Archive for the ‘Vector Space Model (VSM)’ Category

From Frequency to Meaning: Vector Space Models of Semantics

Thursday, September 18th, 2014

From Frequency to Meaning: Vector Space Models of Semantics by Peter D. Turney and Patrick Pantel.


Computers understand very little of the meaning of human language. This profoundly limits our ability to give instructions to computers, the ability of computers to explain their actions to us, and the ability of computers to analyse and process text. Vector space models (VSMs) of semantics are beginning to address these limits. This paper surveys the use of VSMs for semantic processing of text. We organize the literature on VSMs according to the structure of the matrix in a VSM. There are currently three broad classes of VSMs, based on term–document, word–context, and pair–pattern matrices, yielding three classes of applications. We survey a broad range of applications in these three categories and we take a detailed look at a specific open source project in each category. Our goal in this survey is to show the breadth of applications of VSMs for semantics, to provide a new perspective on VSMs for those who are already familiar with the area, and to provide pointers into the literature for those who are less familiar with the field.

At forty-eight (48) pages with a thirteen (13) page bibliography, this survey of vector space models (VSMs) of semantics should keep you busy for a while. You will have to fill in VSMs developments since 2010 but mastery of this paper will certain give you the foundation to do so. Impressive work.

I do disagree with the authors when they say:

Computers understand very little of the meaning of human language.

Truth be told, I would say:

Computers have no understanding of the meaning of human language.

What happens with a VSM of semantics is that we as human readers choose a model we think represents semantics we see in a text. Our computers blindly apply that model to text and report the results. We as human readers choose results that we think are closer to the semantics we see in the text, and adjust the model accordingly. Our computers then blindly apply the adjusted model to the text again and so on. At no time does the computer have any “understanding” of the text or of the model that it is applying to the text. Any “understanding” in such a model is from a human reader who adjusted the model based on their perception of the semantics of a text.

I don’t dispute that VSMs have been incredibly useful and like the authors, I think there is much mileage left in their development for text processing. That is not the same thing as imputing “understanding” of human language to devices that in fact have none at all. (full stop)


I first saw this in a tweet by Christopher Phipps.

PS: You probably recall that VSMs are based on creating a metric space for semantics, which have no preordained metric space. Transitioning from a non-metric space to a metric space isn’t subject to validation, at least in my view.

New Directions in Vector Space Models of Meaning

Tuesday, September 16th, 2014

New Directions in Vector Space Models of Meaning by Edward Grefenstette, Karl Moritz Hermann, Georgiana Dinu, and Phil Blunsom. (video)

From the description:

This is the video footage, aligned with slides, of the ACL 2014 Tutorial on New Directions in Vector Space Models of Meaning, by Edward Grefenstette (Oxford), Karl Moritz Hermann (Oxford), Georgiana Dinu (Trento) and Phil Blunsom (Oxford).

This tutorial was presented at ACL 2014 in Baltimore by Ed, Karl and Phil.

The slides can be found at

Running time is 2:45:12 so you had better get a cup of coffee before you start.

Includes a review of distributional models of semantics.

The sound isn’t bad but the acoustics are so you will have to listen closely. Having the slides in front of you helps as well.

The semantics part starts to echo topic map theory with the realization that having a single token isn’t going to help you with semantics. Tokens don’t stand alone but in a context of other tokens. Each of which has some contribution to make to the meaning of a token in question.

Topic maps function in a similar way with the realization that identifying any subject of necessity involves other subjects, which have their own identifications. For some purposes, we may assume some subjects are sufficiently identified without specifying the subjects that in our view identify it, but that is merely a design choice that others may choose to make differently.

Working through this tutorial and the cited references (one advantage to the online version) will leave you with a background in vector space models and the contours of the latest research.

I first saw this in a tweet by Kevin Safford.

The history of the vector space model

Wednesday, May 14th, 2014

The history of the vector space model by Suresh Venkatasubramanian.

From the post:

Gerald Salton is generally credited with the invention of the vector space model: the idea that we could represent a document as a vector of keywords and use things like cosine similarity and dimensionality reduction to compare documents and represent them.

But the path to this modern interpretation was a lot twistier than one might think. David Dubin wrote an article in 2004 titled ‘The Most Influential Paper Gerard Salton Never Wrote‘. In it, he points out that most citations that refer to the vector space model refer to a paper that doesn’t actually exist (hence the title). Taking that as a starting point, he then traces the lineage of the ideas in Salton’s work.

Suresh summarizes some of the discoveries made by Dubin in his post but this sounds like an interesting research project. To take Dubin’s article as a starting point and follow the development of the vector space model.

Particularly since it is used so often for “similarity.” Understanding the mathematics is good, understanding how that particular model was arrived at would be even better.


An Indexing Structure for Dynamic Multidimensional Data in Vector Space

Saturday, September 1st, 2012

An Indexing Structure for Dynamic Multidimensional Data in Vector Space by Elena Mikhaylova, Boris Novikov and Anton Volokhov. (Advances in Databases and Information Systems, Advances in Intelligent Systems and Computing, 2013, Volume 186, 185-193, DOI: 10.1007/978-3-642-32741-4_17)


The multidimensional k – NN (k nearest neighbors) query problem is relevant to a large variety of database applications, including information retrieval, natural language processing, and data mining. To solve it efficiently, the database needs an indexing structure that provides this kind of search. However, attempts to find an exact solution are hardly feasible in multidimensional space. In this paper, a novel indexing technique for the approximate solution of k – NN problem is described and analyzed. The construction of the indexing tree is based on clustering. Indexing structure is implemented on top of high-performance industrial DBMS.

The review of recent work is helpful but when the paper reaches the algorithm for indexing “…dynamic multidimensional data…,” it slips away from me.

Where is the dynamic nature of the data that is being overcome by the indexing?

I ask because we are human observers are untroubled by the curse of dimensionality, even when data is dynamically changing.

Although those are two important aspects when we process it by machine:

  • The number of dimensions of data, and
  • The rate at which the data is changing.

Documents as geometric objects: how to rank documents for full-text search

Wednesday, January 25th, 2012

Documents as geometric objects: how to rank documents for full-text search Michael Nielsen on July 7, 2011.

From the post:

When we type a query into a search engine – say “Einstein on relativity” – how does the search engine decide which documents to return? When the document is on the web, part of the answer to that question is provided by the PageRank algorithm, which analyses the link structure of the web to determine the importance of different webpages. But what should we do when the documents aren’t on the web, and there is no link structure? How should we determine which documents most closely match the intent of the query?

In this post I explain the basic ideas of how to rank different documents according to their relevance. The ideas used are very beautiful. They are based on the fearsome-sounding vector space model for documents. Although it sounds fearsome, the vector space model is actually very simple. The key idea is to transform search from a linguistic problem into a geometric problem. Instead of thinking of documents and queries as strings of letters, we adopt a point of view in which both documents and queries are represented as vectors in a vector space. In this point of view, the problem of determining how relevant a document is to a query is just a question of determining how parallel the query vector and the document vector are. The more parallel the vectors, the more relevant the document is.

This geometric way of treating documents turns out to be very powerful. It’s used by most modern web search engines, including (most likely) web search engines such as Google and Bing, as well as search libraries such as Lucene. The ideas can also be used well beyond search, for problems such as document classification, and for finding clusters of related documents. What makes this approach powerful is that it enables us to bring the tools of geometry to bear on the superficially very non-geometric problem of understanding text.

Very much looking forward to future posts in this series. There is no denying the power of “vector space model” but that leaves unasked what is lost in the transition from linguistic to geometric space?

We Are Not Alone!

Thursday, October 20th, 2011

While following some references I ran across: A proposal for transformation of topic-maps into similarities of topics (pdf) by Dr. Dominik Kuropka.


Newer information filtering and retrieval models like the Fuzzy Set Model or the Topic-based Vector Space Model consider term dependencies by means of numerical similarities between two terms. This leads to the question from what and how these numerical values can be deduced? This paper proposes an algorithm for the transformation of topic-maps into numerical similarities of paired topics. Further the relation of this work towards the above named information filtering and retrieval models is discussed.

Based in part on his paper Topic-Based Vector Space (2003).

This usage differs from ours in part because the work is designed to work at the document level in a traditional IR type context. “Topic maps,” in the ISO sense, are not limited to retrieval of documents or comparison by a particular method, however useful that method may be.

Still, it is good to get to know one’s neighbours so I will be sending him a note about our efforts.

Text Feature Extraction (tf-idf) – Part 1

Sunday, September 18th, 2011

Text Feature Extraction (tf-idf) – Part 1 by Christian Perone.

To give you a taste of the post:

Short introduction to Vector Space Model (VSM)

In information retrieval or text mining, the term frequency – inverse document frequency also called tf-idf, is a well know method to evaluate how important is a word in a document. tf-idf are also a very interesting way to convert the textual representation of information into a Vector Space Model (VSM), or into sparse features, we’ll discuss more about it later, but first, let’s try to understand what is tf-idf and the VSM.

VSM has a very confusing past, see for example the paper The most influential paper Gerard Salton Never Wrote that explains the history behind the ghost cited paper which in fact never existed; in sum, VSM is an algebraic model representing textual information as a vector, the components of this vector could represent the importance of a term (tf–idf) or even the absence or presence (Bag of Words) of it in a document; it is important to note that the classical VSM proposed by Salton incorporates local and global parameters/information (in a sense that it uses both the isolated term being analyzed as well the entire collection of documents). VSM, interpreted in a lato sensu, is a space where text is represented as a vector of numbers instead of its original string textual representation; the VSM represents the features extracted from the document.

The link to the The most influential paper Gerard Salton Never Wrote fails. Try the cached copy at CiteSeer: The most influential paper Gerard Salton Never Wrote.

Recommended reading.