Unsupervised Attributed Dynamic Network Embedding with Stability Guarantees

While most existing network embedding techniques focus solely on the network features, nodes in real-world networks are associated with a rich set of attributes. For example, in a social network, the user's posts are significantly correlated with trust and following relationships, and it has been shown that jointly exploiting both information sources improves learning performance [Tang et al., 2013]. Network embeddings for static attributed networks include frameworks based on matrix factorisation [Yang et al., 2015], or deep learning [Gao and Huang, 2018, Tu et al., 2017, Tan et al., 2023, Sun et al., 2016, Zhang et al., 2018, Li et al., 2021]. Some existing dynamic network embeddings leverage node attributes, but their exploitation of node attributes is rather limited, as they are usually solely used to initialise the first layer [Sankar et al., 2020, Dwivedi et al., 2023, Liu et al., 2021, Xu et al., 2020b,a]. Approaches that purposefully exploit node attributes include frameworks based on matrix factorisation [Liu et al., 2020, Li et al., 2017], deep learning [Tang et al., 2022, Ahmed et al., 2024, Wei et al., 2019], or Bayesian modelling [Luodi et al., 2024]. However, to the best of our knowledge, none of these methods have stability guarantees, which ensure that if two node/time pairs "behave the same" in the network, their representation is the same up to noise. Stability allows for the comparison of embeddings over time because the embedding space has a consistent interpretation. Attributed unfolded adjacency spectral embedding (AUASE) is a framework for unsupervised dynamic attributed network embedding with stability guarantees.