Topic modeling

• Keywords
• Links
• Themes
• Probabilistic topic models
  • Latent Dirichlet allocation

Food and animals

1. I ate a banana and spinach smoothie for breakfast.
2. I like to eat broccoli and bananas.
3. Chinchillas and kittens are cute.
4. My sister adopted a kitten yesterday.
5. Look at this cute hamster munching on a piece of broccoli.

LDA document structure

• Decide on the number of words N the document will have
  • Dirichlet probability distribution
  • Fixed set of \(k\) topics
• Generate each word in the document:
  • Pick a topic
  • Generate the word
• LDA backtracks from this assumption

Food and animals

• Decide that \(D\) will be 1/2 about food and 1/2 about cute animals.
• Pick 5 to be the number of words in \(D\).
• Pick the first word to come from the food topic
• Pick the second word to come from the cute animals topic
• Pick the third word to come from the cute animals topic
• Pick the fourth word to come from the food topic
• Pick the fifth word to come from the food topic

How does LDA learn?

• Randomly assign each word in the document to one of \(K\) topics
• For each document \(d\):
  • Go through each word \(w\) in \(d\)
    • And for each topic \(t\), compute two things:
      1. \(p(t | d)\)
      2. \(p(w | t)\)
    • Reassign \(w\) a new topic \(t\) with probability \(p(t|d) \times p(w|t)\)

• Rinse and repeat

• Estimate from LDA
  1. The topic mixtures of each document
  2. The words associated to each topic

LDA with a known topic structure

• Great Expectations by Charles Dickens
• The War of the Worlds by H.G. Wells
• Twenty Thousand Leagues Under the Sea by Jules Verne
• Pride and Prejudice by Jane Austen

topicmodels

## <<DocumentTermMatrix (documents: 193, terms: 18215)>>
## Non-/sparse entries: 104721/3410774
## Sparsity           : 97%
## Maximal term length: 19
## Weighting          : term frequency (tf)

Terms associated with each topic

Per-document classification

Consensus topic

## # A tibble: 4 × 2
##                               consensus topic
##                                   <chr> <int>
## 1                    Great Expectations     4
## 2                   Pride and Prejudice     1
## 3                 The War of the Worlds     3
## 4 Twenty Thousand Leagues under the Sea     2

Mis-identification

chapter_classifications %>%
  inner_join(book_topics, by = "topic") %>%
  count(title, consensus) %>%
  knitr::kable()

Incorrectly classified words

Most commonly mistaken words

## # A tibble: 3,500 × 4
##                 title             consensus     term     n
##                 <chr>                 <chr>    <chr> <dbl>
## 1  Great Expectations   Pride and Prejudice     love    44
## 2  Great Expectations   Pride and Prejudice sergeant    37
## 3  Great Expectations   Pride and Prejudice     lady    32
## 4  Great Expectations   Pride and Prejudice     miss    26
## 5  Great Expectations The War of the Worlds     boat    25
## 6  Great Expectations   Pride and Prejudice   father    19
## 7  Great Expectations The War of the Worlds    water    19
## 8  Great Expectations   Pride and Prejudice     baby    18
## 9  Great Expectations   Pride and Prejudice  flopson    18
## 10 Great Expectations   Pride and Prejudice   family    16
## # ... with 3,490 more rows

LDA with an unknown topic structure

Associated Press articles

## <<DocumentTermMatrix (documents: 2246, terms: 10134)>>
## Non-/sparse entries: 259208/22501756
## Sparsity           : 99%
## Maximal term length: 18
## Weighting          : term frequency (tf)

Perplexity

• A statistical measure of how well a probability model predicts a sample
• Given the theoretical word distributions represented by the topics, compare that to the actual topic mixtures, or distribution of words in your documents
• Perplexity for LDA model with 12 topics
  • 2301.8138725

Topics from \(k=100\)

Acknowledgments

• This page is derived in part from “Tidy Text Mining with R” and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License.
• This page is derived in part from “What is a good explanation of Latent Dirichlet Allocation?”