PPT-The Vector Space Models

VSM doc1 Documents as Vectors Terms are axes of the space Documents are points or vectors in this space So we have a Vdimensional vector space The Matrix Doc 1 makan makan. moritzhermannphilblunsom csoxacuk Abstract Modelling the compositional process by which the meaning of an utterance arises from the meaning of its parts is a funda mental task of Natural Language Process ing In this paper we draw upon recent advances Corpora and Statistical Methods. Lecture 6. Semantic similarity. Part 1. Synonymy. Different phonological. /orthographic. words. highly related meanings. :. sofa / couch. boy / lad. Traditional definition:. Real Vector Spaces. Subspaces. Linear Independence. Basis and Dimension. Row Space, Column Space, and Nullspace. Rank and Nullity. 2. 5-2 Subspaces. A . subset. . W. of a vector space . V. is called a . Daniel Svozil. based on excelent video lectures by Gilbert Strang, MIT. http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/index.htm. Lectur. e. 5, Lecture 6. Transposes. How to write tra. More formally: Definitions. Definition: A . stream. is a sequence whose . codomain. . is a non empty set.. Definition: A. structure . is a . tuple. (. G, L, F. ) where . G. = (. V,E. ) is a directed graph with vertex set . & Subspaces. Kristi Schmit. Definitions. A subset W of vector space V is called a . subspace . of V . iff. The. . zero vector of V is in W.. W. is closed under vector addition, for each . u. . Lexical Semantics. 2. Information Retrieval System. IR. System. Query String. Document. corpus. Ranked. Documents. 1. Doc1. 2. Doc2. 3. Doc3. .. .. The Vector-Space Model. Graphic Representation. INTRODUCTION. An approach for classification that was developed in the computer science community in the 1990s.. Generalization of a classifier called the Maximal Margin Classifier.. HYPERPLANE. In a . Lexical Semantics. 2. Information Retrieval System. IR. System. Query String. Document. corpus. Ranked. Documents. 1. Doc1. 2. Doc2. 3. Doc3. .. .. The Vector-Space Model. Graphic Representation. 4.1 Vectors in . R. n. 4.2 Vector Spaces. 4.3 Subspaces of Vector Spaces. 4.4 Spanning Sets and Linear Independence. 4.5 Basis and Dimension. 4.6 Rank of a Matrix and Systems of Linear Equations. Scott Wen-tau Yih . (Microsoft Research). Joint work with. . Vahed Qazvinian . (University of . Michigan). Measuring Semantic Word Relatedness. How related are words “movie” and “popcorn”?. Guillermo . Garrido. and . Anselmo. . Peñas. NLP & IR Group at UNED. Madrid, Spain. {. ggarrido,anselmo. }@. lsi.uned.es. Shared. . Task. . System. . Description. ACL-HLT 2011 . Workshop. . . H. HABEEB RANI. Assistant professor of Mathematics. Department of mathematics. Hajee. . Karutha. . Rowther. . Howdia. College. VECTOR SPACES. Definition. Examples. THEOREM. Subspaces. Many slides in this section are adapted from Prof. Joydeep Ghosh (UT ECE) who in turn adapted them from Prof. Dik Lee (Univ. of Science and Tech, Hong Kong). 1. These notes are based, in part, on notes by Dr. Raymond J. Mooney at the University of Texas at Austin. .