Create a vector space with Latent Semantic Analysis (LSA)
Calculates a latent semantic space from a given document-term matrix.
a document-term matrix (recommeded to be of class textmatrix), containing documents in colums, terms in rows and occurrence frequencies in the cells.
either the number of dimensions or a configuring function.
LSA combines the classical vector space model — well known in textmining — with a Singular Value Decomposition (SVD), a two-mode factor analysis. Thereby, bag-of-words representations of texts can be mapped into a modified vector space that is assumed to reflect semantic structure.
lsa() a new latent semantic space can
be constructed over a given document-term matrix. To ease
comparisons of terms and documents with common
correlation measures, the space can be converted into
a textmatrix of the same format as
To add more documents or queries to this latent semantic
space in order to keep them from influencing the original
factor distribution (i.e., the latent semantic structure calculated
from a primary text corpus), they can be ‘folded-in’ later on
(with the function
Background information (see also Deerwester et al., 1990):
A document-term matrix M is constructed
textmatrix() from a given text base of n documents
containing m terms.
This matrix M of the size m \times n is then decomposed via a
singular value decomposition into: term vector matrix T (constituting
left singular vectors), the document vector matrix D (constituting
right singular vectors) being both orthonormal, and the diagonal matrix
S (constituting singular values).
M = T S t(D)
These matrices are then reduced to the given number of dimensions k=dims to result into truncated matrices Tk, Sk and Dk — the latent semantic space.
Mk = t\[,1:k\] s\[1:k,1:k\] t(d\[,1:k\])
If these matrices Tk, Sk, Dk were multiplied, they would give a new matrix Mk (of the same format as M, i.e., rows are the same terms, columns are the same documents), which is the least-squares best fit approximation of M with k singular values.
In the case of folding-in, i.e., multiplying new documents into a given latent semantic space, the matrices Tk and Sk remain unchanged and an additional Dk is created (without replacing the old one). All three are multiplied together to return a (new and appendable) document-term matrix Mnew in the term-order of M.
a list with components (Tk, Sk, Dk), representing the latent semantic space.
Fridolin Wild email@example.com
Deerwester, S., Dumais, S., Furnas, G., Landauer, T., and Harshman, R. (1990) Indexing by Latent Semantic Analysis. In: Journal of the American Society for Information Science 41(6), pp. 391–407.
Landauer, T., Foltz, P., and Laham, D. (1998) Introduction to Latent Semantic Analysis. In: Discourse Processes 25, pp. 259–284.
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# create some files td = tempfile() dir.create(td) write( c("dog", "cat", "mouse"), file=paste(td, "D1", sep="/") ) write( c("ham", "mouse", "sushi"), file=paste(td, "D2", sep="/") ) write( c("dog", "pet", "pet"), file=paste(td, "D3", sep="/") ) # LSA data(stopwords_en) myMatrix = textmatrix(td, stopwords=stopwords_en) myMatrix = lw_logtf(myMatrix) * gw_idf(myMatrix) myLSAspace = lsa(myMatrix, dims=dimcalc_share()) as.textmatrix(myLSAspace) # clean up unlink(td, recursive=TRUE)
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