Qualitative classification and evaluation in possibilistic decision trees
|
|
- Amber Henry
- 6 years ago
- Views:
Transcription
1 Qualitative classification evaluation in possibilistic decision trees Nahla Ben Amor Institut Supérieur de Gestion de Tunis, 41 Avenue de la liberté, 2000 Le Bardo, Tunis, Tunisia Salem Benferhat CRIL - CNRS, Université d Artois, Rue Jean Souvraz SP Lens, Cedex France benferhat@criluniv-artoisfr Zied Elouedi Institut Supérieur de Gestion de Tunis, 41 Avenue de la liberté, 2000 Le Bardo, Tunis, Tunisia ziedelouedi@gmxfr Abstract This paper presents a method for classifying objects in an uncertain context using decision trees Uncertainty is related to attributes values of objects to classify is hled in a qualititative possibilistic framework Then, an evaluation method to judge the classification efficiency, in an uncertain context, is proposed I INTRODUCTION Decision trees are efficient methods used in classification problems They consist of decision nodes for testing attributes, edges for branching attribute values leaves for labeling classes [9], [7] The decision tree technique is composed of two major procedures [2], [11]: 1) Building the tree: A decision tree can be built based on a given training set It consists in finding for each decision node the appropriate test attribute by using an attribute selection measure also to define the class labeling each leaf satisfying one of the stopping criteria 2) Classifying objects: We start by the root of the decision tree, then we test the attribute specified by this node According to the result of the test, we move down the tree branch relative to the attribute value of the given object This process will be repeated until a leaf is encountered This leaf is labeled by a class As pointed out in several researches [1], [4], [5], [6], [10], the classical methods of induction of decision trees do not deal with uncertain data Ignoring it can affect the value of the results of classification In order to adapt decision trees to uncertainty imprecision, we first propose different manners to classify objects with uncertain/missing attributes using qualitative possibility theory Then, we propose a criterion allowing to judge the efficiency of the classifier in an uncertain context We illustrate our approach with a same running example from an intrusion detection system area The paper will be organized as follows: Section 2 presents an overview of the possibility theory Section 3 recalls the basics of possibilistic decision trees In Section 4, we describe our leximin/leximax classification in possibilistic decision trees In Section 5, the evaluation of the classification efficiency of possibilistic decision trees will be detailed II POSSIBILITY THEORY This Section gives a brief recalling on possibility theory (for more details see [3]) Uncertainty is here assumed to be represented qualitatively by a finite totally ordered scale denoted by such that If is a set of uncertainty degrees, we define (resp ) such that such that (resp ) The basic concept of possibility theory, when uncertainty is represented qualitatively, is the notion of Qualitative Possibility Distribution (QPD), simply denoted by A QPD is a function which associates to each element of the universe of discourse an element from, ( encodes our beliefs on a real world) By convention, means that it is completely possible is the real world, means that cannot be the real world, means that is at least as possible as to be the real world A QPD is said to be normalized if there exists at least one state which is totally possible (ie ) We define the possibility measure of any event by: This measure evaluates at which level our knowledge represented by III POSSIBILISTIC DECISION TREES (1) is consistent with In this section, we do not detail the construction of decision trees which is based on a given training set where attribute values classes are defined precisely (for more details see [11]) We are rather interested on how to classify objects characterized by uncertain attributes values where the uncertainty is presented by qualitative possibility distributions We assign for each attribute a possibility distribution expressing the uncertainty in a qualitative way by encoding it in the interval Let be different attributes of the problem The instance to classify is described by a vector of possibility distributions An attribute is precisely
2 defined if there exists exactly one value such that, for all other values A missing data regarding an attribute, is represented by a uniform possibility distribution (ie, In stard possibility theory, the basic operators min/max are used in order to choose the more plausible path in the tree At first, we should compute the possibility degree of each path (from a root to a leaf class) by applying the minimum operator on its attributes values Then, the most plausible path is the one presenting the highest possibility degree, in other words, we should apply the maximum operator on these paths degrees Hence the class of the object to classify is the one labeling the leaf corresponding to this path Example 1: In order to illustrate the different notions presented in this paper, we will consider an example in the intrusion detection field where we hle formatted connections corresponding to a TCP/IP dump rows Note that, for the sake of simplicity, each connection is described by only four attributes which are: service, flag, count, wrong fragment The attributes are defined as follows: - We also hle three classes: ; where Normal corresponds to a normal connection while DOS Probing are relative to two categories of attacks N Fig 1 Service http domain u private count P SF flag REJ RSTO wrong fragment count wrong fragment P N D D N P N Example of decision tree in intrusion detection field Assume that the connection to classify is with the possibility distributions given in Table I According to the decision tree (see Figure 1) we have nine paths, then applying the minimum operator on the different degrees relative to each path, we get: TABLE I POSSIBILITY DISTRIBUTIONS ON http 1 SF 1 domain u, 1 REJ private 1 RSTO 1 According to the maximum operator, the most plausible paths are 3 9, thus the connection will be classified as Probing or DOS with a possibility degree 1 It is clear that the use of the maximum operator makes it difficult to choose between the equally plausible paths IV LEXIMIN/LEXIMAX CLASSIFICATION IN POSSIBILISTIC DECISION TREES The min-max combination mode is not satisfactory since it is somewhat cautious which makes the number of cidate classes important especially when the number of missing attributes is important Furthermore, min/max operators are not discriminatory Indeed, we can check that, for any attribute, for any value of such that, replacing by does not change the selected cidate classes This is explained by the fact that if are normalized, then there exists at least one path from the root to a leaf class such that the possibility degree of each node s value in this path is equal to 1 Hence, with min/max combination mode, only paths where possibility degrees of attributes values are equal to 1 are considered One idea to overcome drawbacks of the min/max combination is to extend these two operators by using leximin leximax criteria which are natural extensions of the minimum maximum operators used in the qualitative
3 setting [8] defined by: Definition 1:!!expliquer be two vectors, let be two permutations of indices such that Then, is said to be leximin-preferred (resp leximaxpreferred) to, denoted by (resp ), if only if there exists such that (resp ) is said to be leximin-equal (resp leximax-equal) to, denoted by (resp ), if only if, Let be the set of all different paths from the root to leaves For each class, we associate a vector containing paths having as a leaf classified in a leximinorder To apply this criterion, all paths should be described by the same attributes already defined in the training set However, since paths are pruned, the idea will be to assign a degree 1 to the missing values The justification of adding the degree 1 can be explained as follows: In some path, a class is obtained without an attribute, this in fact means that can be obtained independently of the value of In other terms, can be obtained from a path composed by the most plausible instance of (namely those having the degree 1 since only normalized distributions are considered) Definition 2: Let be two vectors relative to paths leading to Let be two permutations of indices such that is said to be leximin-leximax preferred to, denoted by, - if there exists such that - or if, (ie is supported by a greater number of paths than ) is said to be leximin-leximax equal to, denoted by, if only if, Definition 3: Let be a set of classes, the class is leximin-leximax preferred iff there is no class, such that The selection mode based on the leximin/leximax operators proceeds in two steps: 1) Establish a total pre-order of all paths using leximin operator Then, select a first set of cidate classes corresponding to leaves of best paths in the total preorder Let be this set of classes 2) Refine by selecting its leximax-preferred class(s) using Definition 3 Example 2: Let us continue the previous example According to the leximin criterion, we get the following total preorder between different paths: Thus which are the classes labeling, respectively In other terms the connection will be classified as a Probing or a DOS attack Then, since Thus, it is possible to have a more precise result the connection will be classified as a Probing attack V EVALUATION OF POSSIBILISTIC DECISION TREES When dealing with an uncertain context, the evaluation of a classifier namely a possibilistic decision tree is not so obvious A Percent of Correct Classification In the classical case, the corresponds to the proportion of the number of well classified objects on the whole number of objects However, as within a possibilistic decision tree, a new object may not be classified in a unique class, it will be necessary to adopt the to the uncertainty pervading classes Thus, the idea is to choose for each object to classify the class having the highest degree of possibility degree If more than one class is obtained, then one of them is chosen romly The obtained class is considered as the class of the testing object Hence, the relative to the whole testing set is computed by making comparison, for each testing instance, between its real class (known by us) the class obtained by the induced tree number of well classified objects number of testing objects where the number of well classified objects is computed as the sum of testing objects for which the class obtained by the possibilistic decision tree (the most plausible class) is the same as their real class B Distance criterion The limitation of the adaptative is that it ignores the order that exists between the different classes that may correspond to the chosen class It only considers the most plausible class So, we propose a criterion allowing to take into account the order of the classes characterizing the object to classify More exactly, we propose to compare the ranking assigned to classes with the real class of the given testing object Such comparison is based on a kind of distance At first, we should define a qualitative possibility distribution assigned to the object as follows: (2)
4 Assume we hle n classes (,,, ), then: if if does not appear in the order of the classes relative to the object to classify (3) Where represents the decreasing classing of over the other Next, we define the distance criterion for a testing object (where its possibility distribution is ) with respect to its real class denoted as follows: Assume that the real class of the object DOS (D) Using the Equation 4, we get: Then, we get the distance : is the attack where if otherwise This distance verifies the following property: when is close to 2, the classifier is bad, whereas when it falls to 0, it is considered as a good classifier In order to give to this distance a signification more close to the, we propose to make changes on ( it will be denoted ), so as it satisfies the following property: Next, we have to compute the average total distance relative to all the classified testing instances denoted So, we get: classified objects number of classified objects Thus, will be considered as a calibrated on the whole testing set C Example Let s continue with our example where we deal with three classes namely, To classify the connection given in Example 2, we get (according to the induced tree) the following order: Hence, the corresponding possibility distribution (see Equation 2) will be: (4) (5) (6) (7) (8) So, Thus, we get 39% of chance that the induced tree detects the real class of whereas, applying directly the classical PCC on the most plausible class leads directly to an erroneous result Obviously, we can apply this distance criterion on all the testing set using Equation 8 VI CONCLUSION In this paper, we have presented two contributions The first one concerns the classification, using decision trees, of objects characterized by uncertain attribute values where uncertainty is represented in a qualititative possibilistic framework Indeed, to overcome limitations of the stard min-max combination, we have proposed a lexmin/leximax combination mode in the classification phase In the second part, we have proposed a new criterion to judge the efficiency of classifiers under an uncertain context, namely the qualitative possibilistic decision trees This criterion takes into account the total pre-order of classes relative to each testing instance not only the best one as in the classical Percent of Correct Classification A future work will be to introduce a semantic distance to this criterion allowing to adjust the degree of similarity between classes REFERENCES [1] Ben Amor N, Benferhat S, Elouedi Z, Mellouli K: Decision Trees Qualitative Possibilistic Inference: Application to the Intrusion Detection Problem Proceedings of European Conference of Symbolic Quantitative Approaches to Reasoning Uncertainty (ECSQARU 2003), , 2003 [2] Breiman, L, Friedman, J H, Olshen, R A, Stone, C J: Classification regression trees Monterey, CA, Wadsworth & Brooks, 1984 [3] D Dubois H Prade: Possibility theory: An approach to computerized Processing of uncertainty Plenium Press, New York, 1988 [4] Denoeux T, Skarstein-Bjanger M: Induction of decision trees for partially classified data Proceedings of the IEEE International Conference on Systems, Man, Cybernetics, Nashville, USA, , 2000 [5] Elouedi Z, Mellouli K, Smets P: Belief decision trees: Theoretical foundations International Journal of Approximate Reasoning 28, , 2001 [6] Hullermeier E, Possibilistic induction in decision-tree learning, ECML 02, 2002 [7] Mitchell, T M: Decision tree learning Chapter 3 of Machine Learning, Co-published by the MIT Press the McGraw-Hill Compagnies, Inc, 1997
5 [8] Moulin H: Axioms for cooperative decision-making Cambridge University Press, 1988 [9] Quinlan, J R: Induction of decision trees, Machine Learning 1, 1-106, 1986 [10] Quinlan, J R: Probabilistic decision trees, Machine Learning, Vol 3, Chap 5, Morgan Kaufmann, , 1990 [11] Quinlan, J R: C45: Programs for machine learning Morgan Kaufmann San Mateo Ca, 1993
Improving Quality of Products in Hard Drive Manufacturing by Decision Tree Technique
Improving Quality of Products in Hard Drive Manufacturing by Decision Tree Technique Anotai Siltepavet 1, Sukree Sinthupinyo 2 and Prabhas Chongstitvatana 3 1 Computer Engineering, Chulalongkorn University,
More informationImproving Quality of Products in Hard Drive Manufacturing by Decision Tree Technique
www.ijcsi.org 29 Improving Quality of Products in Hard Drive Manufacturing by Decision Tree Technique Anotai Siltepavet 1, Sukree Sinthupinyo 2 and Prabhas Chongstitvatana 3 1 Computer Engineering, Chulalongkorn
More informationWeighted Attacks in Argumentation Frameworks
Weighted Attacks in Argumentation Frameworks Sylvie Coste-Marquis Sébastien Konieczny Pierre Marquis Mohand Akli Ouali CRIL - CNRS, Université d Artois, Lens, France {coste,konieczny,marquis,ouali}@cril.fr
More informationFUZZY BOOLEAN ALGEBRAS AND LUKASIEWICZ LOGIC. Angel Garrido
Acta Universitatis Apulensis ISSN: 1582-5329 No. 22/2010 pp. 101-111 FUZZY BOOLEAN ALGEBRAS AND LUKASIEWICZ LOGIC Angel Garrido Abstract. In this paper, we analyze the more adequate tools to solve many
More informationMining High Order Decision Rules
Mining High Order Decision Rules Y.Y. Yao Department of Computer Science, University of Regina Regina, Saskatchewan, Canada S4S 0A2 e-mail: yyao@cs.uregina.ca Abstract. We introduce the notion of high
More informationFuzzy Partitioning with FID3.1
Fuzzy Partitioning with FID3.1 Cezary Z. Janikow Dept. of Mathematics and Computer Science University of Missouri St. Louis St. Louis, Missouri 63121 janikow@umsl.edu Maciej Fajfer Institute of Computing
More informationRPKM: The Rough Possibilistic K-Modes
RPKM: The Rough Possibilistic K-Modes Asma Ammar 1, Zied Elouedi 1, and Pawan Lingras 2 1 LARODEC, Institut Supérieur de Gestion de Tunis, Université de Tunis 41 Avenue de la Liberté, 2000 Le Bardo, Tunisie
More informationAv. Prof. Mello Moraes, 2231, , São Paulo, SP - Brazil
" Generalizing Variable Elimination in Bayesian Networks FABIO GAGLIARDI COZMAN Escola Politécnica, University of São Paulo Av Prof Mello Moraes, 31, 05508-900, São Paulo, SP - Brazil fgcozman@uspbr Abstract
More informationEfficient SQL-Querying Method for Data Mining in Large Data Bases
Efficient SQL-Querying Method for Data Mining in Large Data Bases Nguyen Hung Son Institute of Mathematics Warsaw University Banacha 2, 02095, Warsaw, Poland Abstract Data mining can be understood as a
More informationAdaptive Building of Decision Trees by Reinforcement Learning
Proceedings of the 7th WSEAS International Conference on Applied Informatics and Communications, Athens, Greece, August 24-26, 2007 34 Adaptive Building of Decision Trees by Reinforcement Learning MIRCEA
More informationDecision Trees Dr. G. Bharadwaja Kumar VIT Chennai
Decision Trees Decision Tree Decision Trees (DTs) are a nonparametric supervised learning method used for classification and regression. The goal is to create a model that predicts the value of a target
More informationFuzzy Set-Theoretical Approach for Comparing Objects with Fuzzy Attributes
Fuzzy Set-Theoretical Approach for Comparing Objects with Fuzzy Attributes Y. Bashon, D. Neagu, M.J. Ridley Department of Computing University of Bradford Bradford, BD7 DP, UK e-mail: {Y.Bashon, D.Neagu,
More informationA reasoning model based on the production of acceptable. arguments
A reasoning model based on the production of acceptable arguments Leila AMGOUD 1 Claudette CAYROL 2 1 Department of Electronic Engineering, Queen Mary and Westfield College University of London, London
More informationApproximate Discrete Probability Distribution Representation using a Multi-Resolution Binary Tree
Approximate Discrete Probability Distribution Representation using a Multi-Resolution Binary Tree David Bellot and Pierre Bessière GravirIMAG CNRS and INRIA Rhône-Alpes Zirst - 6 avenue de l Europe - Montbonnot
More informationHybrid Feature Selection for Modeling Intrusion Detection Systems
Hybrid Feature Selection for Modeling Intrusion Detection Systems Srilatha Chebrolu, Ajith Abraham and Johnson P Thomas Department of Computer Science, Oklahoma State University, USA ajith.abraham@ieee.org,
More informationSoftening Splits in Decision Trees Using Simulated Annealing
Softening Splits in Decision Trees Using Simulated Annealing Jakub Dvořák and Petr Savický Institute of Computer Science, Academy of Sciences of the Czech Republic {dvorak,savicky}@cs.cas.cz Abstract.
More informationEscola Politécnica, University of São Paulo Av. Prof. Mello Moraes, 2231, , São Paulo, SP - Brazil
Generalizing Variable Elimination in Bayesian Networks FABIO GAGLIARDI COZMAN Escola Politécnica, University of São Paulo Av. Prof. Mello Moraes, 2231, 05508-900, São Paulo, SP - Brazil fgcozman@usp.br
More informationAN APPROXIMATION APPROACH FOR RANKING FUZZY NUMBERS BASED ON WEIGHTED INTERVAL - VALUE 1.INTRODUCTION
Mathematical and Computational Applications, Vol. 16, No. 3, pp. 588-597, 2011. Association for Scientific Research AN APPROXIMATION APPROACH FOR RANKING FUZZY NUMBERS BASED ON WEIGHTED INTERVAL - VALUE
More informationDynamic Load Balancing of Unstructured Computations in Decision Tree Classifiers
Dynamic Load Balancing of Unstructured Computations in Decision Tree Classifiers A. Srivastava E. Han V. Kumar V. Singh Information Technology Lab Dept. of Computer Science Information Technology Lab Hitachi
More informationA Well-Behaved Algorithm for Simulating Dependence Structures of Bayesian Networks
A Well-Behaved Algorithm for Simulating Dependence Structures of Bayesian Networks Yang Xiang and Tristan Miller Department of Computer Science University of Regina Regina, Saskatchewan, Canada S4S 0A2
More informationPRIVACY-PRESERVING MULTI-PARTY DECISION TREE INDUCTION
PRIVACY-PRESERVING MULTI-PARTY DECISION TREE INDUCTION Justin Z. Zhan, LiWu Chang, Stan Matwin Abstract We propose a new scheme for multiple parties to conduct data mining computations without disclosing
More informationLook-Ahead Based Fuzzy Decision Tree Induction
IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 9, NO. 3, JUNE 2001 461 Look-Ahead Based Fuzzy Decision Tree Induction Ming Dong, Student Member, IEEE, and Ravi Kothari, Senior Member, IEEE Abstract Decision
More informationFuzzy Partitioning Using Mathematical Morphology in a Learning Scheme
Fuzzy Partitioning Using Mathematical Morphology in a Learning Scheme Christophe Marsala Bernadette Bouchon-Meunier LAFORIA-IBP, Université Pierre et Marie Curie, Case 69, 4 place Jussieu, 75252 Paris
More informationROUGH MEMBERSHIP FUNCTIONS: A TOOL FOR REASONING WITH UNCERTAINTY
ALGEBRAIC METHODS IN LOGIC AND IN COMPUTER SCIENCE BANACH CENTER PUBLICATIONS, VOLUME 28 INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES WARSZAWA 1993 ROUGH MEMBERSHIP FUNCTIONS: A TOOL FOR REASONING
More informationAN APPROXIMATE POSSIBILISTIC GRAPHICAL MODEL FOR COMPUTING OPTIMISTIC QUALITATIVE DECISION
AN APPROXIMATE POSSIBILISTIC GRAPHICAL MODEL FOR COMPUTING OPTIMISTIC QUALITATIVE DECISION BOUTOUHAMI Khaoula and KHELLAF Faiza Recherche en Informatique Intelligente et Mathématiques Appliquées. Université
More informationMAX-MIN FAIRNESS is a simple, well-recognized
IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 15, NO. 5, OCTOBER 2007 1073 A Unified Framework for Max-Min and Min-Max Fairness With Applications Božidar Radunović, Member, IEEE, and Jean-Yves Le Boudec, Fellow,
More informationSolution of m 3 or 3 n Rectangular Interval Games using Graphical Method
Australian Journal of Basic and Applied Sciences, 5(): 1-10, 2011 ISSN 1991-8178 Solution of m or n Rectangular Interval Games using Graphical Method Pradeep, M. and Renukadevi, S. Research Scholar in
More informationComputing Preferred Extensions for Argumentation Systems with Sets of Attacking Arguments
Book Title Book Editors IOS Press, 2003 1 Computing Preferred Extensions for Argumentation Systems with Sets of Attacking Arguments Søren Holbech Nielsen a, Simon Parsons b a Department of Computer Science
More informationCost Minimization Fuzzy Assignment Problem applying Linguistic Variables
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 6 2017, 404 412 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Cost Minimization
More informationAn Information-Theoretic Approach to the Prepruning of Classification Rules
An Information-Theoretic Approach to the Prepruning of Classification Rules Max Bramer University of Portsmouth, Portsmouth, UK Abstract: Keywords: The automatic induction of classification rules from
More informationIntrusion detection in computer networks through a hybrid approach of data mining and decision trees
WALIA journal 30(S1): 233237, 2014 Available online at www.waliaj.com ISSN 10263861 2014 WALIA Intrusion detection in computer networks through a hybrid approach of data mining and decision trees Tayebeh
More informationRepairing Preference-Based Argumentation Frameworks
Repairing Preference-Based Argumentation Frameworks Leila Amgoud IRIT CNRS 118, route de Narbonne 31062, Toulouse Cedex 09 amgoud@irit.fr Srdjan Vesic IRIT CNRS 118, route de Narbonne 31062, Toulouse Cedex
More informationSolution to Graded Problem Set 4
Graph Theory Applications EPFL, Spring 2014 Solution to Graded Problem Set 4 Date: 13.03.2014 Due by 18:00 20.03.2014 Problem 1. Let V be the set of vertices, x be the number of leaves in the tree and
More informationANALYSIS AND REASONING OF DATA IN THE DATABASE USING FUZZY SYSTEM MODELLING
ANALYSIS AND REASONING OF DATA IN THE DATABASE USING FUZZY SYSTEM MODELLING Dr.E.N.Ganesh Dean, School of Engineering, VISTAS Chennai - 600117 Abstract In this paper a new fuzzy system modeling algorithm
More informationA new parameterless credal method to track-to-track assignment problem
A new parameterless credal method to track-to-track assignment problem Samir Hachour, François Delmotte, and David Mercier Univ. Lille Nord de France, UArtois, EA 3926 LGI2A, Béthune, France Abstract.
More informationFuzzy Analogy: A New Approach for Software Cost Estimation
Fuzzy Analogy: A New Approach for Software Cost Estimation Ali Idri, ENSIAS, Rabat, Morocco co Alain Abran, ETS, Montreal, Canada Taghi M. Khoshgoftaar, FAU, Boca Raton, Florida th International Workshop
More informationA more efficient algorithm for perfect sorting by reversals
A more efficient algorithm for perfect sorting by reversals Sèverine Bérard 1,2, Cedric Chauve 3,4, and Christophe Paul 5 1 Département de Mathématiques et d Informatique Appliquée, INRA, Toulouse, France.
More informationInternational Journal of Software and Web Sciences (IJSWS)
International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) ISSN (Print): 2279-0063 ISSN (Online): 2279-0071 International
More informationImplementation of Classification Rules using Oracle PL/SQL
1 Implementation of Classification Rules using Oracle PL/SQL David Taniar 1 Gillian D cruz 1 J. Wenny Rahayu 2 1 School of Business Systems, Monash University, Australia Email: David.Taniar@infotech.monash.edu.au
More informationFormal Model. Figure 1: The target concept T is a subset of the concept S = [0, 1]. The search agent needs to search S for a point in T.
Although this paper analyzes shaping with respect to its benefits on search problems, the reader should recognize that shaping is often intimately related to reinforcement learning. The objective in reinforcement
More informationLogistic Model Tree With Modified AIC
Logistic Model Tree With Modified AIC Mitesh J. Thakkar Neha J. Thakkar Dr. J.S.Shah Student of M.E.I.T. Asst.Prof.Computer Dept. Prof.&Head Computer Dept. S.S.Engineering College, Indus Engineering College
More informationA Two Stage Zone Regression Method for Global Characterization of a Project Database
A Two Stage Zone Regression Method for Global Characterization 1 Chapter I A Two Stage Zone Regression Method for Global Characterization of a Project Database J. J. Dolado, University of the Basque Country,
More informationTesting Independencies in Bayesian Networks with i-separation
Proceedings of the Twenty-Ninth International Florida Artificial Intelligence Research Society Conference Testing Independencies in Bayesian Networks with i-separation Cory J. Butz butz@cs.uregina.ca University
More informationA Compromise Solution to Multi Objective Fuzzy Assignment Problem
Volume 113 No. 13 2017, 226 235 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu A Compromise Solution to Multi Objective Fuzzy Assignment Problem
More informationOn JAM of Triangular Fuzzy Number Matrices
117 On JAM of Triangular Fuzzy Number Matrices C.Jaisankar 1 and R.Durgadevi 2 Department of Mathematics, A. V. C. College (Autonomous), Mannampandal 609305, India ABSTRACT The fuzzy set theory has been
More informationInduction of Strong Feature Subsets
Induction of Strong Feature Subsets Mohamed Quafafou and Moussa Boussouf IRIN, University of Nantes, 2 rue de la Houssiniere, BP 92208-44322, Nantes Cedex 03, France. quafafou9 Abstract The problem of
More informationFUNDAMENTALS OF FUZZY SETS
FUNDAMENTALS OF FUZZY SETS edited by Didier Dubois and Henri Prade IRIT, CNRS & University of Toulouse III Foreword by LotfiA. Zadeh 14 Kluwer Academic Publishers Boston//London/Dordrecht Contents Foreword
More informationOn the Complexity of the Policy Improvement Algorithm. for Markov Decision Processes
On the Complexity of the Policy Improvement Algorithm for Markov Decision Processes Mary Melekopoglou Anne Condon Computer Sciences Department University of Wisconsin - Madison 0 West Dayton Street Madison,
More informationBelief Hierarchical Clustering
Belief Hierarchical Clustering Wiem Maalel, Kuang Zhou, Arnaud Martin and Zied Elouedi Abstract In the data mining field many clustering methods have been proposed, yet standard versions do not take base
More informationA probabilistic description-oriented approach for categorising Web documents
A probabilistic description-oriented approach for categorising Web documents Norbert Gövert Mounia Lalmas Norbert Fuhr University of Dortmund {goevert,mounia,fuhr}@ls6.cs.uni-dortmund.de Abstract The automatic
More informationEstimating Feature Discriminant Power in Decision Tree Classifiers*
Estimating Feature Discriminant Power in Decision Tree Classifiers* I. Gracia 1, F. Pla 1, F. J. Ferri 2 and P. Garcia 1 1 Departament d'inform~tica. Universitat Jaume I Campus Penyeta Roja, 12071 Castell6.
More informationArnab Bhattacharya, Shrikant Awate. Dept. of Computer Science and Engineering, Indian Institute of Technology, Kanpur
Arnab Bhattacharya, Shrikant Awate Dept. of Computer Science and Engineering, Indian Institute of Technology, Kanpur Motivation Flight from Kolkata to Los Angeles No direct flight Through Singapore or
More informationContextual Co-occurrence Information for Object Representation and Categorization
Vol.8, No.1 (2015), pp.95-104 http://dx.doi.org/10.14257/ijdta.2015.8.1.11 Contextual Co-occurrence Information for Object Representation and Categorization 1 Soheila Sheikhbahaei and 2 Zahra Sadeghi 1
More informationHybrid Approach for Classification using Support Vector Machine and Decision Tree
Hybrid Approach for Classification using Support Vector Machine and Decision Tree Anshu Bharadwaj Indian Agricultural Statistics research Institute New Delhi, India anshu@iasri.res.in Sonajharia Minz Jawaharlal
More informationDECISION TREE INDUCTION USING ROUGH SET THEORY COMPARATIVE STUDY
DECISION TREE INDUCTION USING ROUGH SET THEORY COMPARATIVE STUDY Ramadevi Yellasiri, C.R.Rao 2,Vivekchan Reddy Dept. of CSE, Chaitanya Bharathi Institute of Technology, Hyderabad, INDIA. 2 DCIS, School
More informationBayesian Learning Networks Approach to Cybercrime Detection
Bayesian Learning Networks Approach to Cybercrime Detection N S ABOUZAKHAR, A GANI and G MANSON The Centre for Mobile Communications Research (C4MCR), University of Sheffield, Sheffield Regent Court, 211
More informationCONCEPT FORMATION AND DECISION TREE INDUCTION USING THE GENETIC PROGRAMMING PARADIGM
1 CONCEPT FORMATION AND DECISION TREE INDUCTION USING THE GENETIC PROGRAMMING PARADIGM John R. Koza Computer Science Department Stanford University Stanford, California 94305 USA E-MAIL: Koza@Sunburn.Stanford.Edu
More informationOptimal Variable Length Codes (Arbitrary Symbol Cost and Equal Code Word Probability)* BEN VARN
INFORMATION AND CONTROL 19, 289-301 (1971) Optimal Variable Length Codes (Arbitrary Symbol Cost and Equal Code Word Probability)* BEN VARN School of Systems and Logistics, Air Force Institute of Technology,
More informationData Mining. Decision Tree. Hamid Beigy. Sharif University of Technology. Fall 1396
Data Mining Decision Tree Hamid Beigy Sharif University of Technology Fall 1396 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 1 / 24 Table of contents 1 Introduction 2 Decision tree
More informationFeature-weighted k-nearest Neighbor Classifier
Proceedings of the 27 IEEE Symposium on Foundations of Computational Intelligence (FOCI 27) Feature-weighted k-nearest Neighbor Classifier Diego P. Vivencio vivencio@comp.uf scar.br Estevam R. Hruschka
More informationA Constraint Programming Based Approach to Detect Ontology Inconsistencies
The International Arab Journal of Information Technology, Vol. 8, No. 1, January 2011 1 A Constraint Programming Based Approach to Detect Ontology Inconsistencies Moussa Benaissa and Yahia Lebbah Faculté
More informationFuzzy Ant Clustering by Centroid Positioning
Fuzzy Ant Clustering by Centroid Positioning Parag M. Kanade and Lawrence O. Hall Computer Science & Engineering Dept University of South Florida, Tampa FL 33620 @csee.usf.edu Abstract We
More informationVALCSP solver : a combination of Multi-Level Dynamic Variable Ordering with Constraint Weighting
VALCS solver : a combination of Multi-Level Dynamic Variable Ordering with Constraint Weighting Assef Chmeiss, Lakdar Saïs, Vincent Krawczyk CRIL - University of Artois - IUT de Lens Rue Jean Souvraz -
More informationSOME OPERATIONS ON INTUITIONISTIC FUZZY SETS
IJMMS, Vol. 8, No. 1, (June 2012) : 103-107 Serials Publications ISSN: 0973-3329 SOME OPERTIONS ON INTUITIONISTIC FUZZY SETS Hakimuddin Khan bstract In This paper, uthor Discuss about some operations on
More informationFUZZY INFERENCE SYSTEMS
CHAPTER-IV FUZZY INFERENCE SYSTEMS Fuzzy inference is the process of formulating the mapping from a given input to an output using fuzzy logic. The mapping then provides a basis from which decisions can
More informationGraph Matching: Fast Candidate Elimination Using Machine Learning Techniques
Graph Matching: Fast Candidate Elimination Using Machine Learning Techniques M. Lazarescu 1,2, H. Bunke 1, and S. Venkatesh 2 1 Computer Science Department, University of Bern, Switzerland 2 School of
More informationAcyclic fuzzy preferences and the Orlovsky choice function: A note. Denis BOUYSSOU
Acyclic fuzzy preferences and the Orlovsky choice function: A note Denis BOUYSSOU Abstract This note corrects and extends a recent axiomatic characterization of the Orlovsky choice function for a particular
More informationUsing level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions
Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions Verstraete Jörg Abstract In many applications, spatial data need to be considered but are prone to uncertainty or imprecision.
More informationFACILITY LIFE-CYCLE COST ANALYSIS BASED ON FUZZY SETS THEORY Life-cycle cost analysis
FACILITY LIFE-CYCLE COST ANALYSIS BASED ON FUZZY SETS THEORY Life-cycle cost analysis J. O. SOBANJO FAMU-FSU College of Engineering, Tallahassee, Florida Durability of Building Materials and Components
More informationLecture 2 :: Decision Trees Learning
Lecture 2 :: Decision Trees Learning 1 / 62 Designing a learning system What to learn? Learning setting. Learning mechanism. Evaluation. 2 / 62 Prediction task Figure 1: Prediction task :: Supervised learning
More informationCSC 373: Algorithm Design and Analysis Lecture 8
CSC 373: Algorithm Design and Analysis Lecture 8 Allan Borodin January 23, 2013 1 / 19 Lecture 8: Announcements and Outline Announcements No lecture (or tutorial) this Friday. Lecture and tutorials as
More informationSolution of Rectangular Interval Games Using Graphical Method
Tamsui Oxford Journal of Mathematical Sciences 22(1 (2006 95-115 Aletheia University Solution of Rectangular Interval Games Using Graphical Method Prasun Kumar Nayak and Madhumangal Pal Department of Applied
More informationPost-processing the hybrid method for addressing uncertainty in risk assessments. Technical Note for the Journal of Environmental Engineering
Post-processing the hybrid method for addressing uncertainty in risk assessments By: Cédric Baudrit 1, Dominique Guyonnet 2, Didier Dubois 1 1 : Math. Spec., Université Paul Sabatier, 31063 Toulouse, France
More informationFuzzyDT- A Fuzzy Decision Tree Algorithm Based on C4.5
FuzzyDT- A Fuzzy Decision Tree Algorithm Based on C4.5 Marcos E. Cintra 1, Maria C. Monard 2, and Heloisa A. Camargo 3 1 Exact and Natural Sciences Dept. - Federal University of the Semi-arid - UFERSA
More informationCoefficient of Variation based Decision Tree (CvDT)
Coefficient of Variation based Decision Tree (CvDT) Hima Bindu K #1, Swarupa Rani K #2, Raghavendra Rao C #3 # Department of Computer and Information Sciences, University of Hyderabad Hyderabad, 500046,
More informationReview of Fuzzy Logical Database Models
IOSR Journal of Computer Engineering (IOSRJCE) ISSN: 2278-0661, ISBN: 2278-8727Volume 8, Issue 4 (Jan. - Feb. 2013), PP 24-30 Review of Fuzzy Logical Database Models Anupriya 1, Prof. Rahul Rishi 2 1 (Department
More informationGeneralized Implicative Model of a Fuzzy Rule Base and its Properties
University of Ostrava Institute for Research and Applications of Fuzzy Modeling Generalized Implicative Model of a Fuzzy Rule Base and its Properties Martina Daňková Research report No. 55 2 Submitted/to
More informationGenerating Optimized Decision Tree Based on Discrete Wavelet Transform Kiran Kumar Reddi* 1 Ali Mirza Mahmood 2 K.
Generating Optimized Decision Tree Based on Discrete Wavelet Transform Kiran Kumar Reddi* 1 Ali Mirza Mahmood 2 K.Mrithyumjaya Rao 3 1. Assistant Professor, Department of Computer Science, Krishna University,
More informationA note on the pairwise Markov condition in directed Markov fields
TECHNICAL REPORT R-392 April 2012 A note on the pairwise Markov condition in directed Markov fields Judea Pearl University of California, Los Angeles Computer Science Department Los Angeles, CA, 90095-1596,
More informationBipolar Fuzzy Line Graph of a Bipolar Fuzzy Hypergraph
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 13, No 1 Sofia 2013 Print ISSN: 1311-9702; Online ISSN: 1314-4081 DOI: 10.2478/cait-2013-0002 Bipolar Fuzzy Line Graph of a
More informationDevelopment of Prediction Model for Linked Data based on the Decision Tree for Track A, Task A1
Development of Prediction Model for Linked Data based on the Decision Tree for Track A, Task A1 Dongkyu Jeon and Wooju Kim Dept. of Information and Industrial Engineering, Yonsei University, Seoul, Korea
More informationc 2004 Society for Industrial and Applied Mathematics
SIAM J. MATRIX ANAL. APPL. Vol. 26, No. 2, pp. 390 399 c 2004 Society for Industrial and Applied Mathematics HERMITIAN MATRICES, EIGENVALUE MULTIPLICITIES, AND EIGENVECTOR COMPONENTS CHARLES R. JOHNSON
More informationSupervised Variable Clustering for Classification of NIR Spectra
Supervised Variable Clustering for Classification of NIR Spectra Catherine Krier *, Damien François 2, Fabrice Rossi 3, Michel Verleysen, Université catholique de Louvain, Machine Learning Group, place
More informationLoopy Belief Propagation
Loopy Belief Propagation Research Exam Kristin Branson September 29, 2003 Loopy Belief Propagation p.1/73 Problem Formalization Reasoning about any real-world problem requires assumptions about the structure
More informationEvolutionary Decision Trees and Software Metrics for Module Defects Identification
World Academy of Science, Engineering and Technology 38 008 Evolutionary Decision Trees and Software Metrics for Module Defects Identification Monica Chiş Abstract Software metric is a measure of some
More informationFuzzy interpolation and level 2 gradual rules
Fuzzy interpolation and level 2 gradual rules Sylvie Galichet, Didier Dubois, Henri Prade To cite this version: Sylvie Galichet, Didier Dubois, Henri Prade. Fuzzy interpolation and level 2 gradual rules.
More informationA NEW MULTI-CRITERIA EVALUATION MODEL BASED ON THE COMBINATION OF NON-ADDITIVE FUZZY AHP, CHOQUET INTEGRAL AND SUGENO λ-measure
A NEW MULTI-CRITERIA EVALUATION MODEL BASED ON THE COMBINATION OF NON-ADDITIVE FUZZY AHP, CHOQUET INTEGRAL AND SUGENO λ-measure S. Nadi a *, M. Samiei b, H. R. Salari b, N. Karami b a Assistant Professor,
More informationExact Optimal Solution of Fuzzy Critical Path Problems
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 93-9466 Vol. 6, Issue (June 0) pp. 5 67 (Previously, Vol. 6, Issue, pp. 99 008) Applications and Applied Mathematics: An International Journal
More informationCombining Qualitative and Quantitative Knowledge to Generate Models of Physical Systems
Combining Qualitative and Quantitative Knowledge to Generate Models of Physical Systems Ulf Soderman Dept. of Computer Science, Linkoping University S-581 83 Linkoping, Sweden Email: uso@ida.liu.se Jan-Erik
More informationExemplar Learning in Fuzzy Decision Trees
Exemplar Learning in Fuzzy Decision Trees C. Z. Janikow Mathematics and Computer Science University of Missouri St. Louis, MO 63121 Abstract Decision-tree algorithms provide one of the most popular methodologies
More informationEfficient Case Based Feature Construction
Efficient Case Based Feature Construction Ingo Mierswa and Michael Wurst Artificial Intelligence Unit,Department of Computer Science, University of Dortmund, Germany {mierswa, wurst}@ls8.cs.uni-dortmund.de
More information7. Decision or classification trees
7. Decision or classification trees Next we are going to consider a rather different approach from those presented so far to machine learning that use one of the most common and important data structure,
More informationTHE FOUNDATIONS OF MATHEMATICS
THE FOUNDATIONS OF MATHEMATICS By: Sterling McKay APRIL 21, 2014 LONE STAR - MONTGOMERY Mentor: William R. Brown, MBA Mckay 1 In mathematics, truth is arguably the most essential of its components. Suppose
More informationStructured System Theory
Appendix C Structured System Theory Linear systems are often studied from an algebraic perspective, based on the rank of certain matrices. While such tests are easy to derive from the mathematical model,
More informationSimilarity Measures of Pentagonal Fuzzy Numbers
Volume 119 No. 9 2018, 165-175 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Similarity Measures of Pentagonal Fuzzy Numbers T. Pathinathan 1 and
More informationBiology Project 1
Biology 6317 Project 1 Data and illustrations courtesy of Professor Tony Frankino, Department of Biology/Biochemistry 1. Background The data set www.math.uh.edu/~charles/wing_xy.dat has measurements related
More informationDesigning and Building an Automatic Information Retrieval System for Handling the Arabic Data
American Journal of Applied Sciences (): -, ISSN -99 Science Publications Designing and Building an Automatic Information Retrieval System for Handling the Arabic Data Ibrahiem M.M. El Emary and Ja'far
More informationClassification and Regression Trees
Classification and Regression Trees Matthew S. Shotwell, Ph.D. Department of Biostatistics Vanderbilt University School of Medicine Nashville, TN, USA March 16, 2018 Introduction trees partition feature
More informationFuzzy Transportation Problems with New Kind of Ranking Function
The International Journal of Engineering and Science (IJES) Volume 6 Issue 11 Pages PP 15-19 2017 ISSN (e): 2319 1813 ISSN (p): 2319 1805 Fuzzy Transportation Problems with New Kind of Ranking Function
More informationA framework for fuzzy models of multiple-criteria evaluation
INTERNATIONAL CONFERENCE ON FUZZY SET THEORY AND APPLICATIONS Liptovský Ján, Slovak Republic, January 30 - February 3, 2012 A framework for fuzzy models of multiple-criteria evaluation Jana Talašová, Ondřej
More information