# lsaModel

Latent semantic analysis (LSA) model

## Description

A latent semantic analysis (LSA) model discovers relationships between documents and the words that they contain. An LSA model is a dimensionality reduction tool useful for running low-dimensional statistical models on high-dimensional word counts. 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 LSA model using the `fitlsa`

function.

## Properties

`NumComponents`

— Number of components

nonnegative integer

Number of components, specified as a nonnegative integer. The number of
components is the dimensionality of the result vectors. Changing the value
of `NumComponents`

changes the length of the resulting
vectors, without influencing the initial values. You can only set
`NumComponents`

to be less than or equal to the
number of components used to fit the LSA model.

**Example: **100

`FeatureStrengthExponent`

— Exponent scaling feature component strengths

nonnegative scalar

Exponent scaling feature component strengths for the
`DocumentScores`

and `WordScores`

properties, and the `transform`

function, specified as a
nonnegative scalar. The LSA model scales the properties by their singular
values (feature strengths), with an exponent of
`FeatureStrengthExponent/2`

.

**Example: **2.5

`ComponentWeights`

— Component weights

numeric vector

Component weights, specified as a numeric vector. The component weights of
an LSA model are the singular values, squared.
`ComponentWeights`

is a
1-by-`NumComponents`

vector where the
*j*th entry corresponds to the weight of component
*j*. The components are ordered by decreasing weights.
You can use the weights to estimate the importance of components.

`DocumentScores`

— Score vectors per input document

matrix

Score vectors per input document, specified as a matrix. The document
scores of an LSA model are the score vectors in lower dimensional space of
each document used to fit the LSA model. `DocumentScores`

is a *D*-by-`NumComponents`

matrix where
*D* is the number of documents used to fit the LSA
model. The *(i,j)*th entry of
`DocumentScores`

corresponds to the score of
component *j* in document *i*.

`WordScores`

— Word scores per component

matrix

Word scores per component, specified as a matrix. The word scores of an
LSA model are the scores of each word in each component of the LSA model.
`WordScores`

is a
*V*-by-`NumComponents`

matrix where
*V* is the number of words in
`Vocabulary`

. The *(v,j)*th entry of
`WordScores`

corresponds to the score of word
*v* in component *j*.

`Vocabulary`

— Unique words in model

string vector

Unique words in the model, specified as a string vector.

**Data Types: **`string`

## Object Functions

`transform` | Transform documents into lower-dimensional space |

## Examples

### Fit LSA Model

Fit a Latent Semantic Analysis model to a collection of documents.

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: ["fairest" "creatures" "desire" "increase" "thereby" "beautys" "rose" "might" "never" "die" "riper" "time" "decease" "tender" "heir" "bear" "memory" "thou" "contracted" ... ] NumWords: 3092 NumDocuments: 154

Fit an LSA model with 20 components.

numComponents = 20; mdl = fitlsa(bag,numComponents)

mdl = lsaModel with properties: NumComponents: 20 ComponentWeights: [2.7866e+03 515.5889 443.6428 316.4191 295.4065 261.8927 226.1649 186.2160 170.6413 156.6033 151.5275 146.2553 141.6741 135.5318 134.1694 128.9931 124.2382 122.2931 116.5035 116.2590] DocumentScores: [154x20 double] WordScores: [3092x20 double] Vocabulary: ["fairest" "creatures" "desire" "increase" "thereby" "beautys" "rose" "might" "never" "die" "riper" "time" "decease" "tender" "heir" "bear" "memory" "thou" ... ] FeatureStrengthExponent: 2

Transform new documents into lower dimensional space using the LSA model.

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."]); dscores = transform(mdl,newDocuments)

`dscores = `*2×20*
0.1338 0.1623 0.1680 -0.0541 -0.2464 -0.0134 0.2604 0.0205 0.1127 0.0627 0.3311 -0.2327 0.1689 -0.2695 0.0228 0.1241 0.1198 0.2535 -0.0607 0.0305
0.2547 0.5576 -0.0095 0.5660 -0.0643 -0.1236 -0.0082 -0.0522 -0.0690 -0.0330 0.0385 0.0803 -0.0373 0.0384 -0.0005 0.1943 0.0207 0.0278 0.0001 -0.0469

### Calculate Document Similarity

Create a bag-of-words model from some text data.

str = [ "I enjoy ham, eggs and bacon for breakfast." "I sometimes skip breakfast." "I eat eggs and ham for dinner." ]; documents = tokenizedDocument(str); bag = bagOfWords(documents);

Fit an LSA model with two components. Set the feature strength exponent to 0.5.

numComponents = 2; exponent = 0.5; mdl = fitlsa(bag,numComponents, ... 'FeatureStrengthExponent',exponent)

mdl = lsaModel with properties: NumComponents: 2 ComponentWeights: [16.2268 4] DocumentScores: [3x2 double] WordScores: [14x2 double] Vocabulary: ["I" "enjoy" "ham" "," "eggs" "and" "bacon" "for" "breakfast" "." "sometimes" "skip" "eat" "dinner"] FeatureStrengthExponent: 0.5000

Calculate the cosine distance between the documents score vectors using `pdist`

. View the distances in a matrix `D`

using `squareform`

. `D(i,j)`

denotes the distance between document `i`

and `j`

.

```
dscores = mdl.DocumentScores;
distances = pdist(dscores,'cosine');
D = squareform(distances)
```

`D = `*3×3*
0 0.6244 0.1489
0.6244 0 1.1670
0.1489 1.1670 0

Visualize the similarity between documents by plotting the document score vectors in a compass plot.

figure compass(dscores(1,1),dscores(1,2),'red') hold on compass(dscores(2,1),dscores(2,2),'green') compass(dscores(3,1),dscores(3,2),'blue') hold off title("Document Scores") legend(["Document 1" "Document 2" "Document 3"],'Location','bestoutside')

## Version History

**Introduced in R2017b**

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