基于网络的模糊性约简技术中信息损失的量化
Quantifying Loss of Information in Network-based Dimensionality Reduction Techniques
摘要：
为了应对大型网络的复杂性，已经开发了许多图的降维技术。然而，在采用这些技术时，信息丢失或保存的程度尚不清楚。在这里，我们开发了一个框架，基于算法信息理论，量化的程度时，网络模体分析，图谱和光谱稀疏化方法被应用到超过20个不同的生物和人工网络的信息被保存。我们发现，频谱稀疏化是高度敏感的高数量的边缘删除，导致显着的不一致性，和图频谱方法是最不规则的，捕捉代数信息在一个浓缩的方式，但在很大程度上失去了大部分的原始网络的信息内容。然而，该方法表明，网络模体分析擅长于保留网络的相对算法信息内容，因此验证和推广了一个显著的事实，即尽管它们固有的组合可能性，但局部模体保留信息的程度使得基本属性在不同的网络中完全可恢复，以确定它们所属的家族组（例如遗传网络与社会网络）。因此，我们的算法信息方法提供了一个严格的框架，使不同的数据降维方法之间的基本评估和比较，从而促进识别和评估新旧方法的能力。
英文摘要：
To cope with the complexity of large networks, a number of dimensionality reduction techniques for graphs have been developed. However, the extent to which information is lost or preserved when these techniques are employed has not yet been clear. Here we develop a framework, based on algorithmic information theory, to quantify the extent to which information is preserved when network motif analysis, graph spectra and spectral sparsification methods are applied to over twenty different biological and artificial networks. We find that the spectral sparsification is highly sensitive to high number of edge deletion, leading to significant inconsistencies, and that graph spectral methods are the most irregular, capturing algebraic information in a condensed fashion but largely losing most of the information content of the original networks. However, the approach shows that network motif analysis excels at preserving the relative algorithmic information content of a network, hence validating and generalizing the remarkable fact that despite their inherent combinatorial possibilities, local regularities preserve information to such an extent that essential properties are fully recoverable across different networks to determine their family group to which they belong to (eg genetic vs social network). Our algorithmic information methodology thus provides a rigorous framework enabling a fundamental assessment and comparison between different data dimensionality reduction methods thereby facilitating the identification and evaluation of the capabilities of old and new methods.
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。
