cosineSimilarity

Document similarities with cosine similarity

Syntax

similarities = cosineSimilarity(documents)

similarities = cosineSimilarity(documents,queries)

similarities = cosineSimilarity(bag)

similarities = cosineSimilarity(bag,queries)

similarities = cosineSimilarity(M)

similarities = cosineSimilarity(M1,M2)

Description

similarities = cosineSimilarity(documents) returns the pairwise cosine similarities for the specified documents using the tf-idf matrix derived from their word counts. The score in similarities(i,j) represents the similarity between documents(i) and documents(j).

similarities = cosineSimilarity(documents,queries) returns similarities between documents and queries using tf-idf matrices derived from the word counts in documents. The score in similarities(i,j) represents the similarity between documents(i) and queries(j).

similarities = cosineSimilarity(bag) returns pairwise similarities for the documents encoded by the specified bag-of-words or bag-of-n-grams model using the tf-idf matrix derived from the word counts in bag. The score in similarities(i,j) represents the similarity between the ith and jth documents encoded by bag.

similarities = cosineSimilarity(bag,queries) returns similarities between the documents encoded by the bag-of-words or bag-of-n-grams model bag and queries using tf-idf matrices derived from the word counts in bag. The score in similarities(i,j) represents the similarity between the ith document encoded by bag and queries(j).

similarities = cosineSimilarity(M) returns similarities for the data encoded in the row vectors of the matrix M. The score in similarities(i,j) represents the similarity between M(i,:) and M(j,:).

similarities = cosineSimilarity(M1,M2) returns similarities between the documents encoded in the matrices M1 and M2. The score in similarities(i,j) corresponds to the similarity between M1(i,:) and M2(j,:).

Examples

Similarity Between Documents

Create an array of tokenized documents.

textData = [
    "the quick brown fox jumped over the lazy dog"
    "the fast brown fox jumped over the lazy dog"
    "the lazy dog sat there and did nothing"
    "the other animals sat there watching"];
documents = tokenizedDocument(textData)

documents = 
  4×1 tokenizedDocument:

    9 tokens: the quick brown fox jumped over the lazy dog
    9 tokens: the fast brown fox jumped over the lazy dog
    8 tokens: the lazy dog sat there and did nothing
    6 tokens: the other animals sat there watching

Calculate the similarities between them using the cosineSimilarity function. The output is a sparse matrix.

similarities = cosineSimilarity(documents);

Visualize the similarities between the documents in a heat map.

figure
heatmap(similarities);
xlabel("Document")
ylabel("Document")
title("Cosine Similarities")

Scores close to one indicate strong similarity. Scores close to zero indicate weak similarity.

Similarity to Query

Create an array of input documents.

str = [
    "the quick brown fox jumped over the lazy dog"
    "the fast fox jumped over the lazy dog"
    "the dog sat there and did nothing"
    "the other animals sat there watching"];
documents = tokenizedDocument(str)

documents = 
  4×1 tokenizedDocument:

    9 tokens: the quick brown fox jumped over the lazy dog
    8 tokens: the fast fox jumped over the lazy dog
    7 tokens: the dog sat there and did nothing
    6 tokens: the other animals sat there watching

Create an array of query documents.

str = [
    "a brown fox leaped over the lazy dog"
    "another fox leaped over the dog"];
queries = tokenizedDocument(str)

queries = 
  2×1 tokenizedDocument:

    8 tokens: a brown fox leaped over the lazy dog
    6 tokens: another fox leaped over the dog

Calculate the similarities between input and query documents using the cosineSimilarity function. The output is a sparse matrix.

similarities = cosineSimilarity(documents,queries);

Visualize the similarities of the documents in a heat map.

figure
heatmap(similarities);
xlabel("Query Document")
ylabel("Input Document")
title("Cosine Similarities")

Scores close to one indicate strong similarity. Scores close to zero indicate weak similarity.

Document Similarities Using Bag-of-Words Model

Create a bag-of-words model from the text data in sonnets.csv.

filename = "sonnets.csv";
tbl = readtable(filename,'TextType','string');
textData = tbl.Sonnet;
documents = tokenizedDocument(textData);
bag = bagOfWords(documents)

bag = 
  bagOfWords with properties:

        NumWords: 3527
          Counts: [154×3527 double]
      Vocabulary: ["From"    "fairest"    "creatures"    "we"    "desire"    "increase"    ","    "That"    "thereby"    "beauty's"    "rose"    "might"    "never"    "die"    "But"    "as"    "the"    "riper"    "should"    "by"    …    ] (1×3527 string)
    NumDocuments: 154

Calculate similarities between the sonnets using the cosineSimilarity function. The output is a sparse matrix.

similarities = cosineSimilarity(bag);

Visualize the similarities of the first five documents in a heat map.

figure
heatmap(similarities(1:5,1:5));
xlabel("Document")
ylabel("Document")
title("Cosine Similarities")

Scores close to one indicate strong similarity. Scores close to zero indicate weak similarity.

Similarities Within Word Count Matrix

For bag-of-words input, the cosineSimilarity function calculates the cosine similarity using the tf-idf matrix derived from the model. To compute the cosine similarities on the word count vectors directly, input the word counts to the cosineSimilarity function as a matrix.

Create a bag-of-words model from the text data in sonnets.csv.

filename = "sonnets.csv";
tbl = readtable(filename,'TextType','string');
textData = tbl.Sonnet;
documents = tokenizedDocument(textData);
bag = bagOfWords(documents)

bag = 
  bagOfWords with properties:

        NumWords: 3527
          Counts: [154×3527 double]
      Vocabulary: ["From"    "fairest"    "creatures"    "we"    "desire"    "increase"    ","    "That"    "thereby"    "beauty's"    "rose"    "might"    "never"    "die"    "But"    "as"    "the"    "riper"    "should"    "by"    …    ] (1×3527 string)
    NumDocuments: 154

Get the matrix of word counts from the model.

M = bag.Counts;

Calculate the cosine document similarities of the word count matrix using the cosineSimilarity function. The output is a sparse matrix.

similarities = cosineSimilarity(M);

Visualize the similarities of the first five documents in a heat map.

figure
heatmap(similarities(1:5,1:5));
xlabel("Document")
ylabel("Document")
title("Cosine Similarities")

Scores close to one indicate strong similarity. Scores close to zero indicate weak similarity.

Input Arguments

documents — Input documents

tokenizedDocument array | string array | cell array of character vectors

Input documents, specified as a tokenizedDocument array, a string array of words, or a cell array of character vectors. If documents is not a tokenizedDocument array, then it must be a row vector representing a single document, where each element is a word. To specify multiple documents, use a tokenizedDocument array.

bag — Input model

bagOfWords object | bagOfNgrams object

Input bag-of-words or bag-of-n-grams model, specified as a bagOfWords object or a bagOfNgrams object. If bag is a bagOfNgrams object, then the function treats each n-gram as a single word.

queries — Set of query documents

tokenizedDocument array | string array of words | cell array of character vectors

Set of query documents, specified as one of the following:

• A tokenizedDocument array

• A 1-by-N string array representing a single document, where each element is a word

• A 1-by-N cell array of character vectors representing a single document, where each element is a word

To compute term frequency and inverse document frequency statistics, the function encodes queries using a bag-of-words model. The model it uses depends on the syntax you call it with. If your syntax specifies the input argument documents, then it uses bagOfWords(documents). If your syntax specifies bag, then the function encodes queries using bag then uses the resulting tf-idf matrix.

M — Input data

matrix

Input data, specified as a matrix. For example, M can be a matrix of word or n-gram counts or a tf-idf matrix.

Data Types: double
Complex Number Support: Yes

Output Arguments

similarities — Cosine similarity scores

sparse matrix

Cosine similarity scores, returned as a sparse matrix:

• Given a single array of tokenized documents, similarities is a N-by-N symmetric matrix, where similarities(i,j) represents the similarity between documents(i) and documents(j), and N is the number of input documents.

• Given an array of tokenized documents and a set of query documents, similarities is an N1-by-N2 matrix, where similarities(i,j) represents the similarity between documents(i) and the jth query document, and N1 and N2 represents the number of documents in documents and queries, respectively.

• Given a single bag-of-words or bag-of-n-grams model, similarities is a bag.NumDocuments-by-bag.NumDocuments symmetric matrix, where similarities(i,j) represents the similarity between the ith and jth documents encoded by bag.

• Given a bag-of-words or bag-of-n-grams models and a set of query documents, similarities is a bag.NumDocuments-by-N2 matrix, where similarities(i,j) represents the similarity between the ith document encoded by bag and the jth document in queries, and N2 corresponds to the number of documents in queries.

• Given a single matrix, similarities is a size(M,1)-by-size(M,1) symmetric matrix, where similarities(i,j) represents the similarity between M(i,:) and M(j,:).

• Given two matrices, similarities is an size(M1,1)-by-size(M2,1) matrix, where similarities(i,j) represents the similarity between M1(i,:) and M2(j,:).

Version History

Introduced in R2020a

R2024b: Input data can be complex-valued

The input data argument M now supports complex matrices.