Jakob - 1 year ago 131
R Question

# dtm sparsity different depending on tf/tfidf , same corpus

Can anybody explain?

My understanding:

``````tf >= 0 (absolute frequency value)

tfidf >= 0 (for negative idf, tf=0)

sparse entry = 0

nonsparse entry > 0
``````

So the exact sparse/nonsparse proportion should be the same in the two DTMs created with the code below.

``````library(tm)
data(crude)

dtm <- DocumentTermMatrix(crude, control=list(weighting=weightTf))
dtm2 <- DocumentTermMatrix(crude, control=list(weighting=weightTfIdf))
dtm
dtm2
``````

But:

``````> dtm
<<DocumentTermMatrix (documents: 20, terms: 1266)>>
**Non-/sparse entries: 2255/23065**
Sparsity           : 91%
Maximal term length: 17
Weighting          : term frequency (tf)
> dtm2
<<DocumentTermMatrix (documents: 20, terms: 1266)>>
**Non-/sparse entries: 2215/23105**
Sparsity           : 91%
Maximal term length: 17
Weighting          : term frequency - inverse document frequency (normalized) (tf-idf)
``````

The sparsity can differ. The TF-IDF value will be zero if TF is zero or if IDF is zero, and IDF is zero if a term occurs in every document. Consider the following example:

``````txts <- c("super World", "Hello World", "Hello super top world")
library(tm)
tf <- TermDocumentMatrix(Corpus(VectorSource(txts)), control=list(weighting=weightTf))
tfidf <- TermDocumentMatrix(Corpus(VectorSource(txts)), control=list(weighting=weightTfIdf))

inspect(tf)
# <<TermDocumentMatrix (terms: 4, documents: 3)>>
# Non-/sparse entries: 9/3
# Sparsity           : 25%
# Maximal term length: 5
# Weighting          : term frequency (tf)
#
#        Docs
# Terms   1 2 3
#   hello 1 1 1
#   super 1 0 1
#   top   0 0 1
#   world 1 1 1

inspect(tfidf)
# <<TermDocumentMatrix (terms: 4, documents: 3)>>
# Non-/sparse entries: 5/7
# Sparsity           : 58%
# Maximal term length: 5
# Weighting          : term frequency - inverse document frequency (normalized) (tf-idf)
#
#        Docs
# Terms           1         2         3
#   hello 0.0000000 0.2924813 0.1462406
#   super 0.2924813 0.0000000 0.1462406
#   top   0.0000000 0.0000000 0.3962406
#   world 0.0000000 0.0000000 0.0000000
``````

The term super occurs 1 time in document 1, which has 2 terms, and it occurs in 2 out of 3 documents:

``````1/2 * log2(3/2)
# [1] 0.2924813
``````

The term world occurs 1 time in document 3, which has 4 terms, and it occurs in all 3 documents:

``````1/3 * log2(3/3) # 1/3 * 0
# [1] 0
``````
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