advertisement

advertisement

Information about Latent Semantic Indexing For Information Retrieval

Published on October 30, 2007

Author: sudarsun

Source: slideshare.net

Introducing Latent Semantic Analysis through Singular Value Decomposition on Text Data for Information Retrieval

advertisement

What is NLP ? What is Natural Language ? Can a machine understand NL ? How are we understanding NL ? How can we make a machine understand NL ? What are the limitations ?

What is Natural Language ?

Can a machine understand NL ?

How are we understanding NL ?

How can we make a machine understand NL ?

What are the limitations ?

Major Entities … What is Syntactic Analysis ? Deal Synonymy Deal Polysemy ? What is Semantics ? Represent meanings as a Semantic Net What is Knowledge ? How to represent knowledge ? What are Inferences and Reasoning ? How to use the accumulated knowledge ?

What is Syntactic Analysis ?

Deal Synonymy

Deal Polysemy ?

What is Semantics ?

Represent meanings as a Semantic Net

What is Knowledge ?

How to represent knowledge ?

What are Inferences and Reasoning ?

How to use the accumulated knowledge ?

LSA for Information Retrieval What is LSA? Singular Value Decomposition Method of LSA Computation of Similarity using Cosine Measuring Similarities Construction of Pseudo-document Limitations of LSA Alternatives to LSA

What is LSA?

Singular Value Decomposition

Method of LSA

Computation of Similarity using Cosine

Measuring Similarities

Construction of Pseudo-document

Limitations of LSA

Alternatives to LSA

What is LSA A Statistical Method that provides a way to describe the underlying structure of texts Used in author recognition, search engines, detecting plagiarism, and comparing texts for similarities The contexts in which a certain word exists or does not exist determine the similarity of the documents Closely models human learning, especially the manner in which people learn a language and acquire a vocabulary

A Statistical Method that provides a way to describe the underlying structure of texts

Used in author recognition, search engines, detecting plagiarism, and comparing texts for similarities

The contexts in which a certain word exists or does not exist determine the similarity of the documents

Closely models human learning, especially the manner in which people learn a language and acquire a vocabulary

Multivariate Data Reduction technique. Reduces large dataset to a concentrated dataset containing only the significant information from the original data . Singular Value Decomposition

Multivariate Data Reduction technique.

Reduces large dataset to a concentrated dataset containing only the significant information from the original data .

Mathematical Background of SVD SVD decomposes a matrix as a product of 3 matrices. Let A be matrix of m x n, then SVD of A is SVD(A) = U MxK S KxK V t KxN U, V Left and Right Singular matrices respectively U and V are Orthogonal matrix whose vectors are of unit length S Diagonal matrix whose diagonal elements are Singular Values arranged in descending order K Rank of A; K<=min(M,N).

SVD decomposes a matrix as a product of 3 matrices.

Let A be matrix of m x n, then SVD of A is

SVD(A) = U MxK S KxK V t KxN

U, V Left and Right Singular matrices respectively

U and V are Orthogonal matrix whose vectors are of unit length

S Diagonal matrix whose diagonal elements are Singular Values arranged in descending order

K Rank of A; K<=min(M,N).

Computation of SVD To Find U,S and V matrices Find Eigen Values and their corresponding Eigen Vectors of the matrix AA t Singular values = Square root of Eigen Values. These Singular values arranged in descending order forms the diagonal elements of the diagonal matrix S . Divide each Eigen vector by its length. These Eigen vectors forms the columns of the matrix U . Similarly Eigen Vectors of the matrix A t A forms the columns of matrix V. [ Note : Eigen Values of AA t and A t A are equal.]

To Find U,S and V matrices

Find Eigen Values and their corresponding Eigen Vectors of the matrix AA t

Singular values = Square root of Eigen Values.

These Singular values arranged in descending order forms the diagonal elements of the diagonal matrix S .

Divide each Eigen vector by its length.

These Eigen vectors forms the columns of the matrix U .

Similarly Eigen Vectors of the matrix A t A forms the columns of matrix V.

[ Note : Eigen Values of AA t and A t A are equal.]

Eigen Value & Vectors A scalar Lamba is called an Eigen Value of a matrix A if there is a non-zero vector V such that A.V = Lamba.V. This non-zero vector is the Eigen vector of A. Eigen values can be found by solving the equation | A – Lamba.I | = 0.

A scalar Lamba is called an Eigen Value of a matrix A if there is a non-zero vector V such that A.V = Lamba.V. This non-zero vector is the Eigen vector of A.

Eigen values can be found by solving the equation | A – Lamba.I | = 0.

How to Build LSA ? Preprocess the document collection Stemming Stop words removal Build Frequency Matrix Apply Pre-weights Decompose FM into U, S, V Project Queries

Preprocess the document collection

Stemming

Stop words removal

Build Frequency Matrix

Apply Pre-weights

Decompose FM into U, S, V

Project Queries

Step #1: Construct the term-document matrix; TDM One column for each document One row for every word The value of cell (i, j) is the frequency of word i in document j Frequency Matrix

Step #1: Construct the term-document matrix; TDM

One column for each document

One row for every word

The value of cell (i, j) is the frequency of word i in document j

Step #2: Weight Functions Increase the efficiency of the information retrieval. Allocates weights to the terms based on their occurrences. Each element is replaced with the product of a Local Weight Function(LWF) and a Global Weight Function(GWF) . LWF considers the frequency of a word within a particular text GWF examines a term’s frequency across all the documents. Pre-weightings Applied on the TDM before computing SVD. Post-weightings Applied to terms of a query when projected for matching or searching.

Step #2: Weight Functions

Increase the efficiency of the information retrieval.

Allocates weights to the terms based on their occurrences.

Each element is replaced with the product of a Local Weight Function(LWF) and a Global Weight Function(GWF) .

LWF considers the frequency of a word within a particular text

GWF examines a term’s frequency across all the documents.

Pre-weightings

Applied on the TDM before computing SVD.

Post-weightings

Applied to terms of a query when projected for matching or searching.

Step #3: SVD Perform SVD on term-document matrix X. SVD removes noise or infrequent words that do not help to classify a document. Octave/Mat lab can be used [u, s, v] = svd(A);

Step #3: SVD

Perform SVD on term-document matrix X.

SVD removes noise or infrequent words that do not help to classify a document.

Octave/Mat lab can be used

[u, s, v] = svd(A);

A U S V t m x n m x k k x k k x n · · Terms Documents 0 0

Documents TDM SVD Terms U S V

Similarity Computation Using Cosine Consider 2 vectors A & B. Similarity between these 2 vectors is A.B CosØ = ------------------ |A|. |B| CosØ ranges between –1 to +1

Consider 2 vectors A & B. Similarity between these 2 vectors is

A.B

CosØ = ------------------

|A|. |B|

CosØ ranges between –1 to +1

Similarity Computations in LSA

Term-term Similarity Compute the Cosine for the row vectors of term ‘i’ and term ‘j’ in the U*S matrix. US

Compute the Cosine for the row vectors of term ‘i’ and term ‘j’ in the U*S matrix.

US

Document – Document Similarity Compute the Cosine for the column vectors of document ‘i’ and document ‘j’ in the S*V t matrix. SV t

Compute the Cosine for the column vectors of document ‘i’ and document ‘j’ in the S*V t matrix.

Term – Document Similarity Compute Cosine between row vector of term ‘i’ in U*S 1/2 matrix and column vector of document ‘j’ in S 1/2 *V t matrix.

Compute Cosine between row vector of term ‘i’ in U*S 1/2 matrix and column vector of document ‘j’ in S 1/2 *V t matrix.

U*S 1/2 S 1/2 *V t

Construction of Pseudo-document A Query is broken in to terms and represented as a column vector (say ‘ q ’ ) consisting of ‘M’ terms as rows. Then Pseudo-document ( Q ) for the query( q ) can be constructed with the help of following mathematical formula. Q = qt*U*S -1 After constructing the Pseudo-document, we can compute the similarities of query-term, query-document using earlier mentioned techniques.

A Query is broken in to terms and represented as a column vector (say ‘ q ’ ) consisting of ‘M’ terms as rows.

Then Pseudo-document ( Q ) for the query( q ) can be constructed with the help of following mathematical formula.

Q = qt*U*S -1

After constructing the Pseudo-document, we can compute the similarities of query-term, query-document using earlier mentioned techniques.

Alternatives to LSA LSA is limited to Synonymy problem PLSA – Probabilistic Latent Semantic Analysis to handle Polysemy. LDA – Latent Dirichlet Allocation.

LSA is limited to Synonymy problem

PLSA – Probabilistic Latent Semantic Analysis to handle Polysemy.

LDA – Latent Dirichlet Allocation.

References http://www.cs.utk.edu/~lsi/papers/ http://www.cs.utk.edu/~berry/lsi++ http://people.csail.mit.edu/fergus/iccv2005/bagwords.html http://research.nitle.org/lsi/lsa_explanation.htm http://en.wikipedia.org/wiki/Latent_semantic_analysis http://www-psych.nmsu.edu/~pfoltz/reprints/BRMIC96.html http://www.pcug.org.au/~jdowling/ http://www.ucl.ac.uk/oncology/MicroCore/HTML_resource/PCA_1.htm http://public.lanl.gov/mewall/kluwer2002.html http://www.cs.utexas.edu/users/suvrit/work/progs/ssvd.html

http://www.cs.utk.edu/~lsi/papers/

http://www.cs.utk.edu/~berry/lsi++

http://people.csail.mit.edu/fergus/iccv2005/bagwords.html

http://research.nitle.org/lsi/lsa_explanation.htm

http://en.wikipedia.org/wiki/Latent_semantic_analysis

http://www-psych.nmsu.edu/~pfoltz/reprints/BRMIC96.html

http://www.pcug.org.au/~jdowling/

http://www.ucl.ac.uk/oncology/MicroCore/HTML_resource/PCA_1.htm

http://public.lanl.gov/mewall/kluwer2002.html

http://www.cs.utexas.edu/users/suvrit/work/progs/ssvd.html

Thanks.. You may send in your queries to sudar@burning-glass.com

You may send in your queries to sudar@burning-glass.com

Latent semantic indexing is an information retrieval technique which indexes and ... Latent Semantic Analysis for Information Retrieval

Read more

Latent Semantic Indexing for Image Retrieval ... Matrix computation is used as a basis for information retrieval ... R. Harshman, Indexing by latent ...

Read more

An information retrieval technique using latent semantic ... Called Latent Semantic Indexing because of its ... of information retrieval and ...

Read more

... Latent Semantic Indexing (LSI) • Several Applications – Information Retrieval ... • Use truncated SVD to model latent semantic structure

Read more

Latent semantic indexing is an information ... This matrix is www.erpublication.org Latent Semantic Analysis for Information Retrieval also ...

Read more

The use of latent semantic indexing (LSI) for information retrieval and text mining operations is adapted to work on large heterogeneous data sets by first ...

Read more

Latent Semantic Indexing (kurz LSI) ist ein (nicht mehr patentgeschütztes) Verfahren des Information Retrieval, das 1990 zuerst von Deerwester et al ...

Read more

Bücher bei Weltbild: Jetzt Latent Semantic Indexing and Information Retrieval versandkostenfrei online kaufen bei Weltbild, Ihrem Bücher-Spezialisten!

Read more

for information retrieval, it remains an intriguing approach to clustering in a ... 408 18 Matrix decompositions and latent semantic indexing

Read more

## Add a comment