Inference From Complex Networks: Role of Symmetry and Applicability to Images
Inference From Complex Networks: Role of Symmetry and Applicability to Images
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DOI：
10.3389/fams.2020.00023
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发表时间：
2020-07-09
影响因子：
1.4
通讯作者：
Capobianco, Enrico
中科院分区：
文献类型：
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作者：
Capobianco, Enrico
对称性是一个数学概念，在网络中，特别是在应用层面上，只有部分探索。原因之一是缺乏从网络中获得的可解释的推理。虽然实体（节点）之间的网络系统关联（链接）来自底层依赖结构，但后者通过已建立的直接交互器仅部分显式，并且在一定程度上保持潜在（远距离节点预测路径）。重要枢纽、连接器、路径和模块的可验证性允许构建对推断延迟和/或验证复杂关联有用的知识库。当在图像中搜索对称性时，反射、平移和旋转是计算算法目标的n维欧几里得空间中的适用变换。当原始图像和变换后的图像无法区分时，存在对称性。一旦收集在一起，这样的转换形成一个自同构群，表明一个稳定和强大的全球性的特点。通常从图像到可量化的特征进行推理。深度学习通常用于对从这些图像分解的无数特征重建的整个图像进行分类。然而，考虑到图像在多个尺度和位置，对称性是有价值的描述局部特征。将局部特征投射到网络框架中，可以通过相似性或不相似性标准来探索它们的关联。这是非常有趣的，因为网络配置可能会显示与同步和对称相关的拓扑特征和连接模式，从而将特征的冗余减少到更紧凑的功能描述。然后，从不寻常的事件、行为、模式中识别出异常，就可以发现网络的漏洞和对称性破坏的迹象。
Symmetry is a mathematical concept only partially explored in networks, especially at the applicative level. One reason is a certain lack of interpretable inference obtained from networks. While the network systemic associations (links) between entities (nodes) emerge from the underlying dependence structure, this latter is only partially explicit via the established direct interactors and remains to a certain extent latent (distant node predicted paths). Verifiability of significant hubs, connectors, paths, and modules allows to build a knowledge base useful to infer latencies and/or validate complex associations. When symmetry is searched in images, reflection, translation and rotation are applicable transformations in n-dimensional Euclidean space that computational algorithms target. There is symmetry when original and transformed images cannot be distinguished. Once collected together, such transformations form an automorphism group, indicating a stable and robust global characteristic. It is common to step from images to quantifiable features for conducting inference. Deep learning is typically used to classify whole images reconstructed from the myriads of features in which these images are decomposed. However, with images considered at multiple scales and locations, symmetries are valuable for describing local characteristics. Casting local features into a network framework enables their associations to be explored by similarity or dissimilarity criteria. This is quite intriguing because network configurations may display topological features and connectivity patterns associated with synchronization and symmetry that reduce the redundancy of features to more compact functional descriptions. Then, identifying anomalies from unusual events, behaviors, patterns would spot network vulnerabilities and signs of symmetry breaking.