DOCSLIB.ORG

Matrix Decompositions and Latent Semantic Indexing

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Matrix Decompositions and Latent Semantic Indexing Online edition (c)2009 Cambridge UP DRAFT! © April 1, 2009 Cambridge University Press. Feedback welcome. 403 Matrix decompositions and latent 18 semantic indexing On page 123 we introduced the notion of a term-document matrix: an M N matrix C, each of whose rows represents a term and each of whose column× s represents a document in the collection. Even for a collection of modest size, the term-document matrix C is likely to have several tens of thousands of rows and columns. In Section 18.1.1 we first develop a class of operations from linear algebra, known as matrix decomposition. In Section 18.2 we use a special form of matrix decomposition to construct a low-rank approximation to the term-document matrix. In Section 18.3 we examine the application of such low-rank approximations to indexing and retrieving documents, a technique referred to as latent semantic indexing. While latent semantic in- dexing has not been established as a significant force in scoring and ranking for information retrieval, it remains an intriguing approach to clustering in a number of domains including for collections of text documents (Section 16.6, page 372). Understanding its full potential remains an area of active research. Readers who do not require a refresher on linear algebra may skip Sec- tion 18.1, although Example 18.1 is especially recommended as it highlights a property of eigenvalues that we exploit later in the chapter. 18.1 Linear algebra review We briefly review some necessary background in linear algebra. Let C be an M N matrix with real-valued entries; for a term-document matrix, all × RANK entries are in fact non-negative. The rank of a matrix is the number of linearly independent rows (or columns) in it; thus, rank(C) min M, N . A square r r matrix all of whose off-diagonal entries are≤ zero is{ called} a diagonal matrix× ; its rank is equal to the number of non-zero diagonal entries. If all r diagonal entries of such a diagonal matrix are 1, it is called the identity matrix of dimension r and represented by Ir. For a square M M matrix C and a vector ~x that is not all zeros, the values × Online edition (c)2009 Cambridge UP 404 18 Matrix decompositions and latent semantic indexing of λ satisfying (18.1) C~x = λ~x EIGENVALUE are called the eigenvalues of C . The N-vector ~x satisfying Equation (18.1) for an eigenvalue λ is the corresponding right eigenvector. The eigenvector corresponding to the eigenvalue of largest magnitude is called the principal eigenvector. In a similar fashion, the left eigenvectors of C are the M-vectors y such that (18.2) ~yT C = λ~yT. The number of non-zero eigenvalues of C is at most rank(C). The eigenvalues of a matrix are found by solving the characteristic equation, which is obtained by rewriting Equation (18.1) in the form (C λIM)~x = 0. The eigenvalues of C are then the solutions of (C λI ) =−0, where S | − M | | | denotes the determinant of a square matrix S. The equation (C λIM) = 0 is an Mth order polynomial equation in λ and can have at| most− M roots,| which are the eigenvalues of C. These eigenvalues can in general be complex, even if all entries of C are real. We now examine some further properties of eigenvalues and eigenvectors, to set up the central idea of singular value decompositions in Section 18.2 be- low. First, we look at the relationship between matrix-vector multiplication and eigenvalues. ✎ Example 18.1: Consider the matrix 30 0 0 S = 0 20 0 . 0 0 1 λ λ Clearly the matrix has rank 3, and has 3 non-zero eigenvalues 1 = 30, 2 = 20 and λ 3 = 1, with the three corresponding eigenvectors 1 0 0 x~1 = 0 , x~2 = 1 and x~3 = 0 . 0 0 1 For each of the eigenvectors, multiplication by S acts as if we were multiplying the eigenvector by a multiple of the identity matrix; the multiple is different for each 2 eigenvector. Now, consider an arbitrary vector, such as ~v = 4 . We can always 6 express~v as a linear combination of the three eigenvectors of S; in the current example we have 2 ~v = 4 = 2x~1 + 4x~2 + 6x~3. 6 Online edition (c)2009 Cambridge UP 18.1 Linear algebra review 405 Suppose we multiply ~v by S: S~v = S(2x~1 + 4x~2 + 6x~3) = 2Sx~1 + 4Sx~2 + 6Sx~3 λ λ λ = 2 1x~1 + 4 2x~2 + 6 3x~3 (18.3) = 60x~1 + 80x~2 + 6x~3. Example 18.1 shows that even though ~v is an arbitrary vector, the effect of multiplication by S is determined by the eigenvalues and eigenvectors of S. Furthermore, it is intuitively apparent from Equation (18.3) that the product S~v is relatively unaffected by terms arising from the small eigenvalues of S; λ in our example, since 3 = 1, the contribution of the third term on the right hand side of Equation (18.3) is small. In fact, if we were to completely ignore the contribution in Equation (18.3) from the third eigenvector corresponding 60 λ to 3 = 1, then the product S~v would be computed to be 80 rather than 0 60 the correct product which is 80 ; these two vectors are relatively close 6 to each other by any of various metrics one could apply (such as the length of their vector difference). This suggests that the effect of small eigenvalues (and their eigenvectors) on a matrix-vector product is small. We will carry forward this intuition when studying matrix decompositions and low-rank approximations in Sec- tion 18.2. Before doing so, we examine the eigenvectors and eigenvalues of special forms of matrices that will be of particular interest to us. For a symmetric matrix S, the eigenvectors corresponding to distinct eigen- values are orthogonal. Further, if S is both real and symmetric, the eigenvalues are all real. ✎ Example 18.2: Consider the real, symmetric matrix 2 1 (18.4) S = . 1 2 From the characteristic equation S λI = 0, we have the quadratic (2 λ)2 1 = 0, whose solutions yield the eigenvalues| − | 3 and 1. The corresponding eigenvectors− − 1 1 and are orthogonal. 1 1 − Online edition (c)2009 Cambridge UP 406 18 Matrix decompositions and latent semantic indexing 18.1.1 Matrix decompositions In this section we examine ways in which a square matrix can be factored into the product of matrices derived from its eigenvectors; we refer to this MATRIX process as matrix decomposition. Matrix decompositions similar to the ones DECOMPOSITION in this section will form the basis of our principal text-analysis technique in Section 18.3, where we will look at decompositions of non-square term- document matrices. The square decompositions in this section are simpler and can be treated with sufficient mathematical rigor to help the reader un- derstand how such decompositions work. The detailed mathematical deriva- tion of the more complex decompositions in Section 18.2 are beyond the scope of this book. We begin by giving two theorems on the decomposition of a square ma- trix into the product of three matrices of a special form. The first of these, Theorem 18.1, gives the basic factorization of a square real-valued matrix into three factors. The second, Theorem 18.2, applies to square symmetric matrices and is the basis of the singular value decomposition described in Theorem 18.3. Theorem 18.1. (Matrix diagonalization theorem) Let S be a square real-valued M M matrix with M linearly independent eigenvectors. Then there exists an × EIGEN DECOMPOSITION eigen decomposition 1 (18.5) S = UΛU− , where the columns of U are the eigenvectors of S and Λ is a diagonal matrix whose diagonal entries are the eigenvalues of S in decreasing order λ 1 λ (18.6) 2 , λ λ . i ≥ i+1 · · · λ M If the eigenvalues are distinct, then this decomposition is unique. To understand how Theorem 18.1 works, we note that U has the eigenvec- tors of S as columns (18.7) U = (u~ u~ u~ ) . 1 2 · · · M Then we have SU = S (u~ u~ u~ ) 1 2 · · · M = (λ u~ λ u~ λ u~ ) 1 1 2 2 · · · M M λ 1 λ = (u~ u~ u~ ) 2 . 1 2 · · · M · · · λ M Online edition (c)2009 Cambridge UP 18.2 Term-document matrices and singular value decompositions 407 1 Thus, we have SU = UΛ, or S = UΛU− . We next state a closely related decomposition of a symmetric square matrix into the product of matrices derived from its eigenvectors. This will pave the way for the development of our main tool for text analysis, the singular value decomposition (Section 18.2). Theorem 18.2. (Symmetric diagonalization theorem) Let S be a square, sym- metric real-valued M M matrix with M linearly independent eigenvectors. Then × SYMMETRIC DIAGONAL there exists a symmetric diagonal decomposition DECOMPOSITION (18.8) S = QΛQT, where the columns of Q are the orthogonal and normalized (unit length, real) eigen- vectors of S, and Λ is the diagonal matrix whose entries are the eigenvalues of S. 1 T Further, all entries of Q are real and we have Q− = Q . We will build on this symmetric diagonal decomposition to build low-rank approximations to term-document matrices. Exercise 18.1 What is the rank of the 3 3 diagonal matrix below? ? × 1 1 0 0 1 1 1 2 1 Exercise 18.2 Show that λ = 2 is an eigenvalue of 6 2 C = − .
Load more

Recommended publications
  • Some Strands of Wittgenstein's Normative Pragmatism
    Some Strands of Wittgenstein’s Normative Pragmatism, and Some Strains of his Semantic Nihilism ROBERT B. BRANDOM ABSTRACT WORK TYPE In this reflection I address one of the critical questions this monograph is Article about: How to justify proposing yet another semantic theory in the light of Wittgenstein’s strong warnings against it. I see two clear motives for ARTICLE HISTORY Wittgenstein’s semantic nihilism. The first one is the view that philosophical Received: problems arise from postulating hypothetical entities such as ‘meanings’. To 27–January–2018 dissolve the philosophical problems rather than create new ones, Wittgenstein Accepted: suggests substituting ‘meaning’ with ‘use’ and avoiding scientism in philosophy 3–March–2018 together with the urge to penetrate in one's investigation to unobservable depths. I believe this first motive constitutes only a weak motive for ARTICLE LANGUAGE Wittgenstein’s quietism, because there are substantial differences between English empirical theories in natural sciences and semantic theories in philosophy that KEYWORDS leave Wittgenstein’s assimilation of both open to criticism. But Wittgenstein is Meaning and Use right, on the second motive, that given the dynamic character of linguistic Hypothetical Entities practice, the classical project of semantic theory is a disease that can be Antiscientism removed or ameliorated only by heeding the advice to replace concern with Semantic Nihilism meaning by concern with use. On my view, this does not preclude, however, a Linguistic Dynamism different kind of theoretical approach to meaning that avoids the pitfalls of the Procrustean enterprise Wittgenstein complained about. © Studia Humanitatis – Universidad de Salamanca 2019 R. Brandom (✉) Disputatio. Philosophical Research Bulletin University of Pittsburgh, USA Vol.
    [Show full text]
  • Semantic Analysis of the First Cities from a Deconstruction Perspective Doi: 10.23968/2500-0055-2020-5-3-43-48
    Mojtaba Valibeigi, Faezeh Ashuri— Pages 43–48 SEMANTIC ANALYSIS OF THE FIRST CITIES FROM A DECONSTRUCTION PERSPECTIVE DOI: 10.23968/2500-0055-2020-5-3-43-48 SEMANTIC ANALYSIS OF THE FIRST CITIES FROM A DECONSTRUCTION PERSPECTIVE Mojtaba Valibeigi*, Faezeh Ashuri Buein Zahra Technical University Imam Khomeini Blvd, Buein Zahra, Qazvin, Iran *Corresponding author: [email protected] Abstract Introduction: Deconstruction is looking for any meaning, semantics and concepts and then shows how all of them seem to lead to chaos, and are always on the border of meaning duality. Purpose of the study: The study is aimed to investigate urban identity from a deconstruction perspective. Since two important bases of deconstruction are text and meaning and their relationships, we chose the first cities on a symbolic level as a text and tried to analyze their meanings. Methods: The study used a deductive content analysis in three steps including preparation, organization and final report or conclusion. In the first step, we argued deconstruction philosophy based on Derrida’s views accordingly. Then we determined some common semantic features of the first cities. Finally, we presented some conclusions based on a semantic interpretation of the first cities’ identity.Results: It seems that all cities as texts tend to provoke a special imaginary meaning, while simultaneously promoting and emphasizing the opposite meaning of what they want to show. Keywords Deconstruction, text, meaning, urban semantics, the first cities. Introduction to have a specific meaning (Gualberto and Kress, 2019; Expressions are an act of recognizing or displaying Leone, 2019; Stojiljković and Ristić Trajković, 2018).
    [Show full text]
  • Probabilistic Topic Modelling with Semantic Graph
    Probabilistic Topic Modelling with Semantic Graph B Long Chen( ), Joemon M. Jose, Haitao Yu, Fajie Yuan, and Huaizhi Zhang School of Computing Science, University of Glasgow, Sir Alwyns Building, Glasgow, UK [email protected] Abstract. In this paper we propose a novel framework, topic model with semantic graph (TMSG), which couples topic model with the rich knowledge from DBpedia. To begin with, we extract the disambiguated entities from the document collection using a document entity linking system, i.e., DBpedia Spotlight, from which two types of entity graphs are created from DBpedia to capture local and global contextual knowl- edge, respectively. Given the semantic graph representation of the docu- ments, we propagate the inherent topic-document distribution with the disambiguated entities of the semantic graphs. Experiments conducted on two real-world datasets show that TMSG can significantly outperform the state-of-the-art techniques, namely, author-topic Model (ATM) and topic model with biased propagation (TMBP). Keywords: Topic model · Semantic graph · DBpedia 1 Introduction Topic models, such as Probabilistic Latent Semantic Analysis (PLSA) [7]and Latent Dirichlet Analysis (LDA) [2], have been remarkably successful in ana- lyzing textual content. Specifically, each document in a document collection is represented as random mixtures over latent topics, where each topic is character- ized by a distribution over words. Such a paradigm is widely applied in various areas of text mining. In view of the fact that the information used by these mod- els are limited to document collection itself, some recent progress have been made on incorporating external resources, such as time [8], geographic location [12], and authorship [15], into topic models.
    [Show full text]
  • Employee Matching Using Machine Learning Methods
    Master of Science in Computer Science May 2019 Employee Matching Using Machine Learning Methods Sumeesha Marakani Faculty of Computing, Blekinge Institute of Technology, 371 79 Karlskrona, Sweden This thesis is submitted to the Faculty of Computing at Blekinge Institute of Technology in partial fulfillment of the requirements for the degree of Master of Science in Computer Science. The thesis is equivalent to 20 weeks of full time studies. The authors declare that they are the sole authors of this thesis and that they have not used any sources other than those listed in the bibliography and identified as references. They further declare that they have not submitted this thesis at any other institution to obtain a degree. Contact Information: Author(s): Sumeesha Marakani E-mail: [email protected] University advisor: Prof. Veselka Boeva Department of Computer Science External advisors: Lars Tornberg [email protected] Daniel Lundgren [email protected] Faculty of Computing Internet : www.bth.se Blekinge Institute of Technology Phone : +46 455 38 50 00 SE–371 79 Karlskrona, Sweden Fax : +46 455 38 50 57 Abstract Background. Expertise retrieval is an information retrieval technique that focuses on techniques to identify the most suitable ’expert’ for a task from a list of individ- uals. Objectives. This master thesis is a collaboration with Volvo Cars to attempt ap- plying this concept and match employees based on information that was extracted from an internal tool of the company. In this tool, the employees describe themselves in free flowing text. This text is extracted from the tool and analyzed using Natural Language Processing (NLP) techniques.
    [Show full text]
  • Linguistic Relativity Hyp
    THE LINGUISTIC RELATIVITY HYPOTHESIS by Michele Nathan A Thesis Submitted to the Faculty of the College of Social Science in Partial Fulfillment of the Requirements for the Degree of Master of Arts Florida Atlantic University Boca Raton, Florida December 1973 THE LINGUISTIC RELATIVITY HYPOTHESIS by Michele Nathan This thesis was prepared under the direction of the candidate's thesis advisor, Dr. John D. Early, Department of Anthropology, and has been approved by the members of his supervisory committee. It was submitted to the faculty of the College of Social Science and was accepted in partial fulfillment of the requirements for the degree of Master of Arts. SUPERVISORY COMMITTEE: &~ rl7 IC?13 (date) 1 ii ABSTRACT Author: Michele Nathan Title: The Linguistic Relativity Hypothesis Institution: Florida Atlantic University Degree: Master of Arts Year: 1973 Although interest in the linguistic relativity hypothesis seems to have waned in recent years, this thesis attempts to assess the available evidence supporting it in order to show that further investigation of the hypothesis might be most profitable. Special attention is paid to the fact that anthropology has largely failed to substantiate any claims that correlations between culture and the semantics of language do exist. This has been due to the impressionistic nature of the studies in this area. The use of statistics and hypothesis testing to provide mor.e rigorous methodology is discussed in the hope that employing such paradigms would enable anthropology to contribute some sound evidence regarding t~~ hypothesis. iii TABLE OF CONTENTS Page Introduction • 1 CHAPTER I THE.HISTORY OF THE FORMULATION OF THE HYPOTHESIS.
    [Show full text]
  • Latent Semantic Analysis for Text-Based Research
    Behavior Research Methods, Instruments, & Computers 1996, 28 (2), 197-202 ANALYSIS OF SEMANTIC AND CLINICAL DATA Chaired by Matthew S. McGlone, Lafayette College Latent semantic analysis for text-based research PETER W. FOLTZ New Mexico State University, Las Cruces, New Mexico Latent semantic analysis (LSA) is a statistical model of word usage that permits comparisons of se­ mantic similarity between pieces of textual information. This papersummarizes three experiments that illustrate how LSA may be used in text-based research. Two experiments describe methods for ana­ lyzinga subject's essay for determining from what text a subject learned the information and for grad­ ing the quality of information cited in the essay. The third experiment describes using LSAto measure the coherence and comprehensibility of texts. One of the primary goals in text-comprehension re­ A theoretical approach to studying text comprehen­ search is to understand what factors influence a reader's sion has been to develop cognitive models ofthe reader's ability to extract and retain information from textual ma­ representation ofthe text (e.g., Kintsch, 1988; van Dijk terial. The typical approach in text-comprehension re­ & Kintsch, 1983). In such a model, semantic information search is to have subjects read textual material and then from both the text and the reader's summary are repre­ have them produce some form of summary, such as an­ sented as sets ofsemantic components called propositions. swering questions or writing an essay. This summary per­ Typically, each clause in a text is represented by a single mits the experimenter to determine what information the proposition.
    [Show full text]
  • How Latent Is Latent Semantic Analysis?
    How Latent is Latent Semantic Analysis? Peter Wiemer-Hastings University of Memphis Department of Psychology Campus Box 526400 Memphis TN 38152-6400 [email protected]* Abstract In the late 1980's, a group at Bellcore doing re- search on information retrieval techniques developed a Latent Semantic Analysis (LSA) is a statisti• statistical, corpus-based method for retrieving texts. cal, corpus-based text comparison mechanism Unlike the simple techniques which rely on weighted that was originally developed for the task of matches of keywords in the texts and queries, their information retrieval, but in recent years has method, called Latent Semantic Analysis (LSA), cre• produced remarkably human-like abilities in a ated a high-dimensional, spatial representation of a cor• variety of language tasks. LSA has taken the pus and allowed texts to be compared geometrically. Test of English as a Foreign Language and per• In the last few years, several researchers have applied formed as well as non-native English speakers this technique to a variety of tasks including the syn• who were successful college applicants. It has onym section of the Test of English as a Foreign Lan• shown an ability to learn words at a rate sim• guage [Landauer et al., 1997], general lexical acquisi• ilar to humans. It has even graded papers as tion from text [Landauer and Dumais, 1997], selecting reliably as human graders. We have used LSA texts for students to read [Wolfe et al., 1998], judging as a mechanism for evaluating the quality of the coherence of student essays [Foltz et a/., 1998], and student responses in an intelligent tutoring sys• the evaluation of student contributions in an intelligent tem, and its performance equals that of human tutoring environment [Wiemer-Hastings et al., 1998; raters with intermediate domain knowledge.
    [Show full text]
  • Navigating Dbpedia by Topic Tanguy Raynaud, Julien Subercaze, Delphine Boucard, Vincent Battu, Frederique Laforest
    Fouilla: Navigating DBpedia by Topic Tanguy Raynaud, Julien Subercaze, Delphine Boucard, Vincent Battu, Frederique Laforest To cite this version: Tanguy Raynaud, Julien Subercaze, Delphine Boucard, Vincent Battu, Frederique Laforest. Fouilla: Navigating DBpedia by Topic. CIKM 2018, Oct 2018, Turin, Italy. hal-01860672 HAL Id: hal-01860672 https://hal.archives-ouvertes.fr/hal-01860672 Submitted on 23 Aug 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Fouilla: Navigating DBpedia by Topic Tanguy Raynaud, Julien Subercaze, Delphine Boucard, Vincent Battu, Frédérique Laforest Univ Lyon, UJM Saint-Etienne, CNRS, Laboratoire Hubert Curien UMR 5516 Saint-Etienne, France [email protected] ABSTRACT only the triples that concern this topic. For example, a user is inter- Navigating large knowledge bases made of billions of triples is very ested in Italy through the prism of Sports while another through the challenging. In this demonstration, we showcase Fouilla, a topical prism of Word War II. For each of these topics, the relevant triples Knowledge Base browser that offers a seamless navigational expe- of the Italy entity differ. In such circumstances, faceted browsing rience of DBpedia. We propose an original approach that leverages offers no solution to retrieve the entities relative to a defined topic both structural and semantic contents of Wikipedia to enable a if the knowledge graph does not explicitly contain an adequate topic-oriented filter on DBpedia entities.
    [Show full text]
  • Document and Topic Models: Plsa
    10/4/2018 Document and Topic Models: pLSA and LDA Andrew Levandoski and Jonathan Lobo CS 3750 Advanced Topics in Machine Learning 2 October 2018 Outline • Topic Models • pLSA • LSA • Model • Fitting via EM • pHITS: link analysis • LDA • Dirichlet distribution • Generative process • Model • Geometric Interpretation • Inference 2 1 10/4/2018 Topic Models: Visual Representation Topic proportions and Topics Documents assignments 3 Topic Models: Importance • For a given corpus, we learn two things: 1. Topic: from full vocabulary set, we learn important subsets 2. Topic proportion: we learn what each document is about • This can be viewed as a form of dimensionality reduction • From large vocabulary set, extract basis vectors (topics) • Represent document in topic space (topic proportions) 푁 퐾 • Dimensionality is reduced from 푤푖 ∈ ℤ푉 to 휃 ∈ ℝ • Topic proportion is useful for several applications including document classification, discovery of semantic structures, sentiment analysis, object localization in images, etc. 4 2 10/4/2018 Topic Models: Terminology • Document Model • Word: element in a vocabulary set • Document: collection of words • Corpus: collection of documents • Topic Model • Topic: collection of words (subset of vocabulary) • Document is represented by (latent) mixture of topics • 푝 푤 푑 = 푝 푤 푧 푝(푧|푑) (푧 : topic) • Note: document is a collection of words (not a sequence) • ‘Bag of words’ assumption • In probability, we call this the exchangeability assumption • 푝 푤1, … , 푤푁 = 푝(푤휎 1 , … , 푤휎 푁 ) (휎: permutation) 5 Topic Models: Terminology (cont’d) • Represent each document as a vector space • A word is an item from a vocabulary indexed by {1, … , 푉}. We represent words using unit‐basis vectors.
    [Show full text]
  • Vector-Based Word Representations for Sentiment Analysis: a Comparative Study
    CORE Metadata, citation and similar papers at core.ac.uk Provided by SEDICI - Repositorio de la UNLP Vector-based word representations for sentiment analysis: a comparative study M. Paula Villegas1, M. José Garciarena Ucelay1, Juan Pablo Fernández1, Miguel A. 2 1 1,3 Álvarez-Carmona , Marcelo L. Errecalde , Leticia C. Cagnina 1LIDIC, Universidad Nacional de San Luis, San Luis, Argentina 2Language Technologies Laboratory, INAOE, Puebla, México 3CONICET, Argentina {villegasmariapaula74, mjgarciarenaucelay, miguelangel.alvarezcarmona, merrecalde, lcagnina}@gmail.com Abstract. New applications of text categorization methods like opinion mining and sentiment analysis, author profiling and plagiarism detection requires more elaborated and effective document representation models than classical Information Retrieval approaches like the Bag of Words representation. In this context, word representation models in general and vector-based word representations in particular have gained increasing interest to overcome or alleviate some of the limitations that Bag of Words-based representations exhibit. In this article, we analyze the use of several vector-based word representations in a sentiment analysis task with movie reviews. Experimental results show the effectiveness of some vector-based word representations in comparison to standard Bag of Words representations. In particular, the Second Order Attributes representation seems to be very robust and effective because independently the classifier used with, the results are good. Keywords: text mining, word-based representations, text categorization, movie reviews, sentiment analysis 1 Introduction Selecting a good document representation model is a key aspect in text categorization tasks. The usual approach, named Bag of Words (BoW) model, considers that words are simple indexes in a term vocabulary. In this model, originated in the information retrieval field, documents are represented as vectors indexed by those words.
    [Show full text]
  • Similarity Detection Using Latent Semantic Analysis Algorithm Priyanka R
    International Journal of Emerging Research in Management &Technology Research Article August ISSN: 2278-9359 (Volume-6, Issue-8) 2017 Similarity Detection Using Latent Semantic Analysis Algorithm Priyanka R. Patil Shital A. Patil PG Student, Department of Computer Engineering, Associate Professor, Department of Computer Engineering, North Maharashtra University, Jalgaon, North Maharashtra University, Jalgaon, Maharashtra, India Maharashtra, India Abstract— imilarity View is an application for visually comparing and exploring multiple models of text and collection of document. Friendbook finds ways of life of clients from client driven sensor information, measures the S closeness of ways of life amongst clients, and prescribes companions to clients if their ways of life have high likeness. Roused by demonstrate a clients day by day life as life records, from their ways of life are separated by utilizing the Latent Dirichlet Allocation Algorithm. Manual techniques can't be utilized for checking research papers, as the doled out commentator may have lacking learning in the exploration disciplines. For different subjective views, causing possible misinterpretations. An urgent need for an effective and feasible approach to check the submitted research papers with support of automated software. A method like text mining method come to solve the problem of automatically checking the research papers semantically. The proposed method to finding the proper similarity of text from the collection of documents by using Latent Dirichlet Allocation (LDA) algorithm and Latent Semantic Analysis (LSA) with synonym algorithm which is used to find synonyms of text index wise by using the English wordnet dictionary, another algorithm is LSA without synonym used to find the similarity of text based on index.
    [Show full text]
  • LDA V. LSA: a Comparison of Two Computational Text Analysis Tools for the Functional Categorization of Patents
    LDA v. LSA: A Comparison of Two Computational Text Analysis Tools for the Functional Categorization of Patents Toni Cvitanic1, Bumsoo Lee1, Hyeon Ik Song1, Katherine Fu1, and David Rosen1! ! 1Georgia Institute of Technology, Atlanta, GA, USA (tcvitanic3, blee300, hyeoniksong) @gatech.edu (katherine.fu, david.rosen) @me.gatech.edu! !! Abstract. One means to support for design-by-analogy (DbA) in practice involves giving designers efficient access to source analogies as inspiration to solve problems. The patent database has been used for many DbA support efforts, as it is a pre- existing repository of catalogued technology. Latent Semantic Analysis (LSA) has been shown to be an effective computational text processing method for extracting meaningful similarities between patents for useful functional exploration during DbA. However, this has only been shown to be useful at a small-scale (100 patents). Considering the vastness of the patent database and realistic exploration at a large- scale, it is important to consider how these computational analyses change with orders of magnitude more data. We present analysis of 1,000 random mechanical patents, comparing the ability of LSA to Latent Dirichlet Allocation (LDA) to categorize patents into meaningful groups. Resulting implications for large(r) scale data mining of patents for DbA support are detailed. Keywords: Design-by-analogy ! Patent Analysis ! Latent Semantic Analysis ! Latent Dirichlet Allocation ! Function-based Analogy 1 Introduction Exposure to appropriate analogies during early stage design has been shown to increase the novelty, quality, and originality of generated solutions to a given engineering design problem [1-4]. Finding appropriate analogies for a given design problem is the largest challenge to practical implementation of DbA.
    [Show full text]