最大熵、词频、汉字与多重意义
Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings
摘要：
作者所写的文本的词频分布很好地解释了最大熵分布，RGF（随机组形成）预测。RGF分布完全由文本中的单词总数（M）、不同单词的数量（N）和最常见单词的重复次数（k_max）的先验值确定。它在这里示出，这种最大熵预测也描述了一个文本写在汉字。特别是它表明，虽然相同的中文文本写在单词和汉字有很大不同的形状分布，但它们都很好地预测各自的三个先验特征值。有人指出，这是类似的形状的分布时，翻译一个给定的文本到另一种语言的变化。RGF预测的另一个结果是，取长文本的一部分将改变输入参数（M，N，k_max），因此也改变频率分布的形状。这一点在以汉字书写的文本中得到明确证实。由于在三个先验值（M，N，k_max）之外，RGF预测没有系统特定的信息，因此必须在与RGF预测和测量的频率的系统偏差中寻找任何特定的语言特征。一个这样的系统偏差被确定，并通过统计信息理论论证和扩展的RGF模型，提出这种偏差是由汉字的多重含义。对汉字的影响比对汉语单词的影响大。讨论了Zipf定律、Simon模型与本文结果的关系。
英文摘要：
The word-frequency distribution of a text written by an author is well accounted for by a maximum entropy distribution, the RGF (random group formation)-prediction. The RGF-distribution is completely determined by the a priori values of the total number of words in the text (M), the number of distinct words (N) and the number of repetitions of the most common word (k_max). It is here shown that this maximum entropy prediction also describes a text written in Chinese characters. In particular it is shown that although the same Chinese text written in words and Chinese characters have quite differently shaped distributions, they are nevertheless both well predicted by their respective three a priori characteristic values. It is pointed out that this is analogous to the change in the shape of the distribution when translating a given text to another language. Another consequence of the RGF-prediction is that taking a part of a long text will change the input parameters (M, N, k_max) and consequently also the shape of the frequency distribution. This is explicitly confirmed for texts written in Chinese characters. Since the RGF-prediction has no system-specific information beyond the three a priori values (M, N, k_max), any specific language characteristic has to be sought in systematic deviations from the RGF-prediction and the measured frequencies. One such systematic deviation is identified and, through a statistical information theoretical argument and an extended RGF-model, it is proposed that this deviation is caused by multiple meanings of Chinese characters. The effect is stronger for Chinese characters than for Chinese words. The relation between Zipf's law, the Simon-model for texts and the present results are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
