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Software Framework for Topic Modelling with Large Corpora
Radim
ˇ
Reh
˚
u
ˇ
rek and Petr Sojka
Natural Language Processing Laboratory
Masaryk University, Faculty of Informatics
Botanick
´
a 68a, Brno, Czech Republic
{xrehurek,sojka}@fi.muni.cz
Abstract
Large corpora are ubiquitous in today’s world and memory quickly becomes the limiting factor in practical applications of the Vector
Space Model (VSM). In this paper, we identify a gap in existing implementations of many of the popular algorithms, which is their
scalability and ease of use. We describe a Natural Language Processing software framework which is based on the idea of document
streaming, i.e. processing corpora document after document, in a memory independent fashion. Within this framework, we implement
several popular algorithms for topical inference, including Latent Semantic Analysis and Latent Dirichlet Allocation, in a way that makes
them completely independent of the training corpus size. Particular emphasis is placed on straightforward and intuitive framework design,
so that modifications and extensions of the methods and/or their application by interested practitioners are effortless. We demonstrate the
usefulness of our approach on a real-world scenario of computing document similarities within an existing digital library DML-CZ.
1. Introduction
“Controlling complexity is the essence of computer programming.”
Brian Kernighan (Kernighan and Plauger, 1976)
The Vector Space Model (VSM) is a proven and powerful
paradigm in NLP, in which documents are represented as
vectors in a high-dimensional space. The idea of represent-
ing text documents as vectors dates back to early 1970’s
to the SMART system (Salton et al., 1975). The original
concept has since then been criticised, revised and improved
on by a multitude of authors (Wong and Raghavan, 1984;
Deerwester et al., 1990; Papadimitriou et al., 2000) and
became a research field of its own. These efforts seek to ex-
ploit both explicit and implicit document structure to answer
queries about document similarity and textual relatedness.
Connected to this goal is the field of topical modelling (see
e.g. (Steyvers and Griffiths, 2007) for a recent review of
this field). The idea behind topical modelling is that texts
in natural languages can be expressed in terms of a limited
number of underlying concepts (or topics), a process which
both improves efficiency (new representation takes up less
space) and eliminates noise (transformation into topics can
be viewed as noise reduction). A topical search for related
documents is orthogonal to the more well-known “fulltext”
search, which would match particular words, possibly com-
bined through boolean operators.
Research on topical models has recently picked up pace,
especially in the field of generative topic models such as La-
tent Dirichlet Allocation (Blei et al., 2003), their hierarchical
extensions (Teh et al., 2006), topic quality assessment and
visualisation (Chang et al., 2009; Blei and Lafferty, 2009).
In fact, it is our observation that the research has rather got-
ten ahead of applications—the interested public is only just
catching up with Latent Semantic Analysis, a method which
is now more than 20 years old (Deerwester et al., 1990). We
attribute reasons for this gap between research and practice
partly to inherent mathematical complexity of the inference
algorithms, partly to high computational demands of most
methods and partly to the lack of a “sandbox” environment,
which would enable practitioners to apply the methods to
their particular problem on real data, in an easy and hassle-
free manner. The research community has recognised these
challenges and a lot of work has been done in the area of
accessible NLP toolkits in the past couple of years; our con-
tribution here is one such step in the direction of closing the
gap between academia and ready-to-use software packages
1
.
Existing Systems
The goal of this paper is somewhat orthogonal to much of
the previous work in this area. As an example of another
possible direction of applied research, we cite (Elsayed et
al., 2008). While their work focuses on how to compute
pair-wise document similarities from individual document
representations in a scalable way, using Apache Hadoop
and clusters of computers, our work here is concerned with
how to scalably compute these document representations
in the first place. Although both steps are necessary for a
complete document similarity pipeline, the scope of this
paper is limited to constructing topical representations, not
answering similarity queries.
There exist several mature toolkits which deal with Vec-
tor Space Modelling. These include NLTK (Bird and
Loper, 2004), Apache’s UIMA and ClearTK (Ogren et al.,
2008), Weka (Frank et al., 2005), OpenNLP (Baldridge
et al., 2002), Mallet (McCallum, 2002), MDP (Zito et al.,
2008), Nieme (Maes, 2009), Gate (Cunningham, 2002), Or-
ange (Dem
ˇ
sar et al., 2004) and many others.
These packages generally do a very good job at their in-
tended purpose; however, from our point of view, they also
suffer from one or more of the following shortcomings:
1
Interest in the field of document similarity can also be seen
from the significant number of requests for a VSM software pack-
age which periodically crop up in various NLP mailing lists. An-
other indicator of interest are tutorials aimed at business appli-
cations; see web search results for “SEO myths and LSI” for an
interesting treatment on Latent Semantic Indexing marketing.
46
No topical modelling.
Packages commonly offer super-
vised learning functionality (i.e. classification); topic
inference is an unsupervised task.
Models do not scale.
Package requires that the whole cor-
pus be present in memory before the inference of top-
ics takes place, usually in the form of a sparse term-
document matrix.
Target domain not NLP/IR.
The package was created
with physics, neuroscience, image processing, etc. in
mind. This is reflected in the choice of terminology as
well as emphasis on different parts of the processing
pipeline.
The Grand Unified Framework.
The package covers a
broad range of algorithms, approaches and use case
scenarios, resulting in complex interfaces and depen-
dencies. From the user’s perspective, this is very desir-
able and convenient. From the developer’s perspective,
this is often a nightmare—tracking code logic requires
major effort and interface modifications quickly cas-
cade into a large set of changes.
In fact, we suspect that the last point is also the reason why
there are so many packages in the first place. For a developer
(as opposed to a user), the entry level learning curve is so
steep that it is often simpler to “roll your own” package
rather than delve into intricacies of an existing, proven one.
2. System Design
“Write programs that do one thing and do it well. Write programs
to work together. Write programs to handle text streams, because
that is a universal interface.”
Doug McIlroy (McIlroy et al., 1978)
Our choices in designing the proposed framework are a
reflection of these perceived shortcomings. They can be
explicitly summarised into:
Corpus size independence.
We want the package to be
able to detect topics based on corpora which are larger
than the available RAM, in accordance with the current
trends in NLP (see e.g. (Kilgarriff and Grefenstette,
2003)).
Intuitive API.
We wish to minimise the number of method
names and interfaces that need to be memorised in
order to use the package. The terminology is NLP-
centric.
Easy deployment.
The package should work out-of-the-
box on all major platforms, even without root privileges
and without any system-wide installations.
Cover popular algorithms.
We seek to provide novel,
scalable implementations of algorithms such as TF-
-IDF, Latent Semantic Analysis, Random Projections
or Latent Dirichlet Allocation.
We chose Python as the programming language, mainly be-
cause of its straightforward, compact syntax, multiplatform
nature and ease of deployment. Python is also suitable for
handling strings and boasts a fast, high quality library for
numerical computing, numpy, which we use extensively.
Core interfaces
As mentioned earlier, the core concept of our framework is
document streaming. A corpus is represented as a sequence
of documents and at no point is there a need for the whole
corpus to be stored in memory. This feature is not an after-
thought on lazy evaluation, but rather a core requirement
for our application and as such reflected in the package
philosophy. To ensure transparent ease of use, we define
corpus to be any iterable returning documents:
>>> for document in corpus:
>>> pass
In turn, a document is a sparse vector representation of its
constituent fields (such as terms or topics), again realised as
a simple iterable:
2
>>> for fieldId, fieldValue in document:
>>> pass
This is a deceptively simple interface; while a corpus is
allowed to be something as simple as
>>> corpus = [[(1, 0.8), (8, 0.6)]]
this streaming interface also subsumes loading/storing matri-
ces from/to disk (e.g. in the Matrix Market (Boisvert et al.,
1996) or SVMlight (Joachims, 1999) format), and allows for
constructing more complex real-world IR scenarios, as we
will show later. Note the lack of package-specific keywords,
required method names, base class inheritance etc. This is
in accordance with our main selling points: ease of use and
data scalability.
Needless to say, both corpora and documents are not re-
stricted to these interfaces; in addition to supporting itera-
tion, they may (and usually do) contain additional methods
and attributes, such as internal document ids, means of visu-
alisation, document class tags and whatever else is needed
for a particular application.
The second core interface are transformations. Where a
corpus represents data, transformation represents the pro-
cess of translating documents from one vector space into
another (such as from a TF-IDF space into an LSA space).
Realization in Python is through the dictionary
[ ]
mapping
notation and is again quite intuitive:
>>> from gensim.models import LsiModel
>>> lsi = LsiModel(corpus, numTopics = 2)
>>> lsi[new_document]
[(0, 0.197), (1, -0.056)]
>>> from gensim.models import LdaModel
>>> lda = LdaModel(corpus, numTopics = 2)
>>> lda[new_document]
[(0, 1.0)]
2
In terms of the underlying VSM, which is essentially a sparse
field-document matrix, this interface effectively abstracts away
from both the number of documents and the number of fields.
We note, however, that the abstraction focus is on the number
of documents, not fields. The number of terms and/or topics is
usually carefully chosen, with unwanted token types removed via
document frequency thresholds and stoplists. The hypothetical
use case of introducing new fields in a streaming fashion does not
come up as often in NLP.
47
2.1. Novel Implementations
While an intuitive interface is important for software adop-
tion, it is of course rather trivial and useless in itself. We
have therefore implemented some of the popular VSM meth-
ods, two of which we will describe here in greater detail.
Latent Semantic Analysis, LSA.
Developed in late 80’s
in Bell Laboratories (Deerwester et al., 1990), this method
gained popularity due to its solid theoretical background
and efficient inference of topics. The method exploits co-
occurrence between terms to project documents into a low-
dimensional space. Inference is done using linear algebra
routines for truncated Singular Value Decomposition (SVD)
on the sparse term-document matrix, which is usually first
weighted by some TF-IDF scheme. Once the SVD has been
completed, it can be used to project new documents into the
latent space, in a process called folding-in.
Since linear algebra routines have always been the front
runner of numerical computing (see e.g. (Press et al., 1992)),
some highly optimised packages for sparse SVD exist. For
example, PROPACK and SVDPACK are both based on the
Lanczos algorithm with smart reorthogonalizations, and
both are written in FORTRAN (the latter also has a C-
language port called SVDLIBC). Lightning fast as they are,
adapting the FORTRAN code is rather tricky once we hit the
memory limit for representing sparse matrices directly in
memory. For this and other reasons, research has gradually
turned to incremental algorithms for computing SVD, in
which the matrix is presented sequentially—an approach
equivalent to our document streaming. This problem refor-
mulation is not trivial and only recently have there appeared
practical algorithms for incremental SVD.
Within our framework, we have implemented Gorrell’s
Generalised Hebbian Algorithm (Gorrell, 2006), a stochas-
tic method for incremental SVD. However, this algorithm
proved much too slow in practice and we also found its inter-
nal parameters hard to tune, resulting in convergence issues.
We have therefore also implemented Brand’s algorithm for
fast incremental SVD updates (Brand, 2006). This algorithm
is much faster and contains no internal parameters to tune
3
.
To the best of our knowledge, our pure Python (numpy) im-
plementation is the only publicly available implementation
of LSA that does not require the term-document matrix to
be stored in memory and is therefore independent of the
corpus size
4
. Together with our straightforward document
streaming interface, this in itself is a powerful addition to
the set of publicly available NLP tools.
Latent Dirichlet Allocation, LDA.
LDA is another topic
modelling technique based on the bag-of-words paradigm
and word-document counts (Blei et al., 2003). Unlike La-
tent Semantic Analysis, LDA is a fully generative model,
3
This algorithm actually comes from the field of image process-
ing rather than NLP. Singular Value Decomposition, which is at
the heart of LSA, is a universal data compression/noise reduction
technique and has been successfully applied to many application
domains.
4
This includes completely ignoring the right singular vectors
during SVD computations, as the left vectors together with singular
values are enough to determine the latent space projection for new
documents.
where documents are assumed to have been generated ac-
cording to a per-document topic distribution (with a Dirich-
let prior) and per-topic word distribution. In practice, the
goal is of course not generating random documents through
these distributions, but rather inferring the distributions from
observed documents. This can be accomplished by varia-
tional Bayes approximations (Blei et al., 2003) or by Gibbs
sampling (Griffiths and Steyvers, 2004). Both of these ap-
proaches are incremental in their spirit, so that our imple-
mentation (again, in pure Python with numpy, and again
the only of its kind that we know of) “only” had to abstract
away from the original notations and implicit corpus-size
allocations to be made truly memory independent. Once the
distributions have been obtained, it is possible to assign top-
ics to new, unseen documents, through our transformation
interface.
2.2. Deployment
The framework is heavily documented and is avail-
able from
http://nlp.fi.muni.cz/projekty/
gensim/
. This website contains sections which describe
the framework and provide usage tutorials, as well as instal-
lation instructions.
The framework is open sourced and distributed under an
OSI-approved LGPL license.
3. Application of the Framework
“An idea that is developed and put into action is more important
than an idea that exists only as an idea.”
Hindu Prince Gautama Siddharta, the founder of Buddhism,
563–483 B.C.
3.1. Motivation
Many digital libraries today start to offer browsing features
based on pairwise document content similarity. For collec-
tions having hundreds of thousands documents, computation
of similarity scores is a challenge (Elsayed et al., 2008). We
have faced this task during the project of The Digital Mathe-
matics Library DML-CZ (Sojka, 2009). The emphasis was
not on developing new IR methods for this task, although
some modifications were obviously necessary—such as an-
swering the question of what constitutes a “token”, which
differs between mathematics and the more common English
ASCII texts.
With the collection’s growth and a steady feed of new papers,
lack of scalability appeared to be the main issue. This drove
us to develop our new document similarity framework.
3.2. Data
As of today, the corpus contains over 61,293 fulltext docu-
ments for a total of about 270 million tokens. There are
mathematical papers from the Czech Digital Mathemat-
ics Library DML-CZ
http://dml.cz
(22,991 papers),
from the NUMDAM repository
http://numdam.org
(17,636 papers) and from the math part of arXiv
http:
//arxiv.org/archive/math
(20,666 papers). After
filtering out word types that either appear less than five times
in the corpus (mostly OCR errors) or in more than one half
of the documents (stop words), we are left with 315,167
48
distinct word types. Although this is by no means an excep-
tionally big corpus, it already prohibits storing the sparse
term-document matrices in main memory, ruling out most
available VSM software systems.
3.3. Results
We have tried several VSM approaches to representing doc-
uments as vectors: term weighting by TF-IDF, Latent Se-
mantic Analysis, Random Projections and Latent Dirichlet
Allocation. In all cases, we used the cosine measure to
assess document similarity.
When evaluating data scalability, one of our two main design
goals (together with ease of use), we note memory usage is
now dominated by the transformation models themselves.
These in turn depend on the vocabulary size and the number
of topics (but not on the training corpus size). With 315,167
word types and 200 latent topics, both LSA and LDA models
take up about 480 MB of RAM.
Although evaluation of the quality of the obtained similari-
ties is not the subject of this paper, it is of course of utmost
practical importance. Here we note that it is notoriously
hard to evaluate the quality, as even the preferences of differ-
ent types of similarity are subjective (match of main topic,
or subdomain, or specific wording/plagiarism) and depends
on the motivation of the reader. For this reason, we have
decided to present all the computed similarities to our li-
brary users at once, see e.g.
http://dml.cz/handle/
10338.dmlcz/100785/SimilarArticles
. At the
present time, we are gathering feedback from mathemati-
cians on these results and it is worth noting that the frame-
work proposed in this paper makes such side-by-side com-
parison of methods straightforward and feasible.
4. Conclusion
We believe that our framework makes an important step in
the direction of current trends in Natural Language Process-
ing and fills a practical gap in existing software systems. We
have argued that the common practice, where each novel
topical algorithm gets implemented from scratch (often in-
venting, unfortunately, yet another I/O format for its data in
the process) is undesirable. We have analysed the reasons
for this practice and hypothesised that this partly due to the
steep API learning curve of existing IR frameworks.
Our framework makes a conscious effort to make parsing,
processing and transforming corpora into vector spaces as
intuitive as possible. It is platform independent and requires
no compilation or installations past Python+numpy. As an
added bonus, the package provides ready implementations of
some of the popular IR algorithms, such as Latent Semantic
Analysis and Latent Dirichlet Allocation. These are novel,
pure-Python implementations that make use of modern state-
of-the-art iterative algorithms. This enables them to work
over practically unlimited corpora, which no longer need to
fit in RAM.
We believe this package is useful to topic modelling experts
in implementing new algorithms as well as to the general
NLP community, who is eager to try out these algorithms
but who often finds the task of translating the original im-
plementations (not to say the original articles!) to its needs
quite daunting.
Future work will include comparison of the usefulness of
different topical models to the users of our Digital Math-
ematical Library, as well as further improving the range,
efficiency and scalability of popular topic modelling meth-
ods.
Acknowledgments
We acknowledge the support of grant MUNI/E/0084/2009 of
the Rector of Masaryk University program for PhD students’
research. Partial support of grants by EU #250503 CIP-ICT-
PSP EuDML and by the Ministry of Education of CR within
the Centre of basic research LC536 is acknowledged, too.
We would also like to thank the anonymous reviewer for pro-
viding us with additional pointers and valuable comments.
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