dtm 稀疏度不同，取决于 tf/tfidf ，相同的语料库答案

【问题标题】：dtm sparsity different depending on tf/tfidf , same corpusdtm 稀疏度不同，取决于 tf/tfidf ，相同的语料库
【发布时间】：2017-04-13 11:03:31
【问题描述】：

谁能解释一下？

我的理解：

tf >= 0 (absolute frequency value)

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



sparse entry = 0

nonsparse entry > 0

因此，在使用以下代码创建的两个 DTM 中，精确的稀疏/非稀疏比例应该相同。

library(tm)
data(crude)

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

但是：

> 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)

【问题讨论】：

标签： r text-processing tm tf-idf

【解决方案1】：

稀疏度可以不同。如果 TF 为零或 IDF 为零，则 TF-IDF 值将为零，如果每个文档中都出现一个术语，则 IDF 为零。考虑以下示例：

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: 8/4
# Sparsity           : 33%
# Maximal term length: 5
# Weighting          : term frequency (tf)
# 
#        Docs
# Terms   1 2 3
#   hello 0 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

词super在文档1中出现1次，有2个词，在3个文档中出现2个：

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

world 一词在文档 3 中出现 1 次，有 4 个词条，并且出现在所有 3 个文档中：

1/4 * log2(3/3) # 1/4 * 0
# [1] 0

【讨论】：