Computations based on Latent Semantic Analysis

Description

Offers methods and functions for working with Vector Space Models of semantics/distributional semantic models/word embeddings. The package was originally written for Latent Semantic Analysis (LSA), but can be used with all vector space models. Such models are created by algorithms working on a corpus of text documents. Those algorithms achieve a high-dimensional vector representation for word (and document) meanings. The exact LSA algorithm is described in Martin & Berry (2007).

Such a representation allows for the computation of word (and document) similarities, for example by computing cosine values of angles between two vectors.

The focus of this package

This package is not designed to create LSA semantic spaces. In R, this functionality is provided by the package lsa. The focus of the package LSAfun is to provide functions to be applied on existing LSA (or other) semantic spaces, such as

1. Similarity Computations

2. Neighborhood Computations

3. Applied Functions

4. Composition Methods

Video Tutorials

A video tutorial for this package can be found here: https://youtu.be/IlwIZvM2kg8

A video tutorial for using this package with vision-based representations from deep convolutional neural networks can be found here: https://youtu.be/0PNrXraWfzI

How to obtain a semantic space

LSAfun comes with one example LSA space, the wonderland space.

This package can also directly use LSA semantic spaces created with the lsa-package. Thus, it allows the user to use own LSA spaces. (Note that the function lsa gives a list of three matrices. Of those, the term matrix U should be used.)

The lsa package works with (very) small corpora, but gets difficulties in scaling up to larger corpora. In this case, it is recommended to use specialized software for creating semantic spaces, such as

• S-Space (Jurgens & Stevens, 2010), available here

• SemanticVectors (Widdows & Ferraro, 2008), available here

• gensim (Rehurek & Sojka, 2010), available here

• DISSECT (Dinu, Pham, & Baroni, 2013), available here

Downloading semantic spaces

Another possibility is to use one of the semantic spaces provided at https://sites.google.com/site/fritzgntr/software-resources. These are stored in the .rda format. To load one of these spaces into the R workspace, save them into a directory, set the working directory to that directory, and load the space using load().

Author(s)

Fritz Guenther

Compute cosine similarity

Description

Computes the cosine similarity for two single words

Usage

Cosine(x,y,tvectors=tvectors)

Arguments

Details

Instead of using numeric vectors, as the cosine() function from the lsa package does, this function allows for the direct computation of the cosine between two single words (i.e. Characters). which are automatically searched for in the LSA space given in as tvectors.

Value

The cosine similarity as a numeric

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Dennis, S. (2007). How to use the LSA Web Site. In T. K. Landauer, D. S. McNamara, S. Dennis, & W. Kintsch (Eds.), Handbook of Latent Semantic Analysis (pp. 35-56). Mahwah, NJ: Erlbaum.

http://wordvec.colorado.edu/

See Also

distance asym

Examples

data(wonderland)

Cosine("alice","rabbit",tvectors=wonderland)

Answers Multiple Choice Questions

Description

Selects the nearest word to an input out of a set of options

Usage

MultipleChoice(x,y,tvectors=tvectors,remove.punctuation=TRUE, stopwords = NULL,
   method ="Add", all.results=FALSE)

Arguments

Details

Computes all the cosines between a given sentence/document or word and multiple answer options. Then selects the nearest option to the input (the option with the highest cosine). This function relies entirely on the costring function.

A note will be displayed whenever not all words of one answer alternative are found in the semantic space. Caution: In that case, the function will still produce a result, by omitting the words not found in the semantic space. Depending on the specific requirements of a task, this may compromise the results. Please check your input when you receive this message.

A warning message will be displayed whenever no word of one answer alternative is found in the semantic space.

Using method="Analogy" requires the input in both x and y to only consist of word pairs (for example x = c("helmet head") and y = c("kneecap knee", "atmosphere earth", "grass field")). In that case, the function will try to identify the best-fitting answer in y by applying the king - man + woman = queen rationale to solve man : king = woman : ? (Mikolov et al., 2013): In that case, one should also have king - man = queen - woman. With method="Analogy", the function will compute the difference between the normalized vectors head - helmet, and search the nearest of the vector differences knee - kneecap, earth - atmosphere, and field - grass.

Value

If all.results=FALSE (default), the function will only return the best answer as a character string. If all.results=TRUE, it will return a named numeric vector, where the names are the different answer options in y and the numeric values their respective cosine similarity to x, sorted by decreasing similarity.

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Mikolov, T., Yih, W. T., & Zweig, G. (2013). Linguistic regularities in continuous space word representations. In Proceedings of the 2013 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT-2013). Association for Computational Linguistics.

See Also

cosine, Cosine, costring, multicostring, analogy

Examples

data(wonderland)

LSAfun:::MultipleChoice("who does the march hare celebrate his unbirthday with?",
                 c("mad hatter","red queen","caterpillar","cheshire Cat"),
                 tvectors=wonderland)

Compute Vector for Predicate-Argument-Expressions

Description

Computes vectors for complex expressions of type PREDICATE[ARGUMENT] by applying the method of Kintsch (2001) (see Details).

Usage

Predication(P,A,m,k,tvectors=tvectors,norm="none")

Arguments

Details

The vector for the expression is computed following the Predication Process by Kintsch (2001):

The m nearest neighbors to the Predicate are computed. Of those, the k nearest neighbors to the Argument are selected. The vector for the expression is then computed as the sum of Predicate vector, Argument vector, and the vectors of those k neighbors (the k-neighborhood).

Value

An object of class Pred: This object is a list consisting of:

Author(s)

Fritz Guenther

References

Kintsch, W. (2001). Predication. Cognitive Science, 25, 173-202.

See Also

cosine, neighbors, multicos, compose

Examples

data(wonderland)

Predication(P="mad",A="hatter",m=20,k=3,tvectors=wonderland)

Semantic neighborhood density

Description

Returns semantic neighborhood with semantic neighborhood size and density

Usage

SND(x,n=NA,threshold=3.5,tvectors=tvectors)

Arguments

Details

There are two principle approaches to determine the semantic neighborhood of a target word:

• Set an a priori size of the semantic neighborhood to a fixed value n (e.g., Marelli & Baroni, 2015). The n closest words to the target word are counted as its semantic neighbors. The semantic neighborhood size is then necessarily n; the semantic neighborhood density is the mean similarity between these neighbors and the target word (see also plausibility)

• Determine the semantic neighborhood based on a similarity threshold; all words whose similarity to the target word exceeds this threshold are counted as its semantic neighbors (e.g., Buchanan, Westbury, & Burgess, 2001). First, the similarity between the target word and all words in the semantic space is computed. These similarities are then transformed into z-scores. Traditionally, the threshold is set to z = 3.5 (e.g., Buchanan, Westbury, & Burgess, 2001).

If a single target word is used as x, this target word itself (which always has a similarity of 1 to itself) is excluded from these computations so that it cannot be counted as its own neighbor

Value

A list of three elements:

• neighbors: A names numeric vector of all identified neighbors, with the names being these neighbors and the values their similarity to x

• n_size: The number of neighbors as a numeric

• SND: The semantic neighborhood density (SND) as a numeric

Author(s)

Fritz Guenther

References

Buchanan, L., Westbury, C., & Burgess, C. (2001). Characterizing semantic space: Neighborhood effects in word recognition. Psychonomic Bulletin & Review, 8, 531-544.

Marelli, M., & Baroni, M. (2015). Affixation in semantic space: Modeling morpheme meanings with compositional distributional semantics. Psychological Review, 122, 485-515.

See Also

cosine, plot_neighbors, compose

Examples

data(wonderland)

SND("cheshire",n=20,tvectors=wonderland)

SND("alice",threshold=2,tvectors=wonderland)

Analogy

Description

Implements the king - man + woman = queen analogy solving algorithm

Usage

analogy(x1,x2,y1=NA,n,tvectors=tvectors)

Arguments

Details

The analogy task is a popular benchmark for vector space models of meaning/word embeddings. It is based on the rationale that proportinal analogies x1 is to x2 as y1 is to y2, like man : king = woman : ? (correct answer: queen), can be solved via the following operation on the respective word vectors (all normalized to unit norm) king - man + woman = queen (that is, the nearest vector to king - man + woman should be queen) (Mikolov et al., 2013).

The analogy() function comes in two variants, taking as input either three words (x1, x2, and y1) or two words (x1 and x2)

• The variant with three input words (x1, x2, and y1) implements the standard analogy solving algorithm for analogies of the type x1 : x2 = y1 : ?, searching the n nearest neighbors for x2 - x1 + y1 (all normalized to unit norm) as the best-fitting candidates for y2

• The variant with two input words (x1 and x2) only computes the difference between the two vectors (both normalized to unit norm) and the n nearest neighbors to the resulting difference vector

Value

Returns a list containing a numeric vector and the nearest neighbors to that vector:

• In the variant with three input words (x1, x2, and y1), returns:

  • y2_vec The result of x2 - x1 + y1 (all normalized to unit norm) as a numeric vector

  • y2_neighbors A named numeric vector of the n nearest neighbors to y2_vec. The neighbors are given as names of the vector, and their respective cosines to y2_vec as vector entries.

• In the variant with two input words (x1 and x2), returns:

  • x_diff_vec The result of x2 - x1 (both normalized to unit norm) as a numeric vector

  • x_diff_neighbors A named numeric vector of the n nearest neighbors to x_diff_vec. The neighbors are given as names of the vector, and their respective cosines to x_diff_vec as vector entries.

Author(s)

Fritz Guenther

References

Mikolov, T., Yih, W. T., & Zweig, G. (2013). Linguistic regularities in continuous space word representations. In Proceedings of the 2013 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT-2013). Association for Computational Linguistics.

See Also

neighbors

Examples

data(wonderland)

analogy(x1="hatter",x2="mad",y1="cat",n=10,tvectors=wonderland)

analogy(x1="hatter",x2="mad",n=10,tvectors=wonderland)

Asymmetric Similarity functions

Description

Compute various asymmetric similarities between words

Usage

asym(x,y,method,t=0,tvectors)

Arguments

Details

Asymmetric (or directional) similarities can be useful e.g. for examining hypernymy (category inclusion), for example the relation between dog and animal should be asymmetrical. The general idea is that, if one word is a hypernym of another (i.e. it is semantically narrower), then a significant number of dimensions that are salient in this word should also be salient in the semantically broader term (Lenci & Benotto, 2012).

In the formulas below, w_x(f) denotes the value of vector x on dimension f. Furthermore, F_x is the set of active dimensions of vector x. A dimension f is considered active if w_x(f) > t, with t being a pre-defined, free parameter.

The options for method are defined as follows (see Kotlerman et al., 2010) (1)):

• method = "weedsprec"

  weedsprec(u,v) = \frac{\sum\nolimits_{f \in F_u \cap F_v}w_u(f)}{\sum\nolimits_{f \in F_u}w_u(f)}

• method = "cosweeds"

  cosweeds(u,v) = \sqrt{weedsprec(u,v) \times cosine(u,v)}

• method = "clarkede"

  clarkede(u,v) = \frac{\sum\nolimits_{f \in F_u \cap F_v}min(w_u(f),w_v(f))}{\sum\nolimits_{f \in F_u}w_u(f)}

• method = "invcl"

  invcl(u,v) = \sqrt{clarkede(u,v)\times(1-clarkede(u,v)})

• method = "kintsch"

  Unlike the other methods, this one is not derived from the logic of hypernymy, but rather from asymmetrical similarities between words due to different amounts of knowledge about them. Here, asymmteric similarities between two words are computed by taking into account the vector length (i.e. the amount of information about those words). This is done by projecting one vector onto the other, and normalizing this resulting vector by dividing its length by the length of the longer of the two vectors (Details in Kintsch, 2014, see References).

Value

A numeric giving the asymmetric similarity between x and y

Author(s)

Fritz Guenther

References

Kintsch, W. (2015). Similarity as a Function of Semantic Distance and Amount of Knowledge. Psychological Review, 121, 559-561.

Kotlerman, L., Dagan, I., Szpektor, I., & Zhitomirsky-Geffet, M (2010). Directional distributional similarity for lexical inference. Natural Language Engineering, 16, 359-389.

Lenci, A., & Benotto, G. (2012). Identifying hypernyms in distributional semantic spaces. In Proceedings of *SEM (pp. 75-79), Montreal, Canada.

See Also

Cosine conSIM

Examples

data(wonderland)

asym("alice","girl",method="cosweeds",t=0,tvectors=wonderland)
asym("alice","rabbit",method="cosweeds",tvectors=wonderland)

Centroid Analysis

Description

Performs a centroid analysis for a set of words

Usage

centroid_analysis(responses,targets = NULL,split=" ",unique.responses = FALSE,
reference.list = NULL,verbose = FALSE,rank.responses = FALSE,
tvectors=tvectors)

Arguments

Details

The centroid analysis computes the average vector for a set of words. The intended use case is that these words are responses towards a given concept; the centroid then serves as the estimated vector representation for that concept.

Value

An object of class centroid_analysis. This object is a list consisting of:

Author(s)

Fritz Guenther, Aliona Petrenco

References

Pugacheva, V., & Günther, F. (2024). Lexical choice and word formation in a taboo game paradigm. Journal of Memory and Language, 135, 104477.

See Also

cosine, Cosine, neighbors

Examples

data(wonderland)
centroid_analysis(responses=c("mouse","rabbit","cat","king","queen"),targets=c("alice","hare"),
          tvectors=wonderland)

Random Target Selection

Description

Randomly samples words within a given similarity range to the input

Usage

choose.target(x,lower,upper,n,tvectors=tvectors)

Arguments

Details

Computes cosine values between the input x and all the word vectors in tvectors. Then only selects words with a cosine similarity between lower and upper to the input, and randomly samples n of these words.

This function is designed for randomly selecting target words with a predefined similarity towards a given prime word (or sentence/document).

Value

A named numeric vector. The names of the vector give the target words, the entries their respective cosine similarity to the input.

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

See Also

cosine, Cosine, neighbors

Examples

data(wonderland)

choose.target("mad hatter",lower=.2,upper=.3,
                n=20, tvectors=wonderland)

Coherence of a text

Description

Computes coherence of a given paragraph/document

Usage

coherence(x,split=c(".","!","?"),tvectors=tvectors, remove.punctuation=TRUE, 
stopwords = NULL, method ="Add")

Arguments

Details

This function applies the method described in Landauer & Dumais (1997): The local coherence is the cosine between two adjacent sentences. The global coherence is then computed as the mean value of these local coherences.

The format of x should be of the kind x <- "sentence1. sentence2. sentence3" Every sentence can also just consist of one single word.

To import a document Document.txt to from a directory for coherence computation, set your working directory to this directory using setwd(). Then use the following command lines:

fileName1 <- "Alice_in_Wonderland.txt"

x <- readChar(fileName1, file.info(fileName1)$size)

In the traditional LSA approach, the vector D for a document (or a sentence) consisting of the words (t1, . , tn) is computed as

D = \sum\limits_{i=1}^n t_n

This is the default method (method="Add") for this function. Alternatively, this function provided the possibility of computing the document vector from its word vectors using element-wise multiplication (see Mitchell & Lapata, 2010 and compose).

A note will be displayed whenever not all words of one input string are found in the semantic space. Caution: In that case, the function will still produce a result, by omitting the words not found in the semantic space. Depending on the specific requirements of a task, this may compromise the results. Please check your input when you receive this message.

A warning message will be displayed whenever no word of one input string is found in the semantic space.

Value

A list of two elements; the first element ($local) contains the local coherences as a numeric vector, the second element ($global) contains the global coherence as a numeric.

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Mitchell, J., & Lapata, M. (2010). Composition in Distributional Models of Semantics. Cognitive Science, 34, 1388-1429.

See Also

cosine, Cosine, costring

Examples

data(wonderland)

coherence ("there was certainly too much of it in the air. even the duchess
sneezed occasionally; and as for the baby, it was sneezing and howling
alternately without a moment's pause. the only things in the kitchen
that did not sneeze, were the cook, and a large cat which was sitting on
the hearth and grinning from ear to ear.",
tvectors=wonderland)

Two-Word Composition

Description

Computes the vector of a complex expression p consisting of two single words u and v, following the methods examined in Mitchell & Lapata (2008) (see Details).

Usage

## Default 
compose(x,y,method="Add", a=1,b=1,c=1,m,k,lambda=2,
      tvectors=tvectors, norm="none")

Arguments

Details

Let p be the vector with entries p_i for the two-word phrase consisiting of u with entries u_i and v with entries v_i. The different composition methods as described by Mitchell & Lapata (2008, 2010) are as follows:

• Additive Model (method = "Add")

  p_i = u_i + v_i

• Weighted Additive Model (method = "WeightAdd")

  p_i = a*u_i + b*v_i

• Multiplicative Model (method = "Multiply")

  p_i = u_i * v_i

• Combined Model (method = "Combined")

  p_i = a*u_i + b*v_i + c*u_i*v_i

• Predication (method = "Predication") (see Predication)

  If method="Predication" is used, x will be taken as Predicate and y will be taken as Argument of the phrase (see Examples)

• Circular Convolution (method = "CConv")

  p_i = \sum\limits_{j} u_j * v_{i-j}

  ,

  where the subscripts of v are interpreted modulo n with n = length(x)(= length(y))

• Dilation (method = "Dilation")

  p = (u*u)*v + (\lambda - 1)*(u*v)*u

  ,

  with (u*u) being the dot product of u and u (and (u*v) being the dot product of u and v).

The Add, Multiply, and CConv methods are symmetrical composition methods,

i.e. compose(x="word1",y="word2") will give the same results as compose(x="word2",y="word1")

On the other hand, WeightAdd, Combined, Predication and Dilation are asymmetrical, i.e. compose(x="word1",y="word2") will give different results than compose(x="word2",y="word1")

Value

The phrase vector as a numeric vector

Author(s)

Fritz Guenther

References

Kintsch, W. (2001). Predication. Cognitive science, 25, 173-202.

Mitchell, J., & Lapata, M. (2008). Vector-based Models of Semantic Composition. In Proceedings of ACL-08: HLT (pp. 236-244). Columbus, Ohio.

Mitchell, J., & Lapata, M. (2010). Composition in Distributional Models of Semantics. Cognitive Science, 34, 1388-1429.

See Also

Predication

Examples

data(wonderland)

compose(x="mad",y="hatter",method="Add",tvectors=wonderland)

compose(x="mad",y="hatter",method="Combined",a=1,b=2,c=3,
tvectors=wonderland)

compose(x="mad",y="hatter",method="Predication",m=20,k=3,
tvectors=wonderland)

compose(x="mad",y="hatter",method="Dilation",lambda=3,
tvectors=wonderland)

Similarity in Context

Description

Compute Similarity of a word with a set of two other test words, given a third context word

Usage

conSIM(x,y,z,c,tvectors=tvectors)

Arguments

Details

Following the example from Kintsch (2014): If one has to judge the similarity between France one the one hand and the test words Germany and Spain on the other hand, this similarity judgement varies as a function of a fourth context word. If Portugal is given as a context word, France is considered to be more similar to Germany than to Spain, and vice versa for the context word Poland. Kintsch (2014) proposed a context sensitive, asymmetrical similarity measure for cases like this, which is implemented here

Value

A list of two similarity values

SIM_XY_zc: Similarity of x and y, given the alternative z and the context c

SIM_XZ_yc: Similarity of x and z, given the alternative y and the context c

Author(s)

Fritz Guenther

References

Kintsch, W. (2015). Similarity as a Function of Semantic Distance and Amount of Knowledge. Psychological Review, 121, 559-561.

Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327-352.

See Also

Cosine asym

Examples

data(wonderland)

conSIM(x="rabbit",y="alice",z="hatter",c="dormouse",tvectors=wonderland)

Sentence Comparison

Description

Computes cosine values between sentences and/or documents

Usage

costring(x,y,tvectors=tvectors,split=" ",remove.punctuation=TRUE, 
stopwords = NULL, method ="Add")

Arguments

Details

This function computes the cosine between two documents (or sentences) or the cosine between a single word and a document (or sentence).

In the traditional LSA approach, the vector D for a document (or a sentence) consisting of the words (t1, . , tn) is computed as

D = \sum\limits_{i=1}^n t_n

This is the default method (method="Add") for this function. Alternatively, this function provided the possibility of computing the document vector from its word vectors using element-wise multiplication (see Mitchell & Lapata, 2010 and compose).

The format of x (or y) can be of the kind x <- "word1 word2 word3" , but also of the kind x <- c("word1", "word2", "word3"). This allows for simple copy&paste-inserting of text, but also for using character vectors, e.g. the output of neighbors().

To import a document Document.txt to from a directory for comparisons, set your working directory to this directory using setwd(). Then use the following command lines:

fileName1 <- "Alice_in_Wonderland.txt"

x <- readChar(fileName1, file.info(fileName1)$size)

A note will be displayed whenever not all words of one input string are found in the semantic space. Caution: In that case, the function will still produce a result, by omitting the words not found in the semantic space. Depending on the specific requirements of a task, this may compromise the results. Please check your input when you receive this message.

A warning message will be displayed whenever no word of one input string is found in the semantic space.

Value

A numeric giving the cosine between the input documents/sentences

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Dennis, S. (2007). How to use the LSA Web Site. In T. K. Landauer, D. S. McNamara, S. Dennis, & W. Kintsch (Eds.), Handbook of Latent Semantic Analysis (pp. 35-56). Mahwah, NJ: Erlbaum.

Mitchell, J., & Lapata, M. (2010). Composition in Distributional Models of Semantics. Cognitive Science, 34, 1388-1429.

http://wordvec.colorado.edu/

See Also

cosine, Cosine, multicos, multidocs, multicostring

Examples

data(wonderland)
costring("alice was beginning to get very tired.",
      "a white rabbit with a clock ran close to her.",
      tvectors=wonderland)

Compute distance

Description

Computes distance metrics for two single words

Usage

distance(x,y,method="euclidean",tvectors=tvectors)

Arguments

Details

Computes Minkowski metrics, i.e. geometric distances between the vectors for two given words. Possible options are euclidean for the Euclidean Distance, d(x,y) = \sqrt{\sum{(x-y)^2}}, and cityblock for the City Block metric, d(x,y) = \sum{|x-y|}

Value

The distance value as a numeric

Author(s)

Fritz Guenther

See Also

Cosine asym

Examples

data(wonderland)

distance("alice","rabbit",method="euclidean",tvectors=wonderland)

Summarize a text

Description

Selects sentences from a text that best describe its topic

Usage

genericSummary(text,k,split=c(".","!","?"),min=5,...)

Arguments

Details

Applies the method of Gong & Liu (2001) for generic text summarization of text document D via Latent Semantic Analysis:

1. Decompose the document D into individual sentences, and use these sentences to form the candidate sentence set S, and set k = 1.

2. Construct the terms by sentences matrix A for the document D.

3. Perform the SVD on A to obtain the singular value matrix \Sigma, and the right singular vector matrix V^t. In the singular vector space, each sentence i is represented by the column vector \psi _i = [v_i1, v_i2, ... , v_ir]^t of V^t.

4. Select the k'th right singular vector from matrix V^t.

5. Select the sentence which has the largest index value with the k'th right singular vector, and include it in the summary.

6. If k reaches the predefined number, terminate the op- eration; otherwise, increment k by one, and go to Step 4.

(Cited directly from Gong & Liu, 2001, p. 21)

Value

A character vector of the length k

Author(s)

Fritz Guenther

See Also

textmatrix, lsa, svd

Examples

D <- "This is just a test document. It is set up just to throw some random 
sentences in this example. So do not expect it to make much sense. Probably, even 
the summary won't be very meaningful. But this is mainly due to the document not being
meaningful at all. For test purposes, I will also include a sentence in this 
example that is not at all related to the rest of the document. Lions are larger than cats."

genericSummary(D,k=1)

Vector x Vector Comparison

Description

Computes a cosine matrix from given word vectors

Usage

multicos(x,y=x,tvectors=tvectors)

Arguments

Details

Submit a character vector consisting of n words to get a n x n cosine matrix of all their pairwise cosines.

Alternatively, submit two different character vectors to get their pairwise cosines. Single words are also possible arguments.

Also allows for computation of cosines between a given numeric vector with the same dimensionality as the LSA space and a vector consisting of n words.

Value

A matrix containing the pairwise cosines of x and y

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Dennis, S. (2007). How to use the LSA Web Site. In T. K. Landauer, D. S. McNamara, S. Dennis, & W. Kintsch (Eds.), Handbook of Latent Semantic Analysis (pp. 35-56). Mahwah, NJ: Erlbaum.

http://wordvec.colorado.edu/

See Also

cosine, Cosine, costring, multicostring

Examples

data(wonderland)
multicos("mouse rabbit cat","king queen",
          tvectors=wonderland)

Sentence x Vector Comparison

Description

Computes cosines between a sentence/ document and multiple words

Usage

multicostring(x,y,tvectors=tvectors,split=" ",remove.punctuation=TRUE, 
stopwords = NULL, method ="Add")

Arguments

Details

The format of x (or y) can be of the kind x <- "word1 word2 word3" , but also of the kind x <- c("word1", "word2", "word3"). This allows for simple copy&paste-inserting of text, but also for using character vectors, e.g. the output of neighbors.

Both x and y can also just consist of one single word. In the traditional LSA approach, the vector D for the document (or sentence) x consisting of the words (t1, . , tn) is computed as

D = \sum\limits_{i=1}^n t_n

This is the default method (method="Add") for this function. Alternatively, this function provided the possibility of computing the document vector from its word vectors using element-wise multiplication (see Mitchell & Lapata, 2010 and compose). See also costring).

A note will be displayed whenever not all words of one input string are found in the semantic space. Caution: In that case, the function will still produce a result, by omitting the words not found in the semantic space. Depending on the specific requirements of a task, this may compromise the results. Please check your input when you receive this message.

A warning message will be displayed whenever no word of one input string is found in the semantic space.

Value

A numeric giving the cosine between the input sentences/documents

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Dennis, S. (2007). How to use the LSA Web Site. In T. K. Landauer, D. S. McNamara, S. Dennis, & W. Kintsch (Eds.), Handbook of Latent Semantic Analysis (pp. 35-56). Mahwah, NJ: Erlbaum.

Mitchell, J., & Lapata, M. (2010). Composition in Distributional Models of Semantics. Cognitive Science, 34, 1388-1429.

http://wordvec.colorado.edu/

See Also

cosine, Cosine, multicos, costring

Examples

data(wonderland)

multicostring("alice was beginning to get very tired.",
        "a white rabbit with a clock ran close to her.",
        tvectors=wonderland)

multicostring("suddenly, a cat appeared in the woods",
names(neighbors("cheshire",n=20,tvectors=wonderland)), 
tvectors=wonderland)

Comparison of sentence sets

Description

Computes cosine values between sets of sentences and/or documents

Usage

multidocs(x,y=x,chars=10,tvectors=tvectors,remove.punctuation=TRUE,
stopwords = NULL,method ="Add")

Arguments

Details

In the traditional LSA approach, the vector D for a document (or a sentence) consisting of the words (t1, . , tn) is computed as

D = \sum\limits_{i=1}^n t_n

This is the default method (method="Add") for this function. Alternatively, this function provided the possibility of computing the document vector from its word vectors using element-wise multiplication (see Mitchell & Lapata, 2010 and compose).

This function computes the cosines between two sets of documents (or sentences).

The format of x (or y) should be of the kind x <- c("this is the first text","here is another text") (or y <- c("this is a third text","and here is yet another text"))

A note will be displayed whenever not all words of one input string are found in the semantic space. Caution: In that case, the function will still produce a result, by omitting the words not found in the semantic space. Depending on the specific requirements of a task, this may compromise the results. Please check your input when you receive this message.

A warning message will be displayed whenever no word of one input string is found in the semantic space.

Value

A list of three elements:

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Dennis, S. (2007). How to use the LSA Web Site. In T. K. Landauer, D. S. McNamara, S. Dennis, & W. Kintsch (Eds.), Handbook of Latent Semantic Analysis (pp. 35-56). Mahwah, NJ: Erlbaum.

Mitchell, J., & Lapata, M. (2010). Composition in Distributional Models of Semantics. Cognitive Science, 34, 1388-1429.

http://wordvec.colorado.edu/

See Also

cosine, Cosine, multicos, costring

Examples

data(wonderland)
multidocs(x = c("alice was beginning to get very tired.",
                "the red queen greeted alice."),
          y = c("the mad hatter and the mare hare are having a party.",
                "the hatter sliced the cup of tea in half."), 
      tvectors=wonderland)

Find nearest neighbors

Description

Returns the n nearest words to a given word or sentence/document

Usage

neighbors(x,n,tvectors=tvectors)

Arguments

Details

The format of x should be of the kind x <- "word1 word2 word3" instead of

x <- c("word1", "word2", "word3") if sentences/documents are used as input. This allows for simple copy&paste-inserting of text.

To import a document Document.txt to from a directory for comparisons, set your working directory to this directory using setwd(). Then use the following command lines:

fileName1 <- "Alice_in_Wonderland.txt"

x <- readChar(fileName1, file.info(fileName1)$size).

Since x can also be chosen to be any vector of the active LSA Space, this function can be combined with compose() to compute neighbors of complex expressions (see examples)

Value

A named numeric vector. The neighbors are given as names of the vector, and their respective cosines to the input as vector entries.

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Dennis, S. (2007). How to use the LSA Web Site. In T. K. Landauer, D. S. McNamara, S. Dennis, & W. Kintsch (Eds.), Handbook of Latent Semantic Analysis (pp. 35-56). Mahwah, NJ: Erlbaum.

http://wordvec.colorado.edu/

See Also

cosine, plot_neighbors, compose

Examples

data(wonderland)

neighbors("cheshire",n=20,tvectors=wonderland) 

neighbors(compose("mad","hatter",method="Add",tvectors=wonderland),
n=20,tvectors=wonderland)

Normalize a vector

Description

Normalizes a character vector to a unit vector

Usage

normalize(x)

Arguments

Details

The (euclidean) norm of a vector x is defined as

||x|| = \sqrt{\Sigma(x^2)}

To normalize a vector to a unit vector u with ||u|| = 1, the following equation is applied:

x' = x/ ||x||

Value

The normalized vector as a numeric

Author(s)

Fritz Guenther

Examples

normalize(1:2)


## check vector norms:

x <- 1:2

sqrt(sum(x^2))              ## vector norm
sqrt(sum(normalize(x)^2))   ## norm = 1

A collection of five classic books

Description

This object is a list containing five classical books:

• Around the World in Eighty Days by Jules Verne

• The Three Musketeers by Alexandre Dumas

• Frankenstein by Mary Shelley

• Dracula by Bram Stoker

• The Strange Case of Dr Jekyll and Mr Hyde by Robert Stevenson

as single-element character vectors. All five books were taken from the Project Gutenberg homepage and contain formatting symbols, such as \n for breaks.

Usage

data(oldbooks)

Format

A named list containing five character vectors as elements

Source

Project Gutenberg

References

Dumas, A. (1844). The Three Musketeers. Retrieved from http://www.gutenberg.org/ebooks/1257

Shelley, M. W. (1818). Frankenstein; Or, The Modern Prometheus. Retrieved from http://www.gutenberg.org/ebooks/84

Stevenson, R. L. (1886). The Strange Case of Dr. Jekyll and Mr. Hyde. Retrieved from http://www.gutenberg.org/ebooks/42

Stoker, B. (1897). Dracula. Retrieved from http://www.gutenberg.org/ebooks/345

Verne, J.(1873). Around the World in Eighty Days. Retrieved from http://www.gutenberg.org/ebooks/103

Pairwise cosine computation

Description

Computes pairwise cosine similarities

Usage

pairwise(x,y,tvectors=tvectors)

Arguments

Details

Computes pairwise cosine similarities for two vectors of words. These vectors need to have the same length.

Value

A vector of the same length as x and y containing the pairwise cosine similarities. Returns NA if at least one word in a pair is not found in the semantic space.

Author(s)

Fritz Guenther

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Dennis, S. (2007). How to use the LSA Web Site. In T. K. Landauer, D. S. McNamara, S. Dennis, & W. Kintsch (Eds.), Handbook of Latent Semantic Analysis (pp. 35-56). Mahwah, NJ: Erlbaum.

http://wordvec.colorado.edu/

See Also

cosine, Cosine, multicos,

Examples

data(wonderland)
pairwise("mouse rabbit cat","king queen hearts",
          tvectors=wonderland)

Compute word (or compound) plausibility

Description

Gives measures of semantic transparency (plausibility) for words or compounds

Usage

plausibility(x,method, n=10,stem,tvectors=tvectors)

Arguments

Details

The format of x should be of the kind x <- "word1 word2 word3" instead of x <- c("word1", "word2", "word3") if phrases of more than one word are used as input. Simple vector addition of the constituent vectors is then used to compute the phrase vector.

Since x can also be chosen to be any vector of the active LSA Space, this function can be combined with compose() to compute semantic transparency measures of complex expressions (see examples). Since semantic transparency methods were developed as measures for composed vectors, applying them makes most sense for those.

The methods are defined as follows:

• method = "n_density" The average cosine between a (word or phrase) vector and its n nearest neighbors, excluding the word itself when a single word is submitted (see also SND for a more detailed version)

• method = "length" The length of a vector (as computed by the standard Euclidean norm)

• method = "proximity" The cosine similarity between a compound vector and its stem word (for example between mad hatter and hatter or between objectify and object)

• method = "entropy" The entropy of the K-dimensional vector with the vector components t_1,...,t_K , as computed by

  entropy = \log{K} - \sum{t_i * \log{t_i}}

Value

The semantic transparency as a numeric

Author(s)

Fritz Guenther

References

Lazaridou, A., Vecchi, E., & Baroni, M. (2013). Fish transporters and miracle homes: How compositional distributional semantics can help NP parsing. In Proceedings of EMNLP 2013 (pp. 1908 - 1913). Seattle, WA.

Marelli, M., & Baroni, M. (2015). Affixation in semantic space: Modeling morpheme meanings with compositional distributional semantics. Psychological Review, 122,. 485-515.

Vecchi, E. M., Baroni, M., & Zamparelli, R. (2011). (Linear) maps of the impossible: Capturing semantic anomalies in distributional space. In Proceedings of the ACL Workshop on Distributional Semantics and Compositionality (pp. 1-9). Portland, OR.

See Also

Cosine, neighbors, compose, SND

Examples

data(wonderland)

plausibility("cheshire cat",method="n_density",n=10,tvectors=wonderland) 

plausibility(compose("mad","hatter",method="Multiply",tvectors=wonderland),
method="proximity",stem="hatter",tvectors=wonderland)

2D- or 3D-Plot of a list of sentences/documents

Description

2D or 3D-Plot of mutual word similarities to a given list of sentences/documents

Usage

plot_doclist(x,connect.lines="all",method="PCA",dims=3,
   axes=F,box=F,cex=1,chars=10,legend=T, size = c(800,800),
   alpha="graded",alpha.grade=1,col="rainbow",
   tvectors=tvectors,remove.punctuation=TRUE,...)

Arguments

Details

Computes all pairwise similarities within a given list of sentences/documents. On this similarity matrix, a Principal Component Analysis (PCA) or a Multidimensional Sclaing (MDS) is applied to get a two- or three-dimensional solution that best captures the similarity structure. This solution is then plotted.

In the traditional LSA approach, the vector D for a document (or a sentence) consisting of the words (t1, . , tn) is computed as

D = \sum\limits_{i=1}^n t_n

This function then computes the the cosines between two sets of documents (or sentences).

The format of x should be of the kind x <- c("this is the first text","here is another text")

For creating pretty plots showing the similarity structure within this list of words best, set connect.lines="all" and col="rainbow"

Value

see plot3d: this function is called for the side effect of drawing the plot; a vector of object IDs is returned.

plot_doclist further prints a list with two elements:

Author(s)

Fritz Guenther, Taylor Fedechko

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Mardia, K.V., Kent, J.T., & Bibby, J.M. (1979). Multivariate Analysis, London: Academic Press.

See Also

cosine, multidocs, plot_neighbors, plot_wordlist, plot3d, princomp, rainbow

Examples

data(wonderland)

## Standard Plot

docs <- c("alice was beginning to get very tired.",
          "the red queen greeted alice.",
          "the mad hatter and the mare hare are having a party.",
          "the hatter sliced the cup of tea in half.")
          
plot_doclist(docs,tvectors=wonderland,method="MDS",dims=2)

2D- or 3D-Plot of neighbors

Description

2D- or 3D-Approximation of the neighborhood of a given word/sentence

Usage

plot_neighbors(x,n,connect.lines="all",start.lines=T,
   method="PCA",dims=3,axes=F,box=F,cex=1,legend=T, size = c(800,800),
   alpha="graded",alpha.grade = 1, col="rainbow",tvectors=tvectors,...)

Arguments

Details

Attempts to create an image of the semantic neighborhood (based on cosine similarity) to a given word, sentence/ document, or vector. An attempt is made to depict this subpart of the LSA space in a two- or three-dimensional plot.

To achieve this, either a Principal Component Analysis (PCA) or a Multidimensional Scaling (MDS) is computed to preserve the interconnections between all the words in this neighborhod as good as possible. Therefore, it is important to note that the image created from this function is only the best two- or three-dimensional approximation to the true LSA space subpart.

For creating pretty plots showing the similarity structure within this neighborhood best, set connect.lines="all" and col="rainbow"

Value

For three-dimensional plots:see plot3d: this function is called for the side effect of drawing the plot; a vector of object IDs is returned

plot_neighbors also gives the coordinate vectors of the words in the plot as a data frame

Author(s)

Fritz Guenther, Taylor Fedechko

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Mardia, K.V., Kent, J.T., & Bibby, J.M. (1979). Multivariate Analysis, London: Academic Press.

See Also

cosine, neighbors, multicos, plot_wordlist, plot3d, princomp

Examples

data(wonderland)

## Standard Plot
plot_neighbors("cheshire",n=20,tvectors=wonderland)  

## Pretty Plot
plot_neighbors("cheshire",n=20,tvectors=wonderland,
                connect.lines="all",col="rainbow")  



plot_neighbors(compose("mad","hatter",tvectors=wonderland),
                n=20, connect.lines=2,tvectors=wonderland)

2D- or 3D-Plot of a list of words

Description

2D or 3D-Plot of mutual word similarities to a given list of words

Usage

plot_wordlist(x,connect.lines="all",method="PCA",dims=3,
   axes=F,box=F,cex=1,legend=T, size = c(800,800),
   alpha="graded",alpha.grade=1,col="rainbow",
   tvectors=tvectors,...)

Arguments

Details

Computes all pairwise similarities within a given list of words. On this similarity matrix, a Principal Component Analysis (PCA) or a Multidimensional Sclaing (MDS) is applied to get a two- or three-dimensional solution that best captures the similarity structure. This solution is then plotted.

For creating pretty plots showing the similarity structure within this list of words best, set connect.lines="all" and col="rainbow"

Value

see plot3d: this function is called for the side effect of drawing the plot; a vector of object IDs is returned.

plot_wordlist also gives the coordinate vectors of the words in the plot as a data frame

Author(s)

Fritz Guenther, Taylor Fedechko

References

Landauer, T.K., & Dumais, S.T. (1997). A solution to Plato's problem: The Latent Semantic Analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104, 211-240.

Mardia, K.V., Kent, J.T., & Bibby, J.M. (1979). Multivariate Analysis, London: Academic Press.

See Also

cosine, neighbors, multicos, plot_neighbors, plot3d, princomp, rainbow

Examples

data(wonderland)

## Standard Plot

words <- c("alice","hatter","queen","knight","hare","cheshire") 
            
plot_wordlist(words,tvectors=wonderland,method="MDS",dims=2)

Simulated data for a Semantic Priming Experiment

Description

A data frame containing simulated data for a Semantic Priming Experiment. This data contains 514 prime-target pairs, which are taken from the Hutchison, Balota, Cortese and Watson (2008) study. These pairs are generated by pairing each of 257 target words with one semantically related and one semantically unrelated prime.

The data frame contains four columns:

• First column: Prime Words

• Second column: Target Words

• Third column: Simulated Reaction Times

• Fourth column: Specifies whether a prime-target pair is considered semantically related or unrelated

Usage

data(priming)

Format

A data frame with 514 rows and 4 columns

References

Hutchison, K. A., Balota, D. A., Cortese, M. & Watson, J. M. (2008). Predicting semantic priming at the item level. Quarterly Journal of Experimental Psychology, 61, 1036-1066.

A multiple choice test for synonyms and antonyms

Description

This object multiple choice test for synonyms and antonyms, consisting of seven columns.

1. The first column defines the question, i.e. the word a synonym or an antonym has to be found for.

2. The second up to the fifth column show the possible answer alternatives.

3. The sixth column defines the correct answer.

4. The seventh column indicates whether a synonym or an antonym has to be found for the word in question.

The test consists of twenty questions, which are given in the twenty rows of the data frame.

Usage

data(syntest)

Format

A data frame with 20 rows and 7 columns

LSA Space: Alice's Adventures in Wonderland

Description

This data set is a 50-dimensional LSA space derived from Lewis Carrol's book "Alice's Adventures in Wonderland". The book was split into 791 paragraphs which served as documents for the LSA algorithm (Landauer, Foltz & Laham, 1998). Only words that appeared in at least two documents were used for building the LSA space.

This LSA space contains 1123 different terms, all in lower case letters, and was created using the lsa-package. It can be used as tvectors for all the functions in the LSAfun-package.

Usage

data(wonderland)

Format

A 1123x50 matrix with terms as rownames.

Source

Alice in Wonderland from Project Gutenberg

References

Landauer, T., Foltz, P., and Laham, D. (1998) Introduction to Latent Semantic Analysis. In: Discourse Processes 25, pp. 259-284.

Carroll, L. (1865). Alice's Adventures in Wonderland. New York: MacMillan.