Abstract
In this study, we regard written texts as time series data and try to investigate dynamic correlations of word occurrences by utilizing an autocorrelation function (ACF). After defining appropriate formula for the ACF that is suitable for expressing the dynamic correlations of words, we use the formula to calculate ACFs for frequent words in 12 books. The ACFs obtained can be classified into two groups: One group of ACFs shows dynamic correlations, with these ACFs well described by a modified Kohlrausch-Williams-Watts (KWW) function; the other group of ACFs shows no correlations, with these ACFs fitted by a simple stepdown function. A word having the former ACF is called a Type-I word and a word with the latter ACF is called a Type-II word. It is also shown that the ACFs of Type-II words can be derived theoretically by assuming that the stochastic process governing word occurrence is a homogeneous Poisson point process. Based on the fitting of the ACFs by KWW and stepdown functions, we propose a measure of word importance which expresses the extent to which a word is important in a particular text. The validity of the measure is confirmed by using the Kleinburg’s burst detection algorithm.
Highlights
We use language to convey our ideas
The autocorrelation function (ACF) obtained can be classified into two groups: One group of ACFs shows dynamic correlations, with these ACFs well described by a modified Kohlrausch-Williams-Watts (KWW) function; the other group of ACFs shows no correlations, with these ACFs fitted by a simple stepdown function
Starting from the standard definition of an ACF in the signal processing area, we derived a normalized expression for an ACF that is suitable to express the dynamic correlation of word occurrences
Summary
We use language to convey our ideas. Since our physical function is limited to speaking or writing only one word at a time, we must transform our complex ideas into linear strings of words. This approach has been successfully applied to the extraction of semantic representations [1], automatic key word and key phrase extraction [2] [3], local or global context analysis [4], measuring similarities at the word or context level [5], and many other tasks Another way to investigate correlations in linguistic data is to use a mapping scheme, that is, to translate the given sequence of words or characters in a text into a time series and thereby capture the correlations in a dynamical framework. The goal of this study is to find a modification of the word-level mapping that is suitable for defining and calculating appropriate ACFs in the mapping scheme
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