In this document we describe the design and implementation of a (software programming) monad, [Wk1], for Latent Semantic Analysis workflows specification and execution. The design and implementation are done with Mathematica / Wolfram Language (WL).

What is Latent Semantic Analysis (LSA)? : A statistical method (or a technique) for finding relationships in natural language texts that is based on the so called Distributional hypothesis, [Wk2, Wk3]. (The Distributional hypothesis can be simply stated as “linguistic items with similar distributions have similar meanings”; for an insightful philosophical and scientific discussion see [MS1].) LSA can be seen as the application of Dimensionality reduction techniques over matrices derived with the Vector space model.

The goal of the monad design is to make the specification of LSA workflows (relatively) easy and straightforward by following a certain main scenario and specifying variations over that scenario.

The data for this document is obtained from WL’s repository and it is manipulated into a certain ready-to-utilize form (and uploaded to GitHub.)

The monadic programming design is used as a Software Design Pattern. The LSAMon monad can be also seen as a Domain Specific Language (DSL) for the specification and programming of machine learning classification workflows.

Here is an example of using the LSAMon monad over a collection of documents that consists of 233 US state of union speeches.

The table above is produced with the package “MonadicTracing.m”, [AAp2, AA1], and some of the explanations below also utilize that package.

As it was mentioned above the monad LSAMon can be seen as a DSL. Because of this the monad pipelines made with LSAMon are sometimes called “specifications”.

Remark: In this document with “term” we mean “a word, a word stem, or other type of token.”

Remark: LSA and Latent Semantic Indexing (LSI) are considered more or less to be synonyms. I think that “latent semantic analysis” sounds more universal and that “latent semantic indexing” as a name refers to a specific Information Retrieval technique. Below we refer to “LSI functions” like “IDF” and “TF-IDF” that are applied within the generic LSA workflow.

Contents description

The document has the following structure.

The sections “Package load” and “Data load” obtain the needed code and data.

The sections “Design consideration” and “Monad design” provide motivation and design decisions rationale.

The sections “LSAMon overview”, “Monad elements”, and “The utilization of SSparseMatrix objects” provide technical descriptions needed to utilize the LSAMon monad .

(Using a fair amount of examples.)

The section “Unit tests” describes the tests used in the development of the LSAMon monad.

(The random pipelines unit tests are especially interesting.)

The section “Future plans” outlines future directions of development.

The section “Implementation notes” just says that LSAMon’s development process and this document follow the ones of the classifications workflows monad ClCon, [AA6].

Remark: One can read only the sections “Introduction”, “Design consideration”, “Monad design”, and “LSAMon overview”. That set of sections provide a fairly good, programming language agnostic exposition of the substance and novel ideas of this document.

Package load

The following commands load the packages [AAp1–AAp7]:

In this section we load data that is used in the rest of the document. The text data was obtained through WL’s repository, transformed in a certain more convenient form, and uploaded to GitHub.

The text summarization and plots are done through LSAMon, which in turn uses the function RecordsSummary from the package “MathematicaForPredictionUtilities.m”, [AAp7].

In some of the examples below we want to explicitly specify the stop words. Here are stop words derived using the built-in functions DictionaryLookup and DeleteStopwords.

Here is a quote from [Wk1] that fairly well describes why we choose to make a classification workflow monad and hints on the desired properties of such a monad.

[…] The monad represents computations with a sequential structure: a monad defines what it means to chain operations together. This enables the programmer to build pipelines that process data in a series of steps (i.e. a series of actions applied to the data), in which each action is decorated with the additional processing rules provided by the monad. […]

Monads allow a programming style where programs are written by putting together highly composable parts, combining in flexible ways the possible actions that can work on a particular type of data. […]

Remark: Note that quote from [Wk1] refers to chained monadic operations as “pipelines”. We use the terms “monad pipeline” and “pipeline” below.

Monad design

The monad we consider is designed to speed-up the programming of LSA workflows outlined in the previous section. The monad is named LSAMon for “Latent Semantic Analysis** Mon**ad”.

We want to be able to construct monad pipelines of the general form:

LSAMon is based on the State monad, [Wk1, AA1], so the monad pipeline form (1) has the following more specific form:

This means that some monad operations will not just change the pipeline value but they will also change the pipeline context.

In the monad pipelines of LSAMon we store different objects in the contexts for at least one of the following two reasons.

The object will be needed later on in the pipeline, or

The object is (relatively) hard to compute.

Such objects are document-term matrix, Dimensionality reduction factors and the related topics.

Let us list the desired properties of the monad.

Rapid specification of non-trivial LSA workflows.

The text data supplied to the monad can be: (i) a list of strings, or (ii) an association with string values.

The monad uses the Linear vector space model .

The document-term frequency matrix can be created after removing stop words and/or word stemming.

It is easy to specify and apply different LSI weight functions. (Like “IDF” or “GFIDF”.)

The monad can do dimension reduction with SVD and NNMF and corresponding matrix factors are retrievable with monad functions.

Documents (or query strings) external to the monad are easily mapped into monad’s Linear vector space of terms and Linear vector space of topics.

The monad allows of cursory examination and summarization of the data.

The pipeline values can be of different types. (Most monad functions modify the pipeline value; some modify the context; some just echo results.)

It is easy to obtain the pipeline value, context, and different context objects for manipulation outside of the monad.

It is easy to tabulate extracted topics and related statistical thesauri.

The LSAMon components and their interactions are fairly simple.

The main LSAMon operations implicitly put in the context or utilize from the context the following objects:

document-term matrix,

the factors obtained by matrix factorization algorithms,

LSI weight functions specifications,

extracted topics.

Note the that the monadic set of types of LSAMon pipeline values is fairly heterogenous and certain awareness of “the current pipeline value” is assumed when composing LSAMon pipelines.

Obviously, we can put in the context any object through the generic operations of the State monad of the package “StateMonadGenerator.m”, [AAp1].

LSAMon overview

When using a monad we lift certain data into the “monad space”, using monad’s operations we navigate computations in that space, and at some point we take results from it.

With the approach taken in this document the “lifting” into the LSAMon monad is done with the function LSAMonUnit. Results from the monad can be obtained with the functions LSAMonTakeValue, LSAMonContext, or with the other LSAMon functions with the prefix “LSAMonTake” (see below.)

Here is a corresponding diagram of a generic computation with the LSAMon monad:

Remark: It is a good idea to compare the diagram with formulas (1) and (2).

Let us examine a concrete LSAMon pipeline that corresponds to the diagram above. In the following table each pipeline operation is combined together with a short explanation and the context keys after its execution.

Here is the output of the pipeline:

The LSAMon functions are separated into four groups:

operations,

setters and droppers,

takers,

State Monad generic functions.

Monad functions interaction with the pipeline value and context

An overview of the those functions is given in the tables in next two sub-sections. The next section, “Monad elements”, gives details and examples for the usage of the LSAMon operations.

State monad functions

Here are the LSAMon State Monad functions (generated using the prefix “LSAMon”, [AAp1, AA1].)

Main monad functions

Here are the usage descriptions of the main (not monad-supportive) LSAMon functions, which are explained in detail in the next section.

Monad elements

In this section we show that LSAMon has all of the properties listed in the previous section.

The monad head

The monad head is LSAMon. Anything wrapped in LSAMon can serve as monad’s pipeline value. It is better though to use the constructor LSAMonUnit. (Which adheres to the definition in [Wk1].)

The fundamental model of LSAMon is the so called Vector space model (or the closely related Bag-of-words model.) The document-term matrix is a linear vector space representation of the documents collection. That representation is further used in LSAMon to find topics and statistical thesauri.

Here is an example of ad hoc construction of a document-term matrix using a couple of paragraphs from “Hamlet”.

When we construct the document-term matrix we (often) want to stem the words and (almost always) want to remove stop words. LSAMon’s function LSAMonMakeDocumentTermMatrix makes the document-term matrix and takes specifications for stemming and stop words.

After making the document-term matrix we will most likely apply LSI weight functions, [Wk2], like “GFIDF” and “TF-IDF”. (This follows the “standard” approach used in search engines for calculating weights for document-term matrices; see [MB1].)

Frequency matrix

We use the following definition of the frequency document-term matrix F.

Each entry f_{ij} of the matrix F is the number of occurrences of the term j in the document i.

Weights

Each entry of the weighted document-term matrix M derived from the frequency document-term matrix F is expressed with the formula

where g_{j} – global term weight; l_{ij} – local term weight; d_{i} – normalization weight.

Various formulas exist for these weights and one of the challenges is to find the right combination of them when using different document collections.

Here is a table of weight functions formulas.

Computation specifications

LSAMon function LSAMonApplyTermWeightFunctions delegates the LSI weight functions application to the package “DocumentTermMatrixConstruction.m”, [AAp4].

Here we are summaries of the non-zero values of the weighted document-term matrix derived with different combinations of global, local, and normalization weight functions.

Streamlining topic extraction is one of the main reasons LSAMon was implemented. The topic extraction correspond to the so called “syntagmatic” relationships between the terms, [MS1].

Theoretical outline

The original weighed document-term matrix M is decomposed into the matrix factors W and H.

M ≈ W.H, W ∈ ℝ^{m × k}, H ∈ ℝ^{k × n}.

The i-th row of M is expressed with the i-th row of W multiplied by H.

The rows of H are the topics. SVD produces orthogonal topics; NNMF does not.

The i-the document of the collection corresponds to the i-th row W. Finding the Nearest Neighbors (NN’s) of the i-th document using the rows similarity of the matrix W gives document NN’s through topic similarity.

The terms correspond to the columns of H. Finding NN’s based on similarities of H’s columns produces statistical thesaurus entries.

The term groups provided by H’s rows correspond to “syntagmatic” relationships. Using similarities of H’s columns we can produce term clusters that correspond to “paradigmatic” relationships.

Computation specifications

Here is an example using the play “Hamlet” in which we specify additional stop words.

One of the most natural operations is to find the representation of an arbitrary document (or sentence or a list of words) in monad’s Linear vector space of terms. This is done with the function LSAMonRepresentByTerms.

Here is an example in which a sentence is represented as a one-row matrix (in that space.)

obj =
lsaHamlet⟹
LSAMonRepresentByTerms["Hamlet, Prince of Denmark killed the king."]⟹
LSAMonEchoValue;

Here we display only the non-zero columns of that matrix.

obj⟹
LSAMonEchoFunctionValue[MatrixForm[Part[#, All, Keys[Select[SSparseMatrix`ColumnSumsAssociation[#], # > 0& ]]]]& ];

Transformation steps

Assume that LSAMonRepresentByTerms is given a list of sentences. Then that function performs the following steps.

1. The sentence is split into a list of words.

2. If monad’s document-term matrix was made by removing stop words the same stop words are removed from the list of words.

3. If monad’s document-term matrix was made by stemming the same stemming rules are applied to the list of words.

4. The LSI global weights and the LSI local weight and normalizer functions are applied to sentence’s contingency matrix.

Equivalent representation

Let us look convince ourselves that documents used in the monad to built the weighted document-term matrix have the same representation as the corresponding rows of that matrix.

Here is an association of documents from monad’s document collection.

inds = {6, 10};
queries = Part[lsaHamlet⟹LSAMonTakeDocuments, inds];
queries
(* <|"id.0006" -> "Getrude, Queen of Denmark, mother to Hamlet. Ophelia, daughter to Polonius.",
"id.0010" -> "ACT I. Scene I. Elsinore. A platform before the Castle."|> *)
lsaHamlet⟹
LSAMonRepresentByTerms[queries]⟹
LSAMonEchoFunctionValue[MatrixForm[Part[#, All, Keys[Select[SSparseMatrix`ColumnSumsAssociation[#], # > 0& ]]]]& ];

Another natural operation is to find the representation of an arbitrary document (or a list of words) in monad’s Linear vector space of topics. This is done with the function LSAMonRepresentByTopics.

Here is an example.

inds = {6, 10};
queries = Part[lsaHamlet⟹LSAMonTakeDocuments, inds];
Short /@ queries
(* <|"id.0006" -> "Getrude, Queen of Denmark, mother to Hamlet. Ophelia, daughter to Polonius.",
"id.0010" -> "ACT I. Scene I. Elsinore. A platform before the Castle."|> *)
lsaHamlet⟹
LSAMonRepresentByTopics[queries]⟹
LSAMonEchoFunctionValue[MatrixForm[Part[#, All, Keys[Select[SSparseMatrix`ColumnSumsAssociation[#], # > 0& ]]]]& ];

In LSAMon for SVD H^{( − 1)} = H^{T}; for NNMF H^{( − 1)} is the pseudo-inverse of H.

The vector x obtained with LSAMonRepresentByTopics.

Tags representation

Sometimes we want to find the topics representation of tags associated with monad’s documents and the tag-document associations are one-to-many. See [AA3].

Let us consider a concrete example – we want to find what topics correspond to the different presidents in the collection of State of Union speeches.

Here we find the document tags (president names in this case.)

There are several algorithms we can apply for finding the most important documents in the collection. LSAMon utilizes two types algorithms: (1) graph centrality measures based, and (2) matrix factorization based. With certain graph centrality measures the two algorithms are equivalent. In this sub-section we demonstrate the matrix factorization algorithm (that uses SVD.)

Definition: The most important sentences have the most important words and the most important words are in the most important sentences.

That definition can be used to derive an iterations-based model that can be expressed with SVD or eigenvector finding algorithms, [LE1].

Here we pick an important part of the play “Hamlet”.

focusText =
First@Pick[textHamlet, StringMatchQ[textHamlet, ___ ~~ "to be" ~~ __ ~~ "or not to be" ~~ ___, IgnoreCase -> True]];
Short[focusText]
(* "Ham. To be, or not to be- that is the question: Whether 'tis ....y.
O, woe is me T' have seen what I have seen, see what I see!" *)
LSAMonUnit[StringSplit[ToLowerCase[focusText], {",", ".", ";", "!", "?"}]]⟹
LSAMonMakeDocumentTermMatrix["StemmingRules" -> {}, "StopWords" -> Automatic]⟹
LSAMonApplyTermWeightFunctions⟹
LSAMonFindMostImportantDocuments[3]⟹
LSAMonEchoFunctionValue[GridTableForm];

Setters, droppers, and takers

The values from the monad context can be set, obtained, or dropped with the corresponding “setter”, “dropper”, and “taker” functions as summarized in a previous section.

For example:

p = LSAMonUnit[textHamlet]⟹LSAMonMakeDocumentTermMatrix[Automatic, Automatic];
p⟹LSAMonTakeMatrix

If other values are put in the context they can be obtained through the (generic) function LSAMonTakeContext, [AAp1]:

Short@(p⟹QRMonTakeContext)["documents"]
(* <|"id.0001" -> "1604", "id.0002" -> "THE TRAGEDY OF HAMLET, PRINCE OF DENMARK", <<220>>, "id.0223" -> "THE END"|> *)

Another generic function from [AAp1] is LSAMonTakeValue (used many times above.)

Here is an example of the “data dropper” LSAMonDropDocuments:

(The “droppers” simply use the state monad function LSAMonDropFromContext, [AAp1]. For example, LSAMonDropDocuments is equivalent to LSAMonDropFromContext[“documents”].)

The utilization of SSparseMatrix objects

The LSAMon monad heavily relies on SSparseMatrix objects, [AAp6, AA5], for internal representation of data and computation results.

A SSparseMatrix object is a matrix with named rows and columns.

In some cases we want to show only columns of the data or computation results matrices that have non-zero elements.

Here is an example (similar to other examples in the previous section.)

lsaHamlet⟹
LSAMonRepresentByTerms[{"this country is rotten",
"where is my sword my lord",
"poison in the ear should be in the play"}]⟹
LSAMonEchoFunctionValue[ MatrixForm[#1[[All, Keys[Select[ColumnSumsAssociation[#1], #1 > 0 &]]]]] &];

In the pipeline code above: (i) from the list of queries a representation matrix is made, (ii) that matrix is assigned to the pipeline value, (iii) in the pipeline echo value function the non-zero columns are selected with by using the keys of the non-zero elements of the association obtained with ColumnSumsAssociation.

Similarities based on representation by terms

Here is way to compute the similarity matrix of different sets of documents that are not required to be in monad’s document collection.

Similarly to weighted Boolean similarities matrix computation above we can compute a similarity matrix using the topics representations. Note that an additional normalization steps is required.

Note the differences with the weighted Boolean similarity matrix in the previous sub-section – the similarities that are less than 1 are noticeably larger.

Unit tests

The development of LSAMon was done with two types of unit tests: (i) directly specified tests, [AAp7], and (ii) tests based on randomly generated pipelines, [AA8].

The unit test package should be further extended in order to provide better coverage of the functionalities and illustrate – and postulate – pipeline behavior.

Since the monad LSAMon is a DSL it is natural to test it with a large number of randomly generated “sentences” of that DSL. For the LSAMon DSL the sentences are LSAMon pipelines. The package “MonadicLatentSemanticAnalysisRandomPipelinesUnitTests.m”, [AAp9], has functions for generation of LSAMon random pipelines and running them as verification tests. A short example follows.

AbsoluteTiming[
res = TestRunLSAMonPipelines[pipelines, "Echo" -> False];
]

From the test report results we see that a dozen tests failed with messages, all of the rest passed.

rpTRObj = TestReport[res]

(The message failures, of course, have to be examined – some bugs were found in that way. Currently the actual test messages are expected.)

Future plans

Dimension reduction extensions

It would be nice to extend the Dimension reduction functionalities of LSAMon to include other algorithms like Independent Component Analysis (ICA), [Wk5]. Ideally with LSAMon we can do comparisons between SVD, NNMF, and ICA like the image de-nosing based comparison explained in [AA8].

Another direction is to utilize Neural Networks for the topic extraction and making of statistical thesauri.

Conversational agent

Since LSAMon is a DSL it can be relatively easily interfaced with a natural language interface.

Here is an example of natural language commands parsed into LSA code using the package [AAp13].

Implementation notes

The implementation methodology of the LSAMon monad packages [AAp3, AAp9] followed the methodology created for the ClCon monad package [AAp10, AA6]. Similarly, this document closely follows the structure and exposition of the `ClCon monad document “A monad for classification workflows”, [AA6].

A lot of the functionalities and signatures of LSAMon were designed and programed through considerations of natural language commands specifications given to a specialized conversational agent.

This document shows a way to chart in Mathematica / WL the evolution of topics in collections of texts. The making of this document (and related code) is primarily motivated by the fascinating concept of the Great Conversation, [Wk1, MA1]. In brief, all western civilization books are based on great ideas; if we find the great ideas each significant book is based on we can construct a time-line (spanning centuries) of the great conversation between the authors; see [MA1, MA2, MA3].

The presented computational results are based on the text collections of State of the Union speeches of USA presidents [D2]. The code in this document can be easily configured to use the much smaller text collection [D1] available online and in Mathematica/WL. (The collection [D1] is fairly small, documents; the collection [D2] is much larger, documents.)

The procedures (and code) described in this document, of course, work on other types of text collections. For example: movie reviews, podcasts, editorial articles of a magazine, etc.

A secondary objective of this document is to illustrate the use of the monadic programming pipeline as a Software design pattern, [AA3]. In order to make the code concise in this document I wrote the package MonadicLatentSemanticAnalysis.m, [AAp5]. Compare with the code given in [AA1].

The very first version of this document was written for the 2017 summer course “Data Science for the Humanities” at the University of Oxford, UK.

Outline of the procedure applied

The procedure described in this document has the following steps.

Get a collection of documents with known dates of publishing.

Or other types of tags associated with the documents.

Do preliminary analysis of the document collection.

Number of documents; number of unique words.

Number of words per document; number of documents per word.

(Some of the statistics of this step are done easier after the Linear vector space representation step.)

Optionally perform Natural Language Processing (NLP) tasks.

In this section we load a text collection from a specified source.

The text collection from “Presidential Nomination Acceptance Speeches”, [D1], is small and can be used for multiple code verifications and re-runnings. The “State of Union addresses of USA presidents” text collection from [D2] was converted to a Mathematica/WL object by Christopher Wolfram (and sent to me in a private communication.) The text collection [D2] provides far more interesting results (and they are shown below.)

If[True,
speeches = ResourceData[ResourceObject["Presidential Nomination Acceptance Speeches"]];
names = StringSplit[Normal[speeches[[All, "Person"]]][[All, 2]], "::"][[All, 1]],
(*ELSE*)
(*State of the union addresses provided by Christopher Wolfram. *)
Get["~/MathFiles/Digital humanities/Presidential speeches/speeches.mx"];
names = Normal[speeches[[All, "Name"]]];
];
dates = Normal[speeches[[All, "Date"]]];
texts = Normal[speeches[[All, "Text"]]];
Dimensions[speeches]
(* {2453, 4} *)

Basic statistics for the texts

Using different contingency matrices we can derive basic statistical information about the document collection. (The document-word matrix is a contingency matrix.)

We can complete this list with additional stop words derived from the collection itself. (Not done here.)

Linear vector space representation and dimension reduction

Remark: In the rest of the document we use “term” to mean “word” or “stemmed word”.

The following code makes a document-term matrix from the document collection, exaggerates the representations of the terms using “TF-IDF”, and then does topic extraction through dimension reduction. The dimension reduction is done with NNMF; see [AAp3, AA1, AA2].

Let us clarify the values by briefly describing the computational steps.

From texts we derive the document-term matrix , where is the number of documents and is the number of terms.

The terms are words or stemmed words.

This is done with LSAMonMakeDocumentTermMatrix.

From docTermMat is derived the (weighted) matrix wDocTermMat using “TF-IDF”.

This is done with LSAMonApplyTermWeightFunctions.

Using docTermMat we find the terms that are present in sufficiently large number of documents and their column indices are assigned to topicColumnPositions.

Matrix factorization.

Assign to , , where .

Compute using NNMF the factorization , where , , and is the number of topics.

The values for the keys “W, “H”, and “topicColumnPositions” are computed and assigned by LSAMonTopicExtraction.

From the top terms of each topic are derived automatic topic names and assigned to the key automaticTopicNames in the monad context.

Also done by LSAMonTopicExtraction.

Statistical thesaurus

At this point in the object mObj we have the factors of NNMF. Using those factors we can find a statistical thesaurus for a given set of words. The following code calculates such a thesaurus, and echoes it in a tabulated form.

By observing the thesaurus entries we can see that the words in each entry are semantically related.

Note, that the word “welfare” strongly associates with “[applause]”. The rest of the query words do not, which can be seen by examining larger thesaurus entries:

The function LSAMonTopicsRepresentation finds the top outliers for each row of NNMF’s left factor . (The outliers are found using the package [AAp4].) The obtained list of indices gives the topic representation of the collection of texts.

Further we can see that if the documents have tags associated with them — like author names or dates — we can make a contingency matrix of tags vs topics. (See [AAp8, AA4].) This is also done by the function LSAMonTopicsRepresentation that takes tags as an argument. If the tags argument is Automatic, then the tags are simply the document indices.

Note that the matrix plots above are very close to the charting of the Great conversation that we are looking for. This can be made more obvious by observing the row names and columns names in the tabulation of the transposed matrix rsmat:

Magnify[#, 0.6] &@MatrixForm[Transpose[rsmat]]

Charting the great conversation

In this section we show several ways to chart the Great Conversation in the collection of speeches.

There are several possible ways to make the chart: using a time-line plot, using heat-map plot, and using appropriate tabulation (with MatrixForm or Grid).

In order to make the code in this section more concise the package RSparseMatrix.m, [AAp7, AA5], is used.

Topic name to topic words

This command makes an Association between the topic names and the top topic words.

Note the value of the option DistanceFunction: there is not re-ordering of the rows and columns are reordered by sorting. Also, the topics on the horizontal names have tool-tips.

[MA1] Mortimer Adler, "The Great Conversation Revisited," in The Great Conversation: A Peoples Guide to Great Books of the Western World, Encyclopædia Britannica, Inc., Chicago,1990, p. 28.

This blog post proclaims the first committed project in the repository ConversationalAgents at GitHub. The project has designs and implementations of a phone calling conversational agent that aims at providing the following functionalities:

The design is based on a Finite State Machine (FSM) and context free grammar(s) for commands that switch between the states of the FSM. The grammar is designed as a context free grammar rules of a Domain Specific Language (DSL) in Extended Backus-Naur Form (EBNF). (For more details on DSLs design and programming see [1].)

The (current) implementation is with Wolfram Language (WL) / Mathematica using the functional parsers package [2, 3].

This movie gives an overview from an end user perspective.

General design

The design of the Phone Conversational Agent (PhCA) is derived in a straightforward manner from the typical work flow of calling a contact (using, say, a mobile phone.)

The main goals for the conversational agent are the following:

contacts retrieval — search, filtering, selection — using both natural language commands and manual interaction,

intuitive integration with the usual work flow of phone calling.

An additional goal is to facilitate contacts retrieval by determining the most appropriate contacts in query responses. For example, while driving to work by pressing the dial button we might prefer the contacts of an up-coming meeting to be placed on top of the prompting contacts list.

In this project we assume that the voice to text conversion is done with an external (reliable) component.

It is assumed that an user of PhCA can react to both visual and spoken query results.

The main algorithm is the following.

1) Parse and interpret a natural language command.

2) If the command is a contacts query that returns a single contact then call that contact.

3) If the command is a contacts query that returns multiple contacts then :

3.1) use natural language commands to refine and filter the query results,

3.2) until a single contact is obtained. Call that single contact.

4) If other type of command is given act accordingly.

PhCA has commands for system usage help and for canceling the current contact search and starting over.

The following FSM diagram gives the basic structure of PhCA:

This movie demonstrates how different natural language commands switch the FSM states.

Grammar design

The derived grammar describes sentences that: 1. fit end user expectations, and 2. are used to switch between the FSM states.

(Note that according to PhCA’s FSM diagram the parsing of pCALLCONTACT is separated from pCALLFILTER, hence the need to combine the two parsers in the code line above.)

PhCA’s FSM implementation provides interpretation and context of the functional programming expressions obtained by the parser.

The imported Wolfram Language file, "./Mathematica/PhoneDialingAgentRunScript.m", uses a fake address book based on movie creators metadata. The code structure of "./Mathematica/PhoneDialingAgentRunScript.m" allows easy experimentation and modification of the running steps.

Here are several screen-shots illustrating a particular usage path (scan left-to-right):

This post is to proclaim the MathematicaVsR at GitHub project “Text analysis of Trump tweets” in which we compare Mathematica and R over text analyses of Twitter messages made by Donald Trump (and his staff) before the USA president elections in 2016.

The blog post [1] links to several sources that claim that during the election campaign Donald Trump tweeted from his Android phone and his campaign staff tweeted from an iPhone. The blog post [1] examines this hypothesis in a quantitative way (using various R packages.)

The hypothesis in question is well summarized with the tweet:

Every non-hyperbolic tweet is from iPhone (his staff).
Every hyperbolic tweet is from Android (from him). pic.twitter.com/GWr6D8h5ed
— Todd Vaziri (@tvaziri) August 6, 2016

This conjecture is fairly well supported by the following mosaic plots, [2]:

We can see the that Twitter messages from iPhone are much more likely to be neutral, and the ones from Android are much more polarized. As Christian Rudder (one of the founders of OkCupid, a dating website) explains in the chapter "Death by a Thousand Mehs" of the book "Dataclysm", [3], having a polarizing image (online persona) is a very good strategy to engage online audience:

[…] And the effect isn’t small — being highly polarizing will in fact get you about 70 percent more messages. That means variance allows you to effectively jump several "leagues" up in the dating pecking order — […]

(The mosaic plots above were made for the Mathematica-part of this project. Mosaic plots and weekday tags are not used in [1].)

The Mathematica-part of this project does not follow closely the blog post [1]. After the ingestion of the data provided in [1], the Mathematica-part applies alternative algorithms to support and extend the analysis in [1].

The sections in the R-part notebook correspond to some — not all — of the sections in the Mathematica-part.

The following list of steps is for the Mathematica-part.

Data ingestion

The blog post [1] shows how to do in R the ingestion of Twitter data of Donald Trump messages.

In the Mathematica-part these associations rules are not needed for the sentiment analysis (because of the built-in classifiers.)

The association rule mining is done mostly to support and extend the text analysis in [1] and, of course, for comparison purposes.

Here is an example of derived association rules together with their most important measures:

In [1] the sentiments are derived from computed device-word associations, so in [1] the order of steps is 1-2-3-5-4. In Mathematica we do not need the steps 3 and 5 in order to get the sentiments in the 4th step.

Comparison

Using Mathematica for sentiment analysis is much more direct because of the built-in classifiers.

The R-based blog post [1] uses heavily the "pipeline" operator %>% which is kind of a recent addition to R (and it is both fashionable and convenient to use it.) In Mathematica the related operators are Postfix (//), Prefix (@), Infix (~~), Composition (@*), and RightComposition (/*).

Making the time series plots with the R package "ggplot2" requires making special data frames. I am inclined to think that the Mathematica plotting of time series is more direct, but for this task the data wrangling codes in Mathematica and R are fairly comparable.

Generally speaking, the R package "arules" — used in this project for Associations rule learning — is somewhat awkward to use:

it is data frame centric, does not work directly with lists of lists, and

In this blog post I will provide links to documents, packages, blog posts, and discussions for creating and utilizing Domain Specific Languages (DSLs). I have discussed a few DSLs in previous blog posts (linked below). This blog post provides a more general, higher level view on the application and creation of DSLs. The concrete examples are with Mathematica, but the steps are general and can be done with any programming languages and tools.

When to apply DSLs

Here are some situations for applying DSLs.

When designing conversational engines.

When there are too many usage scenarios and tuning options for the developed algorithms.

For example, we have a bunch of search, recommendation, and interaction algorithms for a dating site. A different, User Experience Department (UED) designs interactive user interfaces for these algorithms. We make a natural language DSL that invokes the different algorithms according to specified outcomes. With the DSL the different designs produced by UED are much easily prototyped, implemented, or fleshed out. The DSL also gives to UED easier to understand view on the functionalities provided by the algorithms.

When designing an API for a collection of algorithms.

Just designing a DSL can bring clarity of what signatures should be in the API.

NIntegrate‘s Method option was designed and implemented using a DSL. See this video between 25:00 and 27:30.

Designing DSLs

Decide what kind of sentences the DSL is going to have.

Are natural language sentences going to be used?

Are the language words known beforehand or not?

Prepare, create, or accumulate a list of representative sentences.

In some cases using Morphological Analysis can greatly help for coming up with use cases and the corresponding sentences.

Create a context free grammar that describes the sentences from the previous step. (Or a large subset of them.)

In some cases the grammar terminals are not know at the design stage and have to retrieved in some way. (From a database or though natural language processing.)

Some conversational engine systems allow or require to the grammar specification to be done in XML. I would still do BNF and then move to XML

It is not that hard to write a parser-and-interpreter that translates BNF into XML. See the end of this blog post for that kind of translation of BNF into OMPL.

The answer of the MSE question “How to parse a clojure expression?” gives a good introduction with a simple grammar and shows both direct parser programming and automatic generation from EBNF.

Advanced example

The blog post “Simple time series conversational engine” discusses the creation (design and programming) of a simple conversational engine for time series analysis (data loading, finding outliers and trends.)

Natural language Processing (NLP) can be done with a structural approach using grammar rules. (The other type of NLP is using statistical methods.) In this post I discuss the use of functional parsers for the parsing and interpretation of small sets of natural language sentences within specific contexts. Functional parsing is also known as monadic parsing and parsing combinators.

Generally, I am using functional parsers to make Domain-Specific Languages (DSL’s). I use DSL’s to make command interfaces to search and recommendation engines and also to design and prototype conversational engines. I use extensively the so called Backus-Naur Form (BNF) for the grammar specifications. Clearly a DSL can be very close to natural language and provide sufficient means for interpretation within a given (narrow) context. (Like function integration in Calculus, smart phone directory browsing and selection, or search for something to eat nearby.)

The package provides ability to quickly program parsers using a core system of functional parsers as described in the article “Functional parsers” by Jeroen Fokker .

The parsers (in both the package and the article) are categorized in the groups: basic, combinators, and transformers. Immediate interpretation can be done with transformer parsers, but the package also provides functions for evaluation of parser output within a context of data and functions.

Probably most importantly, the package provides functions for automatic generation of parsers from grammars in EBNF.

Here is an example of parsing the sentences of an integration requests language:

Here is the grammar:

The grammar can be visualized with this mind map:

The mind map was hand made with MindNode Pro. Generally, the branches represent alternatives, but if two branches are connected the direction of the arrow connecting them shows a sequence combination.

With the FunctionalParsers.m package we can automatically generate a
mind map parsing the string of the grammar in EBNF to OMPL:

A more complicated example is this conversational engine for manipulation of time series data. (Data loading, finding outliers and trends. More details in the next blog post.)