Hierarchical structures induce long-range dynamical correlations in written texts
Hierarchical structures induce long-range dynamical correlations in written texts
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DOI：
10.1073/pnas.0510673103
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发表时间：
2006-05-23
影响因子：
11.1
通讯作者：
Moses, E.
中科院分区：
文献类型：
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作者：
Alvarez-Lacalle, E.;Dorow, B.;Moses, E.
思想和观念是多方面的，而且往往是同时发生的，然而，通过翻译成语言，它们可以令人惊讶地按顺序表达出来。这种维数的减少自然发生，但需要记忆并需要相关性的存在，例如，书面文本。然而，在字外观的相关性衰减很快，而以前的观察使用随机游走方法的长期相关性产生的记忆或语义上下文的洞察力很小。相反，我们研究的是读者在大约100个单词的“注意力窗口”内接触到的单词组合。我们定义了一个向量空间，这样的词的组合，通过观察的话，共同出现在注意力的窗口，并分析其结构。共生矩阵的奇异值分解识别其向量对应于特定主题或与文本相关的“概念”的基础。当读者阅读文本时，“注意力向量”在这个“概念空间”中划出一条方向轨迹。“我们发现，对方向的记忆会保留很长时间，形成幂律相关性。幂律的出现暗示了底层层级网络的存在。事实上，强加一个类似于由卷、章、段等定义的层次结构，成功地在替代随机文本中创建与原始文本相同的相关性。我们的结论是，在文本中的层次结构有助于创造长期的相关性，并使用读者的记忆在重演一些被表达的思想的多维性。
Thoughts and ideas are multidimensional and often concurrent, yet they can be expressed surprisingly well sequentially by the translation into language. This reduction of dimensions occurs naturally but requires memory and necessitates the existence of correlations, e.g., in written text. However, correlations in word appearance decay quickly, while previous observations of long-range correlations using random walk approaches yield little insight on memory or on semantic context. Instead, we study combinations of words that a reader is exposed to within a "window of attention" spanning about 100 words. We define a vector space of such word combinations by looking at words that co-occur within the window of attention, and analyze its structure. Singular value decomposition of the co-occurrence matrix identifies a basis whose vectors correspond to specific topics, or "concepts" that are relevant to the text. As the reader follows a text, the "vector of attention" traces out a trajectory of directions in this "concept space." We find that memory of the direction is retained over long times, forming power-law correlations. The appearance of power laws hints at the existence of an underlying hierarchical network. Indeed, imposing a hierarchy similar to that defined by volumes, chapters, paragraphs, etc. succeeds in creating correlations in a surrogate random text that are identical to those of the original text. We conclude that hierarchical structures in text serve to create long-range correlations, and use the reader's memory in reenacting some of the multidimensionality of the thoughts being expressed.