Term burstiness: evidence, model and applications

Sarkar, Avik (2008). Term burstiness: evidence, model and applications. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000fa70


The present thesis looks at the phenomenon of term burstiness in text. Term burstiness is defined as the multiple re-occurrences in short succession of a particular term after it has occurred once in a certain text. Term burstiness is important as it aids in providing structure and meaning to a document. Various kinds of term burstiness in text are studied and their effect on a dataset explored in a series of homogeneity experiments. A novel model of term burstiness is proposed and evaluations based on the proposed model are performed on three different applications.

The “bag-of-words” assumption is often used in statistical Natural Language Processing and Information Retrieval applications. Under this assumption all structure and positional information of terms is lost and only frequency counts of the document are retained. As a result of counting frequencies only, the “bag-of-words” representation of text assumes that the probability of a word occurring remains constant throughout the text. This assumption is often used because of its simplicity and the ease it provides for the application of mathematical and statistical techniques on text. Though this assumption is known to be untrue [CG95b, CG95a, ChuOO], but applications [SB97, Lew98, MN98, Seb02] based on this assumption appear not to be much hampered.

A series of homogeneity based experiments are carried out to study the presence and extent of term burstiness against the term independence based homogeneity assumption on the dataset. A null hypothesis stating the homogeneity of a dataset is formulated and defeated in a series of experiments based on the y2 test, which tests the equality between two partitions of a certain dataset. Various schemes of partitioning a dataset are adopted to illustrate the effect of term burstiness and structure in text. This provided evidence of term burstiness in the dataset, and fine-grained information about the distribution of terms that might be used for characterizing or profiling a dataset.

A model for term burstiness in a dataset is proposed based on the gaps between successive occurrences of a particular term. This model is not merely based on frequency counts like other existing models, but takes into account the structural and positional information about the term’s occurrence in the document. The proposed term burstiness model looks at gaps between successive occurrences of the term. These gaps are modeled using a mixture of exponential distributions. The first exponential distribution provides the overall rate of occurrence of a term in a dataset and the second exponential distribution determines the term’s rate of re-occurrence in a burst or when it has already occurred once previously. Since most terms occur in only a few documents, there are a large number of documents with no occurrences of a particular term. In the proposed model, non-occurrence of a term in a document is accounted for by the method of data censoring. It is not straightforward to obtain parameter estimates for such a complex model. So, Bayesian statistics is used for flexibility and ease of fitting this model, and for obtaining parameter estimates.

The model can be used for all kinds of terms, be they rare content words, medium frequency terms or frequent function words. The term re-occurrence model is instantiated and verified against the background of different collections, in the context of three different applications. The applications include studying various terms within a dataset to identify behavioral differences between the terms, studying similar terms across different datasets to detect stylistic features based on the term’s distribution and studying the characteristics of very frequent terms across different datasets. The model aids in the identification of term characteristics in a dataset. It helps distinguish between highly bursty content terms and less bursty function words. The model can differentiate between a frequent function word and a scattered one. It can be used to identify stylistic features in a term’s distribution across text of varying genres. The model also aids in understanding the behaviour of very frequent (usually function) words in a dataset.

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