Browsing by Author "Hailu, Abraham"

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    Amharic Document Categorization Using Itemsets Method
    (Addis Ababa University, 2013-02) Hailu, Abraham; Assabie, Yaregal (PhD)
    Document categorization or document classification is the process of assigning a document to one or more classes or categories. Many researches are conducted in the area of Amharic document categorization. The main focus of those studies is to examine different document categorization techniques and measuring their performance however itemsets method is not so far examined. This study focused to extend Apriori algorithm which is traditionally used for the purpose of knowledge mining in the form of association rules. The research focused on the basic principles of applying itemsets method to categorize Amharic documents. In addition to that the implementation of all the required tools which helps to carry out automatic Amharic Document categorization using itemsets method is developed and the algorithm is examined. Experiment results show itemsets method is an efficient method to categorize Amharic documents. The effectiveness and accuracy of the method to categorize Amharic documents is also evaluated and reported. Finally, factors affecting the performance of the proposed system and the importance of preprocessing training dataset in finding useful information are discussed.
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    Amharic Document Categorization Using Itemsets Method
    (Addis Ababa University, 2013-02) Hailu, Abraham; Assabie, Yaregal (PhD)
    Document categorization or document classification is the process of assigning a document to one or more classes or categories. Many researches are conducted in the area of Amharic document categorization. The main focus of those studies is to examine different document categorization techniques and measuring their performance however itemsets method is not so far examined. This study focused to extend Apriori algorithm which is traditionally used for the purpose of knowledge mining in the form of association rules. The research focused on the basic principles of applying itemsets method to categorize Amharic documents. In addition to that the implementation of all the required tools which helps to carry out automatic Amharic Document categorization using itemsets method is developed and the algorithm is examined. Experiment results show itemsets method is an efficient method to categorize Amharic documents. The effectiveness and accuracy of the method to categorize Amharic documents is also evaluated and reported. Finally, factors affecting the performance of the proposed system and the importance of preprocessing training dataset in finding useful information are discussed.
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    Integral Equations and S ome Basic Preliminary Concepts
    (Addis Ababa University, 2010-06-06) Hailu, Abraham; Mohammed, Sied (PhD)
    In certain problems that we encounter it is common to get equations in which the unknown function occurs under an integral sign. Such equations are termed as integral equations. Integral equations are use full to solve some classes of differential equations. We will see that the solution of a differential equation is an integral equation. This is one nice property that makes integral equations to be studied. The study of integral equations leads to the study of compact operators in a more general setting of infinite dimensional Hilbert spaces. Compact operators in infinite dimensional Hilbert space can be considered as counter parts of matrices as they enjoy many properties in common with linear operators in finite dimensional spaces (matrices). For instance, they satisfy Fredholm alternative theorem and exhibit some spectral properties. The objective of this seminar is therefore to generalize some of the fundamental properties of matrices in finite dimensional case to compact linear operators in infinite dimensional Hilbert spaces. The seminar deals with integral equations in a Hilbert space with emphasis on spectral theorem of eigenvalues and eigenfunctions of a compact operator in an infinite dimensional Hilbert space. Most of the examples and illustrations will be given on space. This seminar also deals with the Fredholm alternative theorem of a general compact linear operator. In this seminar there are four sections. In section one some preliminary concepts that are needed later will be dealt. In section two bounded linear operators in Hilbert space will be studied. Section three deals with compact linear operators and Hilbert-Schmidt kernels. Finaly, Spectral theory on compact operators will be investigated in section four.
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    On Applications of FBI Transforms to Wave Front Sets
    (Addis Ababa University, 2016-06-30) Hailu, Abraham; Berhanu, Shiferaw(Professor)
    In this thesis, we study the application of FBI transforms to the C1; analytic and Gevrey wave front sets of functions. We characterize the C1 wave front set of a function by providing a simpler proof of a result by Berhanu and Hounie. To characterize the analytic wave front set, we generalize the work of Berhanu and Hounie [10] to two polynomials in the generating function of the FBI transform they de_ne. The Gevrey wave front set is characterized _rst as in the paper of Berhanu and Hounie and then generalized to two polynomials. Finally, we apply the standard FBI transform to study the microlocal smoothness of C2 solutions u of the _rst-order nonlinear partial di_erential equation ut = f(x; t; u; ux) where f(x; t; _0; _) is a complex-valued function which is C1 in all the variables (x; t; _0; _) and holomorphic in the variables (_0; _): If the solution u is C2; _ 2 Char(Lu) and i _([Lu; L_u]) < 0; then we show that _ 2= WF(u): Here WF(u) denotes the C1 wave front set of u and Char(Lu) denotes the characteristic set of the linearized operator