Example: Latent Semantic Analysis (LSA)

Haiyan Wang

In this vignette, we show how to perform Latent Semantic Analysis using the quanteda package based on Grossman and Frieder’s Information Retrieval, Algorithms and Heuristics.

LSA decomposes document-feature matrix into a reduced vector space that is assumed to reflect semantic structure.

New documents or queries can be ‘folded-in’ to this constructed latent semantic space for downstream tasks.

library("quanteda")

Create a document-feature matrix

txt <- c(d1 = "Shipment of gold damaged in a fire",
         d2 = "Delivery of silver arrived in a silver truck",
         d3 = "Shipment of gold arrived in a truck" )

dfmat <- txt |> 
    tokens() |> 
    dfm()
dfmat

## Document-feature matrix of: 3 documents, 11 features (36.36% sparse) and 0 docvars.
##     features
## docs shipment of gold damaged in a fire delivery silver arrived
##   d1        1  1    1       1  1 1    1        0      0       0
##   d2        0  1    0       0  1 1    0        1      2       1
##   d3        1  1    1       0  1 1    0        0      0       1
## [ reached max_nfeat ... 1 more feature ]

Construct the LSA model

library("quanteda.textmodels")
tmod_lsa <- textmodel_lsa(dfmat)

## Warning in fun(A, k, nu, nv, opts, mattype = "dgCMatrix"): all singular values
## are requested, svd() is used instead

The new document vector coordinates in the reduced 2-dimensional space is:

tmod_lsa$docs[, 1:2]

##          [,1]       [,2]
## d1 -0.4944666  0.6491758
## d2 -0.6458224 -0.7194469
## d3 -0.5817355  0.2469149

Apply the constructed LSA model to new data

Now the new unseen document can be represented in the reduced 2-dimensional space. The unseen query document:

dfmat_test <- tokens("gold silver truck") |> 
    dfm() |> 
    dfm_match(features = featnames(dfmat))
dfmat_test

## Document-feature matrix of: 1 document, 11 features (72.73% sparse) and 0 docvars.
##        features
## docs    shipment of gold damaged in a fire delivery silver arrived
##   text1        0  0    1       0  0 0    0        0      1       0
## [ reached max_nfeat ... 1 more feature ]

pred_lsa <- predict(tmod_lsa, newdata = dfmat_test)
pred_lsa$docs_newspace[, 1:2]

## [1] -0.2140026 -0.1820571