Documentation

# ldaModel

Latent Dirichlet allocation (LDA) model

## Description

A latent Dirichlet allocation (LDA) model is a topic model which discovers underlying topics in a collection of documents and infers word probabilities in topics. If the model was fit using a bag-of-n-grams model, then the software treats the n-grams as individual words.

## Creation

Create an LDA model using the fitlda function.

## Properties

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Number of topics in the LDA model, specified as a positive integer.

Topic concentration, specified as a positive scalar. The function sets the concentration per topic to TopicConcentration/NumTopics. For more information, see Latent Dirichlet Allocation.

Word concentration, specified as a nonnegative scalar. The software sets the concentration per word to WordConcentration/numWords, where numWords is the vocabulary size of the input documents. For more information, see Latent Dirichlet Allocation.

Topic probabilities of input document set, specified as a vector. The corpus topic probabilities of an LDA model are the probabilities of observing each topic in the entire data set used to fit the LDA model. CorpusTopicProbabilities is a 1-by-K vector where K is the number of topics. The kth entry of CorpusTopicProbabilities corresponds to the probability of observing topic k.

Topic probabilities per input document, specified as a matrix. The document topic probabilities of an LDA model are the probabilities of observing each topic in each document used to fit the LDA model. DocumentTopicProbabilities is a D-by-K matrix where D is the number of documents used to fit the LDA model, and K is the number of topics. The (d,k)th entry of DocumentTopicProbabilities corresponds to the probability of observing topic k in document d.

If any the topics have zero probability (CorpusTopicProbabilities contains zeros), then the corresponding columns of DocumentTopicProbabilities and TopicWordProbabilities are zeros.

The order of the rows in DocumentTopicProbabilities corresponds to the order of the documents in the training data.

Word probabilities per topic, specified as a matrix. The topic word probabilities of an LDA model are the probabilities of observing each word in each topic of the LDA model. TopicWordProbabilities is a V-by-K matrix, where V is the number of words in Vocabulary and K is the number of topics. The (v,k)th entry of TopicWordProbabilities corresponds to the probability of observing word v in topic k.

If any the topics have zero probability (CorpusTopicProbabilities contains zeros), then the corresponding columns of DocumentTopicProbabilities and TopicWordProbabilities are zeros.

The order of the rows in TopicWordProbabilities corresponds to the order of the words in Vocabulary.

Topic order, specified as one of the following:

• 'initial-fit-probability' – Sort the topics by the corpus topic probabilities of the initial model fit. These probabilities are the CorpusTopicProbabilities property of the initial ldaModel object returned by fitlda. The resume function does not reorder the topics of the resulting ldaModel objects.

• 'unordered' – Do not order topics.

Information recorded when fitting LDA model, specified as a struct with the following fields:

• TerminationCode – Status of optimization upon exit

• 0 – Iteration limit reached.

• 1 – Tolerance on log-likelihood satisfied.

• TerminationStatus – Explanation of the returned termination code

• NumIterations – Number of iterations performed

• NegativeLogLikelihood – Negative log-likelihood for the data passed to fitlda

• Perplexity – Perplexity for the data passed to fitlda

• Solver – Name of the solver used

• History – Struct holding the optimization history

• StochasticInfo – Struct holding information for stochastic solvers

Data Types: struct

List of words in the model, specified as a string vector.

Data Types: string

## Object Functions

 logp Document log-probabilities and goodness of fit of LDA model predict Predict top LDA topics of documents resume Resume fitting LDA model topkwords Most important words in bag-of-words model or LDA topic transform Transform documents into lower-dimensional space wordcloud Create word cloud chart from text, bag-of-words model, bag-of-n-grams model, or LDA model

## Examples

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To reproduce the results in this example, set rng to 'default'.

rng('default')

Load the example data. The file sonnetsPreprocessed.txt contains preprocessed versions of Shakespeare's sonnets. The file contains one sonnet per line, with words separated by a space. Extract the text from sonnetsPreprocessed.txt, split the text into documents at newline characters, and then tokenize the documents.

filename = "sonnetsPreprocessed.txt";
str = extractFileText(filename);
textData = split(str,newline);
documents = tokenizedDocument(textData);

Create a bag-of-words model using bagOfWords.

bag = bagOfWords(documents)
bag =
bagOfWords with properties:

Counts: [154x3092 double]
Vocabulary: [1x3092 string]
NumWords: 3092
NumDocuments: 154

Fit an LDA model with four topics.

numTopics = 4;
mdl = fitlda(bag,numTopics)
Initial topic assignments sampled in 0.371892 seconds.
=====================================================================================
| Iteration  |  Time per  |  Relative  |  Training  |     Topic     |     Topic     |
|            | iteration  | change in  | perplexity | concentration | concentration |
|            | (seconds)  |   log(L)   |            |               |   iterations  |
=====================================================================================
|          0 |       0.02 |            |  1.215e+03 |         1.000 |             0 |
|          1 |       0.05 | 1.0482e-02 |  1.128e+03 |         1.000 |             0 |
|          2 |       0.03 | 1.7190e-03 |  1.115e+03 |         1.000 |             0 |
|          3 |       0.04 | 4.3796e-04 |  1.118e+03 |         1.000 |             0 |
|          4 |       0.05 | 9.4193e-04 |  1.111e+03 |         1.000 |             0 |
|          5 |       0.08 | 3.7079e-04 |  1.108e+03 |         1.000 |             0 |
|          6 |       0.05 | 9.5777e-05 |  1.107e+03 |         1.000 |             0 |
=====================================================================================
mdl =
ldaModel with properties:

NumTopics: 4
WordConcentration: 1
TopicConcentration: 1
CorpusTopicProbabilities: [0.2500 0.2500 0.2500 0.2500]
DocumentTopicProbabilities: [154x4 double]
TopicWordProbabilities: [3092x4 double]
Vocabulary: [1x3092 string]
TopicOrder: 'initial-fit-probability'
FitInfo: [1x1 struct]

Visualize the topics using word clouds.

figure
for topicIdx = 1:4
subplot(2,2,topicIdx)
wordcloud(mdl,topicIdx);
title("Topic: " + topicIdx)
end

Create a table of the words with highest probability of an LDA topic.

To reproduce the results, set rng to 'default'.

rng('default')

Load the example data. The file sonnetsPreprocessed.txt contains preprocessed versions of Shakespeare's sonnets. The file contains one sonnet per line, with words separated by a space. Extract the text from sonnetsPreprocessed.txt, split the text into documents at newline characters, and then tokenize the documents.

filename = "sonnetsPreprocessed.txt";
str = extractFileText(filename);
textData = split(str,newline);
documents = tokenizedDocument(textData);

Create a bag-of-words model using bagOfWords.

bag = bagOfWords(documents);

Fit an LDA model with 20 topics. To suppress verbose output, set 'Verbose' to 0.

numTopics = 20;
mdl = fitlda(bag,numTopics,'Verbose',0);

Find the top 20 words of the first topic.

k = 20;
topicIdx = 1;
tbl = topkwords(mdl,k,topicIdx)
tbl=20×2 table
Word        Score
________    _________

"eyes"        0.11155
"beauty"      0.05777
"hath"       0.055778
"still"      0.049801
"true"       0.043825
"mine"       0.033865
"find"       0.031873
"black"      0.025897
"look"       0.023905
"tis"        0.023905
"kind"       0.021913
"seen"       0.021913
"found"      0.017929
"sin"        0.015937
"three"      0.013945
"golden"    0.0099608
⋮

Find the top 20 words of the first topic and use inverse mean scaling on the scores.

tbl = topkwords(mdl,k,topicIdx,'Scaling','inversemean')
tbl=20×2 table
Word       Score
________    ________

"eyes"        1.2718
"beauty"     0.59022
"hath"        0.5692
"still"      0.50269
"true"       0.43719
"mine"       0.32764
"find"       0.32544
"black"      0.25931
"tis"        0.23755
"look"       0.22519
"kind"       0.21594
"seen"       0.21594
"found"      0.17326
"sin"        0.15223
"three"      0.13143
"golden"    0.090698
⋮

Create a word cloud using the scaled scores as the size data.

figure
wordcloud(tbl.Word,tbl.Score);

Get the document topic probabilities (also known as topic mixtures) of the documents used to fit an LDA model.

To reproduce the results, set rng to 'default'.

rng('default')

Load the example data. The file sonnetsPreprocessed.txt contains preprocessed versions of Shakespeare's sonnets. The file contains one sonnet per line, with words separated by a space. Extract the text from sonnetsPreprocessed.txt, split the text into documents at newline characters, and then tokenize the documents.

filename = "sonnetsPreprocessed.txt";
str = extractFileText(filename);
textData = split(str,newline);
documents = tokenizedDocument(textData);

Create a bag-of-words model using bagOfWords.

bag = bagOfWords(documents);

Fit an LDA model with 20 topics. To suppress verbose output, set 'Verbose' to 0.

numTopics = 20;
mdl = fitlda(bag,numTopics,'Verbose',0)
mdl =
ldaModel with properties:

NumTopics: 20
WordConcentration: 1
TopicConcentration: 5
CorpusTopicProbabilities: [1x20 double]
DocumentTopicProbabilities: [154x20 double]
TopicWordProbabilities: [3092x20 double]
Vocabulary: [1x3092 string]
TopicOrder: 'initial-fit-probability'
FitInfo: [1x1 struct]

View the topic probabilities of the first document in the training data.

topicMixtures = mdl.DocumentTopicProbabilities;
figure
bar(topicMixtures(1,:))
title("Document 1 Topic Probabilities")
xlabel("Topic Index")
ylabel("Probability")

To reproduce the results in this example, set rng to 'default'.

rng('default')

Load the example data. The file sonnetsPreprocessed.txt contains preprocessed versions of Shakespeare's sonnets. The file contains one sonnet per line, with words separated by a space. Extract the text from sonnetsPreprocessed.txt, split the text into documents at newline characters, and then tokenize the documents.

filename = "sonnetsPreprocessed.txt";
str = extractFileText(filename);
textData = split(str,newline);
documents = tokenizedDocument(textData);

Create a bag-of-words model using bagOfWords.

bag = bagOfWords(documents)
bag =
bagOfWords with properties:

Counts: [154x3092 double]
Vocabulary: [1x3092 string]
NumWords: 3092
NumDocuments: 154

Fit an LDA model with 20 topics.

numTopics = 20;
mdl = fitlda(bag,numTopics)
Initial topic assignments sampled in 0.30173 seconds.
=====================================================================================
| Iteration  |  Time per  |  Relative  |  Training  |     Topic     |     Topic     |
|            | iteration  | change in  | perplexity | concentration | concentration |
|            | (seconds)  |   log(L)   |            |               |   iterations  |
=====================================================================================
|          0 |       0.31 |            |  1.159e+03 |         5.000 |             0 |
|          1 |       0.11 | 5.4884e-02 |  8.028e+02 |         5.000 |             0 |
|          2 |       0.10 | 4.7400e-03 |  7.778e+02 |         5.000 |             0 |
|          3 |       0.09 | 3.4597e-03 |  7.602e+02 |         5.000 |             0 |
|          4 |       0.12 | 3.4662e-03 |  7.430e+02 |         5.000 |             0 |
|          5 |       0.14 | 2.9259e-03 |  7.288e+02 |         5.000 |             0 |
|          6 |       0.11 | 6.4180e-05 |  7.291e+02 |         5.000 |             0 |
=====================================================================================
mdl =
ldaModel with properties:

NumTopics: 20
WordConcentration: 1
TopicConcentration: 5
CorpusTopicProbabilities: [1x20 double]
DocumentTopicProbabilities: [154x20 double]
TopicWordProbabilities: [3092x20 double]
Vocabulary: [1x3092 string]
TopicOrder: 'initial-fit-probability'
FitInfo: [1x1 struct]

Predict the top topics for an array of new documents.

newDocuments = tokenizedDocument([
"what's in a name? a rose by any other name would smell as sweet."
"if music be the food of love, play on."]);
topicIdx = predict(mdl,newDocuments)
topicIdx = 2×1

19
8

Visualize the predicted topics using word clouds.

figure
subplot(1,2,1)
wordcloud(mdl,topicIdx(1));
title("Topic " + topicIdx(1))
subplot(1,2,2)
wordcloud(mdl,topicIdx(2));
title("Topic " + topicIdx(2))