How much did a network change since yesterday? How different is the wiring
between Bob's brain (a left-handed male) and Alice's brain (a right-handed
female)? Graph similarity with known node correspondence, i.e. the detection of
changes in the connectivity of graphs, arises in numerous settings. In this
work, we formally state the axioms and desired properties of the graph
similarity functions, and evaluate when state-of-the-art methods fail to detect
crucial connectivity changes in graphs. We propose DeltaCon, a principled,
intuitive, and scalable algorithm that assesses the similarity between two
graphs on the same nodes (e.g. employees of a company, customers of a mobile
carrier). Experiments on various synthetic and real graphs showcase the
advantages of our method over existing similarity measures. Finally, we employ
DeltaCon to real applications: (a) we classify people to groups of high and low
creativity based on their brain connectivity graphs, and (b) do temporal
anomaly detection in the who-emails-whom Enron graph.

本研究旨在通过形式化规定图相似性函数的公理和期望属性，评估现有最先进的方法在检测图中关键连通性变化方面的失败情况，并提出了 DeltaCon 算法，在不同种类的合成和真实图上显示了该方法在相似性测量上的优点，同时应用于人脑连接图和电子邮件关系图的分类和异常检测。

DELTACON：基于原则的大规模图相似度函数

DELTACON: A Principled Massive-Graph Similarity Function

Spontaneous brain activity, as observed in functional neuroimaging, has been
shown to display reproducible structure that expresses brain architecture and
carries markers of brain pathologies. An important view of modern neuroscience
is that such large-scale structure of coherent activity reflects modularity
properties of brain connectivity graphs. However, to date, there has been no
demonstration that the limited and noisy data available in spontaneous activity
observations could be used to learn full-brain probabilistic models that
generalize to new data. Learning such models entails two main challenges: i)
modeling full brain connectivity is a difficult estimation problem that faces
the curse of dimensionality and ii) variability between subjects, coupled with
the variability of functional signals between experimental runs, makes the use
of multiple datasets challenging. We describe subject-level brain functional
connectivity structure as a multivariate Gaussian process and introduce a new
strategy to estimate it from group data, by imposing a common structure on the
graphical model in the population. We show that individual models learned from
functional Magnetic Resonance Imaging (fMRI) data using this population prior
generalize better to unseen data than models based on alternative
regularization schemes. To our knowledge, this is the first report of a
cross-validated model of spontaneous brain activity. Finally, we use the
estimated graphical model to explore the large-scale characteristics of
functional architecture and show for the first time that known cognitive
networks appear as the integrated communities of functional connectivity graph.

通过建立整个脑部的概率模型，利用群体数据来推断个体的脑连接结构，进而探索大规模的功能结构，以及首次展示已知的认知网络是如何成为功能连接图的集成社团的。