networks, CNN

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Authors: Ayşe Eldem, Fatih Başçiftçi

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Visually impaired individuals cannot lead their lives as comfortable as others. Therefore, new applications are being developed every passing day in order to make their lives easier. In this study, an electronic and computer-aided audio device was developed with the aim of making the learning of the periodic table easier for the visually impaired. In this device, a board includes buttons for each element of the periodic table. After pressing a button, the visually impaired individual not only hears the name of the element but also feels with his/her hands where that specific element is located.

Keywords: Periodic Table, PIC16F877, Serial port, Visually Impaired Individual.

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Authors: R. Ebrahimpour, M. Abbasnezhad Arabi, H. Babamiri Moghaddam

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Combining classifiers is a useful method for solving complex problems in machine learning. The ECOC (Error Correcting Output Codes) method has been widely used for designing combining classifiers with an emphasis on the diversity of classifiers. In this paper, in contrast to the standard ECOC approach in which individual classifiers are chosen homogeneously, classifiers are selected according to the complexity of the corresponding binary problem. We use SATIMAGE database (containing 6 classes) for our experiments. The recognition error rate in our proposed method is %10.37 which indicates a considerable improvement in comparison with the conventional ECOC and stack generalization methods.

Keywords: Error correcting output code, combining classifiers, neural networks.

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Authors: Ahmad T. Al-Taani, Noor Aldeen K. Al-Awad

Abstract:

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference approaches. These measures are applied and compared using 50 different Arabic web pages. Einstein measure was gave best performance among the other measures. An analysis of these measures and concluding remarks are drawn in this study.

Keywords: Text classification, HTML documents, Web pages, Machine learning, Fuzzy logic, Arabic Web pages.

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Authors: R. Iraz, K. Eryeşil

Abstract:

Employees commitments of vision and mission of organization is effected due to manager’s executes by approach of leadership The leaders who have attributions like vision, confidence and correctitude, sharing and participation, creativeness, progressive learning –improvement and responsibility are effective to increase organizational commitment if they are sensitive to expectation and requirement of employees in an organization. Studies about organizational commitment appear results that employees who have strong organizational commitment have the most contribution. In this study, “Leadership” and “Organizational Commitment” conduct surveys to 31 employees of Ahmet Özdemir Nak. Tic. San. A.Ş. which has operations in road and railway transportation sector. It is analyzed the effects of leadership approach to organizational commitment deals with result of survey.

Keywords: Leadership Approach, Organizational Commitment, Study

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Authors: Tesnim Charrad, Kaouther Nouira, Ahmed Ferchichi

Abstract:

In order to reduce the number of deaths due to heart problems, we propose the use of Hierarchical Temporal Memory Algorithm (HTM) which is a real time anomaly detection algorithm. HTM is a cortical learning algorithm based on neocortex used for anomaly detection. In other words, it is based on a conceptual theory of how the human brain can work. It is powerful in predicting unusual patterns, anomaly detection and classification. In this paper, HTM have been implemented and tested on ECG datasets in order to detect cardiac anomalies. Experiments showed good performance in terms of specificity, sensitivity and execution time.

Keywords: HTM, Real time anomaly detection, ECG, Cardiac Anomalies.

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Authors: Sheetal R. Jadhwani, Daisy Sang, Chang-Shyh Peng

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Web applications are an integral part of modem life. They are mostly based upon the HyperText Markup Language (HTML). While HTML meets the basic needs, there are some shortcomings. For example, applications can cease to work once user goes offline, real-time updates may be lagging, and user interface can freeze on computationally intensive tasks. The latest language specification HTML5 attempts to rectify the situation with new tools and protocols. This paper studies the new Web Storage, Geolocation, Web Worker, Canvas, and Web Socket APIs, and presents applications to test their features and efficiencies.

Keywords: HTML5, Web Worker, Canvas, Web Socket.

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Authors: Jacqueline M. Dias, Amina A Khowaja

Abstract:

Clinical education is one of the most important components of a nursing curriculum as it develops the students’ cognitive, psychomotor and affective skills. Clinical teaching ensures the integration of knowledge into practice. As the numbers of students increase in the field of nursing coupled with the faculty shortage, clinical preceptors are the best choice to ensure student learning in the clinical settings. The clinical preceptor role has been introduced in the undergraduate nursing programme. In Pakistan, this role emerged due to a faculty shortage. Initially, two clinical preceptors were hired. This study will explore clinical preceptors views and experiences of precepting Bachelor of Science in Nursing (BScN) students in an undergraduate program. A case study design was used. As case studies explore a single unit of study such as a person or very small number of subjects; the two clinical preceptors were fundamental to the study and served as a single case. Qualitative data were obtained through an iterative process using in depth interviews and written accounts from reflective journals that were kept by the clinical preceptors. The findings revealed that the clinical preceptors were dedicated to their roles and responsibilities. Another, key finding was that clinical preceptors’ prior knowledge and clinical experience were valuable assets to perform their role effectively. The clinical preceptors found their new role innovative and challenging; it was stressful at the same time. Findings also revealed that in the clinical agencies there were unclear expectations and role ambiguity. Furthermore, clinical preceptors had difficulty integrating theory into practice in the clinical area and they had difficulty in giving feedback to the students. Although this study is localized to one university, generalizations can be drawn from the results. The key findings indicate that the role of a clinical preceptor is demanding and stressful. Clinical preceptors need preparation prior to precepting students on clinicals. Also, institutional support is fundamental for their acceptance. This paper focuses on the views and experiences of clinical preceptors undertaking a newly established role and resonates with the literature. The following recommendations are drawn to strengthen the role of the clinical preceptors: A structured program for clinical preceptors is needed along with mentorship. Clinical preceptors should be provided with formal training in teaching and learning with emphasis on clinical teaching and giving feedback to students. Additionally, for improving integration of theory into practice, clinical modules should be provided ahead of the clinical. In spite of all the challenges, ten more clinical preceptors have been hired as the faculty shortage continues to persist.

Keywords: Baccalaureate nursing education, clinical education, clinical preceptors, nursing curriculum.

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Authors: B. Selma, S. Chouraqui

Abstract:

Nonlinear system identification is becoming an important tool which can be used to improve control performance. This paper describes the application of adaptive neuro-fuzzy inference system (ANFIS) model for controlling a car. The vehicle must follow a predefined path by supervised learning. Backpropagation gradient descent method was performed to train the ANFIS system. The performance of the ANFIS model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed ANFIS model has potential in controlling the non linear system.

Keywords: Adaptive neuro-fuzzy inference system (ANFIS), Fuzzy logic, neural network, nonlinear system, control

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Authors: Abhishek Bansal, G. N. Pillai

Abstract:

This paper presents a new method to detect high impedance faults in radial distribution systems. Magnitudes of third and fifth harmonic components of voltages and currents are used as a feature vector for fault discrimination. The proposed methodology uses a learning vector quantization (LVQ) neural network as a classifier for identifying high impedance arc-type faults. The network learns from the data obtained from simulation of a simple radial system under different fault and system conditions. Compared to a feed-forward neural network, a properly tuned LVQ network gives quicker response.

Keywords: Fault identification, distribution networks, high impedance arc-faults, feature vector, LVQ networks.

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Authors: Junjie Chen

Abstract:

It is usually difficult for students to understand some basic theories in learning thermal energy and power engineering course. A new teaching method was proposed that we should introduce the comparison research method of those theories to help them being understood. “Homogeneous and heterogeneous catalysis” teaching is analyzed as an example by comparison research method.

Keywords: Homogeneous catalysis, heterogeneous catalysis, thermal energy and power engineering, teaching method, comparison research method.

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Authors: Liping Li, Wenan Tan, Na Wang

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With the rapid development of information technology, project management has gained more and more attention recently. Based on CDIO, this paper proposes some teaching reform ideas for software project management curriculum. We first change from Teacher-centered classroom to Student-centered and adopt project-driven, scenario animation show, teaching rhythms, case study and team work practice to improve students' learning enthusiasm. Results showed these attempts have been well received and very effective; as well, students prefer to learn with this curriculum more than before the reform.

Keywords: CDIO, teaching reform, engineering education, project-driven, scenario animation simulation.

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Authors: Kazuhisa Takagi

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This paper is about movies and dynamic objects for mobile phones. Dynamic objects are the software programmed by JavaScript. They consist of geometric figures and work on HTML5-compliant browsers. Mobile phones are very popular among teenagers. They like watching movies and playing games on them. So, mathematics movies and dynamic objects would enhance teaching and learning processes. In the movies, manga characters speak with artificially synchronized voices. They teach trigonometry together with dynamic mathematical objects. Many movies are created. They are Windows Media files or MP4 movies. These movies and dynamic objects are not only used in the classroom but also distributed to students. By watching movies, students can study trigonometry before or after class.

Keywords: Dynamic mathematical object, JavaScript, Google drive, transfer jet.

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Authors: Ivana Scidà, Francesco Alotto, Anna Osello

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Due to the importance given today to innovation, the education sector is evolving thanks digital technologies. Virtual Reality (VR) can be a potential teaching tool offering many advantages in the field of training and education, as it allows to acquire theoretical knowledge and practical skills using an immersive experience in less time than the traditional educational process. These assumptions allow to lay the foundations for a new educational environment, involving and stimulating for students. Starting from the objective of strengthening the innovative teaching offer and the learning processes, the case study of the research concerns the digitalization of MastrLAB, High Quality Laboratory (HQL) belonging to the Department of Structural, Building and Geotechnical Engineering (DISEG) of the Polytechnic of Turin, a center specialized in experimental mechanical tests on traditional and innovative building materials and on the structures made with them. The MastrLAB-VR has been developed, a revolutionary innovative training tool designed with the aim of educating the class in total safety on the techniques of use of machinery, thus reducing the dangers arising from the performance of potentially dangerous activities. The virtual laboratory, dedicated to the students of the Building and Civil Engineering Courses of the Polytechnic of Turin, has been projected to simulate in an absolutely realistic way the experimental approach to the structural tests foreseen in their courses of study: from the tensile tests to the relaxation tests, from the steel qualification tests to the resilience tests on elements at environmental conditions or at characterizing temperatures. The research work proposes a methodology for the virtualization of technical laboratories through the application of Building Information Modelling (BIM), starting from the creation of a digital model. The process includes the creation of an independent application, which with Oculus Rift technology will allow the user to explore the environment and interact with objects through the use of joypads. The application has been tested in prototype way on volunteers, obtaining results related to the acquisition of the educational notions exposed in the experience through a virtual quiz with multiple answers, achieving an overall evaluation report. The results have shown that MastrLAB-VR is suitable for both beginners and experts and will be adopted experimentally for other laboratories of the University departments.

Keywords: Building Information Modelling, digital learning, education, virtual laboratory, virtual reality.

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Authors: Nittaya Kerdprasop, Kittisak Kerdprasop

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Data mining (DM) is the process of finding and extracting frequent patterns that can describe the data, or predict unknown or future values. These goals are achieved by using various learning algorithms. Each algorithm may produce a mining result completely different from the others. Some algorithms may find millions of patterns. It is thus the difficult job for data analysts to select appropriate models and interpret the discovered knowledge. In this paper, we describe a framework of an intelligent and complete data mining system called SUT-Miner. Our system is comprised of a full complement of major DM algorithms, pre-DM and post-DM functionalities. It is the post-DM packages that ease the DM deployment for business intelligence applications.

Keywords: Business intelligence, data mining, functionalprogramming, intelligent system.

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Authors: S. Sarumathi, N. Shanthi, M. Sharmila

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Clustering in data mining is an unsupervised learning technique of aggregating the data objects into meaningful groups such that the intra cluster similarity of objects are maximized and inter cluster similarity of objects are minimized. Over the past decades several clustering tools were emerged in which clustering algorithms are inbuilt and are easier to use and extract the expected results. Data mining mainly deals with the huge databases that inflicts on cluster analysis and additional rigorous computational constraints. These challenges pave the way for the emergence of powerful expansive data mining clustering softwares. In this survey, a variety of clustering tools used in data mining are elucidated along with the pros and cons of each software.

Keywords: Cluster Analysis, Clustering Algorithms, Clustering Techniques, Association, Visualization.

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Authors: Guezouli Larbi, Belkacem Soundes

Abstract:

The automation of the text detection process can help the human in his driving task. Its application can be very useful to help drivers to have more information about their environment by facilitating the reading of road signs such as directional signs, events, stores, etc. In this paper, a system consisting of two stages has been proposed. In the first one, we used pseudo-Zernike moments to pinpoint areas of the image that may contain text. The architecture of this part is based on three main steps, region of interest (ROI) detection, text localization, and non-text region filtering. Then, in the second step, we present a convolutional neural network architecture (On-Road Text Detection Network - ORTDN) which is considered as a classification phase. The results show that the proposed framework achieved ≈ 35 fps and an mAP of ≈ 90%, thus a low computational time with competitive accuracy.

Keywords: Text detection, CNN, PZM, deep learning.

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Authors: Nahla Barakat, Joachim Diederich

Abstract:

Support vector machines (SVMs) have shown superior performance compared to other machine learning techniques, especially in classification problems. Yet one limitation of SVMs is the lack of an explanation capability which is crucial in some applications, e.g. in the medical and security domains. In this paper, a novel approach for eclectic rule-extraction from support vector machines is presented. This approach utilizes the knowledge acquired by the SVM and represented in its support vectors as well as the parameters associated with them. The approach includes three stages; training, propositional rule-extraction and rule quality evaluation. Results from four different experiments have demonstrated the value of the approach for extracting comprehensible rules of high accuracy and fidelity.

Keywords: Data mining, hybrid rule-extraction algorithms, medical diagnosis, SVMs

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Authors: Pairaya J., Buddhagarn R., Sukree S., Punthumadee K.

Abstract:

Application of Information Technology (IT) has revolutionized the functioning of business all over the world. Its impact has been felt mostly among the information of dependent industries. Tourism is one of such industry. The conceptual framework in this study represents an innovation of travel information searching system on mobile devices which is used as tools to deliver travel information (such as hotels, restaurants, tourist attractions and souvenir shops) for each user by travelers segmentation based on data mining technique to segment the tourists- behavior patterns then match them with tourism products and services. This system innovation is designed to be a knowledge incremental learning. It is a marketing strategy to support business to respond traveler-s demand effectively.

Keywords: Tourism, Innovation, Information Searching, Data Mining.

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Authors: Ahmad T. Al-Taani, Noor Aldeen K. Al-Awad

Abstract:

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference approaches. These measures are applied and compared using 50 different Arabic web-pages. Einstein measure was gave best performance among the other measures. An analysis of these measures and concluding remarks are drawn in this study.

Keywords: Text classification, HTML, web pages, machine learning, fuzzy logic, Arabic web pages.

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Authors: Introducing Principles of Land Surveying by Assigning a Practical Project

Abstract:

A practical project is used in an engineering surveying course to expose sophomore and junior civil engineering students to several important issues related to the use of basic principles of land surveying. The project, which is the design of a two-lane rural highway to connect between two arbitrary points, requires students to draw the profile of the proposed highway along with the existing ground level. Areas of all cross-sections are then computed to enable quantity computations between them. Lastly, Mass-Haul Diagram is drawn with all important parts and features shown on it for clarity. At the beginning, students faced challenges getting started on the project. They had to spend time and effort thinking of the best way to proceed and how the work would flow. It was even more challenging when they had to visualize images of cut, fill and mixed cross sections in three dimensions before they can draw them to complete the necessary computations. These difficulties were then somewhat overcome with the help of the instructor and thorough discussions among team members and/or between different teams. The method of assessment used in this study was a well-prepared-end-of-semester questionnaire distributed to students after the completion of the project and the final exam. The survey contained a wide spectrum of questions from students' learning experience when this course development was implemented to students' satisfaction of the class instructions provided to them and the instructor's competency in presenting the material and helping with the project. It also covered the adequacy of the project to show a sample of a real-life civil engineering application and if there is any excitement added by implementing this idea. At the end of the questionnaire, students had the chance to provide their constructive comments and suggestions for future improvements of the land surveying course. Outcomes will be presented graphically and in a tabular format. Graphs provide visual explanation of the results and tables, on the other hand, summarize numerical values for each student along with some descriptive statistics, such as the mean, standard deviation, and coefficient of variation for each student and each question as well. In addition to gaining experience in teamwork, communications, and customer relations, students felt the benefit of assigning such a project. They noticed the beauty of the practical side of civil engineering work and how theories are utilized in real-life engineering applications. It was even recommended by students that such a project be exercised every time this course is offered so future students can have the same learning opportunity they had.

Keywords: Land surveying, highway project, assessment, evaluation, descriptive statistic.

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