Search results for: Rule Extraction
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1098

Search results for: Rule Extraction

588 Effect of Oil Contamination on the Liquefaction Behavior of Sandy

Authors: S. A. Naeini, M. M. Shojaedin

Abstract:

Oil leakage from the pipelines and the tanks carrying them, or during oil extraction, could lead to the changes in the characteristics and properties of the soil. In this paper, conducting a series of experimental cyclic triaxial tests, the effects of oil contamination on the liquefaction potential of sandy soils is investigated. The studied specimens are prepared by mixing the Firoozkuh sand with crude oil in 4, 8 and 12 percent by soil dry weight. The results show that the oil contamination up to 8% causes an increase in the soil liquefaction resistance and then with increase in the contamination, the liquefaction resistance decreases.

Keywords: Cyclic triaxial test, Liquefaction resistance, Oil contamination, Sandy soil.

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587 Assessment of Pollution Reduction

Authors: Katarzyna Strzała-Osuch

Abstract:

Environmental investments, including ecological projects, relating to the protection of atmosphere are today a need. However, investing in the environment should be based on rational management rules. This comes across a problem of selecting a method to assess substances reduced during projects. Therefore, a method allowing for the assessment of decision rationality has to be found. The purpose of this article is to present and systematise pollution reduction assessment methods and illustrate theoretical analyses with empirical data. Empirical results confirm theoretical considerations, which proved that the only method for judging pollution reduction, free of apparent disadvantages, is the Eco 99-ratio method. To make decisions on environmental projects, financing institutions should take into account a rationality rule. Therefore the Eco 99-ratio method could be applied to make decisions relating to environmental investments in the area of air protection.

Keywords: Assessment of pollution reduction, costs of environmental protection, efficiency of environmental investments.

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586 Entropy Based Data Hiding for Document Images

Authors: Swetha Kurup, Sridhar G., Sridhar V.

Abstract:

In this paper we present a novel technique for data hiding in binary document images. We use the concept of entropy in order to identify document specific least distortive areas throughout the binary document image. The document image is treated as any other image and the proposed method utilizes the standard document characteristics for the embedding process. Proposed method minimizes perceptual distortion due to embedding and allows watermark extraction without the requirement of any side information at the decoder end.

Keywords: Entropy, Steganography, Watermarking.

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585 A Constrained Clustering Algorithm for the Classification of Industrial Ores

Authors: Luciano Nieddu, Giuseppe Manfredi

Abstract:

In this paper a Pattern Recognition algorithm based on a constrained version of the k-means clustering algorithm will be presented. The proposed algorithm is a non parametric supervised statistical pattern recognition algorithm, i.e. it works under very mild assumptions on the dataset. The performance of the algorithm will be tested, togheter with a feature extraction technique that captures the information on the closed two-dimensional contour of an image, on images of industrial mineral ores.

Keywords: K-means, Industrial ores classification, Invariant Features, Supervised Classification.

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584 Design and Simulation of Low Noise Amplifier Circuit for 5 GHz to 6 GHz

Authors: Hossein Sahoolizadeh, Alishir Moradi Kordalivand, Zargham Heidari

Abstract:

In first stage of each microwave receiver there is Low Noise Amplifier (LNA) circuit, and this stage has important rule in quality factor of the receiver. The design of a LNA in Radio Frequency (RF) circuit requires the trade-off many importance characteristics such as gain, Noise Figure (NF), stability, power consumption and complexity. This situation Forces desingners to make choices in the desing of RF circuits. In this paper the aim is to design and simulate a single stage LNA circuit with high gain and low noise using MESFET for frequency range of 5 GHz to 6 GHz. The desing simulation process is down using Advance Design System (ADS). A single stage LNA has successfully designed with 15.83 dB forward gain and 1.26 dB noise figure in frequency of 5.3 GHz. Also the designed LNA should be working stably In a frequency range of 5 GHz to 6 GHz.

Keywords: Advance Design System, Low Noise Amplifier, Radio Frequency, Noise Figure.

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583 Study on the Influence of Cladding and Finishing Materials of Apartment Buildings on the Architectural Identity of Amman, Jordan

Authors: Asil Y. Zureigat, Ayat A. Oudat

Abstract:

Analyzing the old and bringing in the new is an ever-ongoing process in driving innovations in architecture. This paper looks at the excessive use of stone in apartment buildings in Amman and speculates on the existing possibilities of changing the cladding material. By looking at architectural exceptions present in Amman, the paper seeks to make the exception the rule, by adding new materials to the architectural library of Amman and in turn, project a series of possible new identities to the existing stone scape. Through distributing a survey, conducting a photographic study on exceptional buildings and shedding light on the historical narrative of stone, the paper highlights the ways in which new finishing materials such as plaster, paint and stone variations could be introduced in an attempt to project a new architectural identity to Amman.

Keywords: Architectural city identity, cladding materials, façade architecture, image of the city.

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582 A Family of Distributions on Learnable Problems without Uniform Convergence

Authors: César Garza

Abstract:

In supervised binary classification and regression problems, it is well-known that learnability is equivalent to uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.

Keywords: Statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization.

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581 Applying Fuzzy FP-Growth to Mine Fuzzy Association Rules

Authors: Chien-Hua Wang, Wei-Hsuan Lee, Chin-Tzong Pang

Abstract:

In data mining, the association rules are used to find for the associations between the different items of the transactions database. As the data collected and stored, rules of value can be found through association rules, which can be applied to help managers execute marketing strategies and establish sound market frameworks. This paper aims to use Fuzzy Frequent Pattern growth (FFP-growth) to derive from fuzzy association rules. At first, we apply fuzzy partition methods and decide a membership function of quantitative value for each transaction item. Next, we implement FFP-growth to deal with the process of data mining. In addition, in order to understand the impact of Apriori algorithm and FFP-growth algorithm on the execution time and the number of generated association rules, the experiment will be performed by using different sizes of databases and thresholds. Lastly, the experiment results show FFPgrowth algorithm is more efficient than other existing methods.

Keywords: Data mining, association rule, fuzzy frequent patterngrowth.

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580 Effects of Polymers and Alkaline on Recovery Improvement from Fractured Models

Authors: Payam Parvasi, Mohammad Hossein Sedaghat, Reza Janamiri, Amir Hatampour

Abstract:

In this work, several ASP solutions were flooded into fractured models initially saturated with heavy oil at a constant flow rate and different geometrical characteristics of fracture. The ASP solutions are constituted from 2 polymers i.e. a synthetic polymer, hydrolyzed polyacrylamide as well as a biopolymer, a surfactant and 2types of alkaline. The results showed that using synthetic hydrolyzed polyacrylamide polymer increases ultimate oil recovery; however, type of alkaline does not play a significant rule on oil recovery. In addition, position of the injection well respect to the fracture system has remarkable effects on ASP flooding. For instance increasing angle of fractures with mean flow direction causes more oil recovery and delays breakthrough time. This work can be accounted as a comprehensive survey on ASP flooding which considers most of effective factors in this chemical EOR method.

Keywords: ASP Flooding, Fractured System, Displacement, Heavy Oil.

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579 A Multi-Agent Intelligent System for Monitoring Health Conditions of Elderly People

Authors: Ayman M. Mansour

Abstract:

In this paper, we propose a multi-agent intelligent system that is used for monitoring the health conditions of elderly people. Monitoring the health condition of elderly people is a complex problem that involves different medical units and requires continuous monitoring. Such expert system is highly needed in rural areas because of inadequate number of available specialized physicians or nurses. Such monitoring must have autonomous interactions between these medical units in order to be effective. A multi-agent system is formed by a community of agents that exchange information and proactively help one another to achieve the goal of elderly monitoring. The agents in the developed system are equipped with intelligent decision maker that arms them with the rule-based reasoning capability that can assist the physicians in making decisions regarding the medical condition of elderly people.

Keywords: Fuzzy Logic, Inference system, Monitoring system, Multi-agent system.

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578 On Musical Information Geometry with Applications to Sonified Image Analysis

Authors: Shannon Steinmetz, Ellen Gethner

Abstract:

In this paper a theoretical foundation is developed to segment, analyze and associate patterns within audio. We explore this on imagery via sonified audio applied to our segmentation framework. The approach involves a geodesic estimator within the statistical manifold, parameterized by musical centricity. We demonstrate viability by processing a database of random imagery to produce statistically significant clusters of similar imagery content.

Keywords: Sonification, musical information geometry, image content extraction, automated quantification, audio segmentation, pattern recognition.

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577 Comparison of Performance between Different SVM Kernels for the Identification of Adult Video

Authors: Hajar Bouirouga, Sanaa El Fkihi , Abdeilah Jilbab, Driss Aboutajdine

Abstract:

In this paper we propose a method for recognition of adult video based on support vector machine (SVM). Different kernel features are proposed to classify adult videos. SVM has an advantage that it is insensitive to the relative number of training example in positive (adult video) and negative (non adult video) classes. This advantage is illustrated by comparing performance between different SVM kernels for the identification of adult video.

Keywords: Skin detection, Support vector machine, Pornographic videos, Feature extraction, Video filtering, Classification.

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576 Using Swarm Intelligence for Improving Accuracy of Fuzzy Classifiers

Authors: Hassan M. Elragal

Abstract:

This paper discusses a method for improving accuracy of fuzzy-rule-based classifiers using particle swarm optimization (PSO). Two different fuzzy classifiers are considered and optimized. The first classifier is based on Mamdani fuzzy inference system (M_PSO fuzzy classifier). The second classifier is based on Takagi- Sugeno fuzzy inference system (TS_PSO fuzzy classifier). The parameters of the proposed fuzzy classifiers including premise (antecedent) parameters, consequent parameters and structure of fuzzy rules are optimized using PSO. Experimental results show that higher classification accuracy can be obtained with a lower number of fuzzy rules by using the proposed PSO fuzzy classifiers. The performances of M_PSO and TS_PSO fuzzy classifiers are compared to other fuzzy based classifiers

Keywords: Fuzzy classifier, Optimization of fuzzy systemparameters, Particle swarm optimization, Pattern classification.

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575 Sensitivity Analysis of Real-Time Systems

Authors: Benjamin Gorry, Andrew Ireland, Peter King

Abstract:

Verification of real-time software systems can be expensive in terms of time and resources. Testing is the main method of proving correctness but has been shown to be a long and time consuming process. Everyday engineers are usually unwilling to adopt formal approaches to correctness because of the overhead associated with developing their knowledge of such techniques. Performance modelling techniques allow systems to be evaluated with respect to timing constraints. This paper describes PARTES, a framework which guides the extraction of performance models from programs written in an annotated subset of C.

Keywords: Performance Modelling, Real-time, SensitivityAnalysis.

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574 Heuristic Continuous-time Associative Memories

Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

Abstract:

In this paper, a novel associative memory model will be proposed and applied to memory retrievals based on the conventional continuous time model. The conventional model presents memory capacity is very low and retrieval process easily converges to an equilibrium state which is very different from the stored patterns. Genetic Algorithms is well-known with the capability of global optimal search escaping local optimum on progress to reach a global optimum. Based on the well-known idea of Genetic Algorithms, this work proposes a heuristic rule to make a mutation when the state of the network is trapped in a spurious memory. The proposal heuristic associative memory show the stored capacity does not depend on the number of stored patterns and the retrieval ability is up to ~ 1.

Keywords: Artificial Intelligent, Soft Computing, NeuralNetworks, Genetic Algorithms, Hopfield Neural Networks, andAssociative Memories.

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573 Novelty as a Measure of Interestingness in Knowledge Discovery

Authors: Vasudha Bhatnagar, Ahmed Sultan Al-Hegami, Naveen Kumar

Abstract:

Rule Discovery is an important technique for mining knowledge from large databases. Use of objective measures for discovering interesting rules leads to another data mining problem, although of reduced complexity. Data mining researchers have studied subjective measures of interestingness to reduce the volume of discovered rules to ultimately improve the overall efficiency of KDD process. In this paper we study novelty of the discovered rules as a subjective measure of interestingness. We propose a hybrid approach based on both objective and subjective measures to quantify novelty of the discovered rules in terms of their deviations from the known rules (knowledge). We analyze the types of deviation that can arise between two rules and categorize the discovered rules according to the user specified threshold. We implement the proposed framework and experiment with some public datasets. The experimental results are promising.

Keywords: Knowledge Discovery in Databases (KDD), Interestingness, Subjective Measures, Novelty Index.

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572 Quantitative and Fourier Transform Infrared Analysis of Saponins from Three Kenyan Ruellia Species: Ruellia prostrata, Ruellia lineari-bracteolata and Ruellia bignoniiflora

Authors: Christine O. Wangia, Jennifer A. Orwa, Francis W. Muregi, Patrick G. Kareru, Kipyegon Cheruiyot, Eric Guantai

Abstract:

Ruellia (syn. Dipteracanthus) species are wild perennial creepers belonging to the Acanthaceae family. These species are reported to possess anti-inflammatory, analgesic, antioxidant, gastroprotective, anticancer, and immuno-stimulant properties. Phytochemical screening of both aqueous and methanolic extracts of Ruellia species revealed the presence of saponins. Saponins have been reported to possess anti-inflammatory, antioxidant, immuno-stimulant, antihepatotoxic, antibacterial, anticarcinogenic, and antiulcerogenic activities. The objective of this study was to quantify and analyze the Fourier transform infrared (FTIR) spectra of saponins in crude extracts of three Kenyan Ruellia species namely Ruellia prostrata (RPM), Ruellia lineari-bracteolata (RLB) and Ruellia bignoniiflora (RBK). Sequential organic extraction of the ground whole plant material was done using petroleum ether (PE), chloroform, ethyl acetate (EtOAc), and absolute methanol by cold maceration, while aqueous extraction was by hot maceration. The plant powders and extracts were mixed with spectroscopic grade KBr and compressed into a pellet. The infrared spectra were recorded using a Shimadzu FTIR spectrophotometer of 8000 series in the range of 3500 cm-1 - 500 cm-1. Quantitative determination of the saponins was done using standard procedures. Quantitative analysis of saponins showed that RPM had the highest quantity of crude saponins (2.05% ± 0.03), followed by RLB (1.4% ± 0.15) and RBK (1.25% ± 0.11), respectively. FTIR spectra revealed the spectral peaks characteristic for saponins in RPM, RLB, and RBK plant powders, aqueous and methanol extracts; O-H absorption (3265 - 3393 cm-1), C-H absorption ranging from 2851 to 2924 cm-1, C=C absorbance (1628 - 1655 cm-1), oligosaccharide linkage (C-O-C) absorption due to sapogenins (1036 - 1042 cm-1). The crude saponins from RPM, RLB and RBK showed similar peaks to their respective extracts. The presence of the saponins in extracts of RPM, RLB and RBK may be responsible for some of the biological activities reported in the Ruellia species.1

Keywords: Ruellia bignoniiflora, Ruellia lineari-bracteolata, Ruellia prostrata, Saponins.

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571 Extracting Road Signs using the Color Information

Authors: Wen-Yen Wu, Tsung-Cheng Hsieh, Ching-Sung Lai

Abstract:

In this paper, we propose a method to extract the road signs. Firstly, the grabbed image is converted into the HSV color space to detect the road signs. Secondly, the morphological operations are used to reduce noise. Finally, extract the road sign using the geometric property. The feature extraction of road sign is done by using the color information. The proposed method has been tested for the real situations. From the experimental results, it is seen that the proposed method can extract the road sign features effectively.

Keywords: Color information, image processing, road sign.

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570 Specialization-based parallel Processing without Memo-trees

Authors: Hidemi Ogasawara, Kiyoshi Akama, Hiroshi Mabuchi

Abstract:

The purpose of this paper is to propose a framework for constructing correct parallel processing programs based on Equivalent Transformation Framework (ETF). ETF regards computation as In the framework, a problem-s domain knowledge and a query are described in definite clauses, and computation is regarded as transformation of the definite clauses. Its meaning is defined by a model of the set of definite clauses, and the transformation rules generated must preserve meaning. We have proposed a parallel processing method based on “specialization", a part of operation in the transformations, which resembles substitution in logic programming. The method requires “Memo-tree", a history of specialization to maintain correctness. In this paper we proposes the new method for the specialization-base parallel processing without Memo-tree.

Keywords: Parallel processing, Program correctness, Equivalent transformation, Specializer generation rule

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569 An Evaluation of Algorithms for Single-Echo Biosonar Target Classification

Authors: Turgay Temel, John Hallam

Abstract:

A recent neurospiking coding scheme for feature extraction from biosonar echoes of various plants is examined with avariety of stochastic classifiers. Feature vectors derived are employedin well-known stochastic classifiers, including nearest-neighborhood,single Gaussian and a Gaussian mixture with EM optimization.Classifiers' performances are evaluated by using cross-validation and bootstrapping techniques. It is shown that the various classifers perform equivalently and that the modified preprocessing configuration yields considerably improved results.

Keywords: Classification, neuro-spike coding, non-parametricmodel, parametric model, Gaussian mixture, EM algorithm.

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568 Hybrid Color-Texture Space for Image Classification

Authors: Hassan El Maia, Ahmed Hammouch, Driss Aboutajdine

Abstract:

This work presents an approach for the construction of a hybrid color-texture space by using mutual information. Feature extraction is done by the Laws filter with SVM (Support Vectors Machine) as a classifier. The classification is applied on the VisTex database and a SPOT HRV (XS) image representing two forest areas in the region of Rabat in Morocco. The result of classification obtained in the hybrid space is compared with the one obtained in the RGB color space.

Keywords: Color, texture, laws filter, mutual information, SVM, hybrid space.

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567 Indoor Mapping by using Smartphone Device

Authors: Shuib Rambat, Ruzsyahriman Jenal, John Elgy

Abstract:

This paper presented the potential of smart phone to provide support on mapping the indoor asset. The advantage of using the smart phone to generate the indoor map is that it has the ability to capture, store and reproduces still or video images; indeed most of us do have this powerful gadget. The captured images usually used by maintenance team to save a record for future reference. Here, these images are used to generate 3D models of an object precisely and accurately for efficient and effective solution in data gathering. Thus, it could be a resource for an informative database in asset management.

Keywords: 3D modeling, Asset Management, Object Extraction, Smart Device

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566 Portfolio Management: A Fuzzy Set Based Approach to Monitoring Size to Maximize Return and Minimize Risk

Authors: Margaret F. Shipley

Abstract:

Fuzzy logic can be used when knowledge is incomplete or when ambiguity of data exists. The purpose of this paper is to propose a proactive fuzzy set- based model for reacting to the risk inherent in investment activities relative to a complete view of portfolio management. Fuzzy rules are given where, depending on the antecedents, the portfolio size may be slightly or significantly decreased or increased. The decision maker considers acceptable bounds on the proportion of acceptable risk and return. The Fuzzy Controller model allows learning to be achieved as 1) the firing strength of each rule is measured, 2) fuzzy output allows rules to be updated, and 3) new actions are recommended as the system continues to loop. An extension is given to the fuzzy controller that evaluates potential financial loss before adjusting the portfolio. An application is presented that illustrates the algorithm and extension developed in the paper.

Keywords: Portfolio Management, Financial Market Monitoring, Fuzzy Controller, Fuzzy Logic,

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565 An Improved Variable Tolerance RSM with a Proportion Threshold

Authors: Chen Wu, Youquan Xu, Dandan Li, Ronghua Yang, Lijuan Wang

Abstract:

In rough set models, tolerance relation, similarity relation and limited tolerance relation solve different situation problems for incomplete information systems in which there exists a phenomenon of missing value. If two objects have the same few known attributes and more unknown attributes, they cannot distinguish them well. In order to solve this problem, we presented two improved limited and variable precision rough set models. One is symmetric, the other one is non-symmetric. They all use more stringent condition to separate two small probability equivalent objects into different classes. The two models are needed to engage further study in detail. In the present paper, we newly form object classes with a different respect comparing to the first suggested model. We overcome disadvantages of non-symmetry regarding to the second suggested model. We discuss relationships between or among several models and also make rule generation. The obtained results by applying the second model are more accurate and reasonable.

Keywords: Incomplete information system, rough set, symmetry, variable precision.

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564 Unified Method to Block Pornographic Images in Websites

Authors: Sakthi Priya Balaji R., Vijayendar G.

Abstract:

This paper proposes a technique to block adult images displayed in websites. The filter is designed so as to perform even in exceptional cases such as, where face detection is not possible or improper face visibility. This is achieved by using an alternative phase to extract the MFC (Most Frequent Color) from the Human Body regions estimated using a biometric of anthropometric distances between fixed rigidly connected body locations. The logical results generated can be protected from overriding by a firewall or intrusion, by encrypting the result in a SSH data packet.

Keywords: Face detection, characteristics extraction andclassification, Component based shape analysis and classification, open source SSH V2 protocol

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563 Classification of Radio Communication Signals using Fuzzy Logic

Authors: Zuzana Dideková, Beata Mikovičová

Abstract:

Characterization of radio communication signals aims at automatic recognition of different characteristics of radio signals in order to detect their modulation type, the central frequency, and the level. Our purpose is to apply techniques used in image processing in order to extract pertinent characteristics. To the single analysis, we add several rules for checking the consistency of hypotheses using fuzzy logic. This allows taking into account ambiguity and uncertainty that may remain after the extraction of individual characteristics. The aim is to improve the process of radio communications characterization.

Keywords: fuzzy classification, fuzzy inference system, radio communication signals, telecommunications

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562 Genetic Mining: Using Genetic Algorithm for Topic based on Concept Distribution

Authors: S. M. Khalessizadeh, R. Zaefarian, S.H. Nasseri, E. Ardil

Abstract:

Today, Genetic Algorithm has been used to solve wide range of optimization problems. Some researches conduct on applying Genetic Algorithm to text classification, summarization and information retrieval system in text mining process. This researches show a better performance due to the nature of Genetic Algorithm. In this paper a new algorithm for using Genetic Algorithm in concept weighting and topic identification, based on concept standard deviation will be explored.

Keywords: Genetic Algorithm, Text Mining, Term Weighting, Concept Extraction, Concept Distribution.

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561 A Learning Agent for Knowledge Extraction from an Active Semantic Network

Authors: Simon Thiel, Stavros Dalakakis, Dieter Roller

Abstract:

This paper outlines the development of a learning retrieval agent. Task of this agent is to extract knowledge of the Active Semantic Network in respect to user-requests. Based on a reinforcement learning approach, the agent learns to interpret the user-s intention. Especially, the learning algorithm focuses on the retrieval of complex long distant relations. Increasing its learnt knowledge with every request-result-evaluation sequence, the agent enhances his capability in finding the intended information.

Keywords: Reinforcement learning, learning retrieval agent, search in semantic networks.

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560 Face Recognition Using Eigen face Coefficients and Principal Component Analysis

Authors: Parvinder S. Sandhu, Iqbaldeep Kaur, Amit Verma, Samriti Jindal, Inderpreet Kaur, Shilpi Kumari

Abstract:

Face Recognition is a field of multidimensional applications. A lot of work has been done, extensively on the most of details related to face recognition. This idea of face recognition using PCA is one of them. In this paper the PCA features for Feature extraction are used and matching is done for the face under consideration with the test image using Eigen face coefficients. The crux of the work lies in optimizing Euclidean distance and paving the way to test the same algorithm using Matlab which is an efficient tool having powerful user interface along with simplicity in representing complex images.

Keywords: Eigen Face, Multidimensional, Matching, PCA.

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559 A Homogenisation Procedure for the Free Vibration Analysis of Functionally Graded Beams at Large Vibration Amplitudes

Authors: A. Zerkane, K. El Bikri, R. Benamar

Abstract:

The purpose of the present paper is to show that the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters by using an homogenization procedure. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the nonlinear fundamental mode are also given for various vibration amplitudes in the case of clamped-clamped FGB.

Keywords: Nonlinear vibrations, functionally graded materials, homogenization procedure.

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