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In machine learning and natural language processing, a topic model is a type of statistical model for discovering the abstract "topics" that occur in a collection of documents. Intuitively, given that a document is about a particular topic, one would expect particular words to appear in the document more or less frequently: "dog" and "bone" will appear more often in documents about dogs, "cat" and "meow" will appear in documents about cats, and "the" and "is" will appear equally in both. A document typically concerns multiple topics in different proportions; thus, in a document that is 10% about cats and 90% about dogs, there would probably be about 9 times more dog words than cat words. A topic model captures this intuition in a mathematical framework, which allows examining a set of documents and discovering, based on the statistics of the words in each, what the topics might be and what each document's balance of topics is.
Although topic models were first described and implemented in the context of natural language processing, they have applications in other fields such as bioinformatics.
An early topic model was described by Papadimitriou, Raghavan, Tamaki and Vempala in 1998.  Another one, called Probabilistic latent semantic indexing (PLSI), was created by Thomas Hofmann in 1999. Latent Dirichlet allocation (LDA), perhaps the most common topic model currently in use, is a generalization of PLSI developed by David Blei, Andrew Ng, and Michael I. Jordan in 2002, allowing documents to have a mixture of topics. Other topic models are generally extensions on LDA, such as Pachinko allocation, which improves on LDA by modeling correlations between topics in addition to the word correlations which constitute topics.
Templeton's survey of work on topic modeling in the humanities grouped previous work into synchronic and diachronic approaches. The synchronic approaches identify topics at a certain time, for example, Jockers used topic modelling to classify 177 bloggers writing on the 2010 'Day of Digital Humanities' and identify the topics they wrote about for that day. Meeks modeled 50 texts in the Humanities Computing/Digital Humanities genre to identify self-definitions of scholars working on digital humanities and visualize networks of researchers and topics. Drouin examined Proust to identify topics and show them as a graphical network
Diachronic approaches include Block and Newman's determination the temporal dynamics of topics in the Martha Ballard's diary to identify thematic trends across the 27-year diary. Mimno used topic modelling with 24 journals on classical philology and archaeology spanning 150 years to look at how topics in the journals change over time and how the journals become more different or similar over time.
In practice researchers attempt to fit appropriate model parameters to the data corpus using one of several heuristics for maximum likelihood fit. A recent survey by Blei describes this suite of algorithms. Several groups of researchers starting with Papadimitriou et al. have attempted to design algorithms with provable guarantees. Assuming that the data was actually generated by the model in question, they try to design algorithms that provably find the model that was used to create the data. Techniques used here include singular value decomposition (SVD), the method of moments, and very recently an algorithm based upon non-negative matrix factorization (NMF). This last algorithm also generalizes to topic models that allow correlations among topics. 
Machine learning, Chinese language, Speech recognition, Corpus linguistics, English language
Singular value, Unitary matrix, QR decomposition, Linear algebra, Signal processing
Natural language processing, Parallel computing, Python (programming language), Open-source software, Vector space model
Statistics, Probability theory, Probability distribution, Symmetric Dirichlet distribution, Dirichlet process
Information retrieval, Natural language processing, Vector space model, Semantics, Reuters