This paper presents a discovery that the length of the entities in various datasets follows a family of scale-free power law distributions. The concept of entity here broadly includes the named entity, entity mention, time expression, aspect term, and domain-specific entity that are well investigated in natural language processing and related areas. The entity length denotes the number of words in an entity. The power law distributions in entity length possess the scale-free property and have well-defined means and finite variances. We explain the phenomenon of power laws in entity length by the principle of least effort in communication and the preferential mechanism.
According to the review by , first demonstrated that the word length in a corpus empirically and theoretically follows a variant of Poisson distributions. The word length of a natural corpus has been observed to follow the variants of Poisson distributions in more than 32 languages @cite_17 .
@cite_17
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Abstract In this study, word length distributions are investigated in Old Icelandic songs and prose texts. Although Old Icelandic is separated from the other languages studied so far within the framework of the Gottingen word length project, the same model, viz. the hyper‐Poisson distribution, can successfully be fitted to the data. This paper presents a model-based, unsupervised algorithm for recovering word boundaries in a natural-language text from which they have been deleted. The algorithm is derived from a probability model of the source that generated the text. The fundamental structure of the model is specified abstractly so that the detailed component models of phonology, word-order, and word frequency can be replaced in a modular fashion. The model yields a language-independent, prior probability distribution on all possible sequences of all possible words over a given alphabet, based on the assumption that the input was generated by concatenating words from a fixed but unknown lexicon. The model is unusual in that it treats the generation of a complete corpus, regardless of length, as a single event in the probability space. Accordingly, the algorithm does not estimate a probability distribution on wordss instead, it attempts to calculate the prior probabilities of various word sequences that could underlie the observed text. Experiments on phonemic transcripts of spontaneous speech by parents to young children suggest that our algorithm is more effective than other proposed algorithms, at least when utterance boundaries are given and the text includes a substantial number of short utterances. Video-on-demand over IP (VOD) is one of the best-known examples of "next-generation" Internet applications cited as a goal by networking and multimedia researchers. Without empirical data, researchers have generally relied on simulated models to drive their design and developmental efforts. In this paper, we present one of the first measurement studies of a large VOD system, using data covering 219 days and more than 150,000 users in a VOD system deployed by China Telecom. Our study focuses on user behavior, content access patterns, and their implications on the design of multimedia streaming systems. Our results also show that when used to model the user-arrival rate, the traditional Poisson model is conservative and overestimates the probability of large arrival groups. We introduce a modified Poisson distribution that more accurately models our observations. We also observe a surprising result, that video session lengths has a weak inverse correlation with the video's popularity. Finally, we gain better understanding of the sources of video popularity through analysis of a number of internal and external factors. In this paper, we introduce an application of matrix factorization to produce corpus-derived, distributional models of semantics that demonstrate cognitive plausibility. We find that word representations learned by Non-Negative Sparse Embedding (NNSE), a variant of matrix factorization, are sparse, effective, and highly interpretable. To the best of our knowledge, this is the first approach which yields semantic representation of words satisfying these three desirable properties. Though extensive experimental evaluations on multiple real-world tasks and datasets, we demonstrate the superiority of semantic models learned by NNSE over other state-of-the-art baselines.