多重社会网络中潜在相似性的低失真推理
Low-distortion Inference of Latent Similarities from a Multiplex Social Network
摘要：
大部分社会网络分析都是--或隐或显--基于这样一个假设，即个人倾向于与他们的朋友而不是陌生人更相似。因此，观察到的社会网络提供了一个关于潜在的“社会空间“的嘈杂信号：个体相似或不相似的方式。通过社会网络分析经常解决的许多研究问题实际上是关于这个社会空间的问题，提出了一个颠倒过程的问题：给定一个社会网络，我们如何准确地重建相似性和差异性的社会结构？我们开始正式解决这个问题。观察到的社交网络通常是多元的，在某种意义上，它们反映了几个不同“类别”的相似性，如地理上的接近性，亲属关系，或职业/爱好的相似性。我们假设，每个这样的类别的特征在于一个潜在的度量捕获（不）在这一类的相似性。每个类别都会产生一个单独的社交网络：一个由这个度量参数化的随机图。对于一个具体的模型，我们考虑Kleinberg的小世界模型和一些变化。观察到的社交网络是这些图的未标记的并集，即，可以观察到边缘的存在或不存在，但不能观察到它们的起源。我们的主要结果是一个算法，重建每个度量可证明低失真。
英文摘要：
Much of social network analysis is - implicitly or explicitly - predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the latent underlying "social space:" the way in which individuals are similar or dissimilar. Many research questions frequently addressed via social network analysis are in reality questions about this social space, raising the question of inverting the process: Given a social network, how accurately can we reconstruct the social structure of similarities and dissimilarities? We begin to address this problem formally. Observed social networks are usually multiplex, in the sense that they reflect (dis)similarities in several different "categories," such as geographical proximity, kinship, or similarity of professions/hobbies. We assume that each such category is characterized by a latent metric capturing (dis)similarities in this category. Each category gives rise to a separate social network: a random graph parameterized by this metric. For a concrete model, we consider Kleinberg's small world model and some variations thereof. The observed social network is the unlabeled union of these graphs, i.e., the presence or absence of edges can be observed, but not their origins. Our main result is an algorithm which reconstructs each metric with provably low distortion.
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。
