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Node embedding is the task of extracting concise and informative representations of certain entities that are connected in a network. Various real-world networks include information about both node connectivity and certain node attributes, in the form of features or time-series data. Modern representation learning techniques employ both the connectivity and attribute information of the nodes to produce embeddings in an unsupervised manner. In this context, deriving embeddings that preserve the geometry of the network and the attribute vectors would be highly desirable, as they would reflect both the topological neighborhood structure and proximity in feature space. While this is fairly straightforward to maintain when only observing the connectivity or attribute information of the network, preserving the geometry of both types of information is challenging. A novel tensor factorization approach for node embedding in attributed networks is proposed in this paper, that preserves the distances of both the connections and the attributes. Furthermore, an effective and lightweight algorithm is developed to tackle the learning task and judicious experiments with multiple state-of-the-art baselines suggest that the proposed algorithm offers significant performance improvements in downstream tasks. 

Tensor decomposition models have proven to be effective analysis tools in various applications, including signal processing, machine learning, and communications, to name a few. Canonical polyadic decomposition (CPD) is a very popular model, which decomposes a higher order tensor signal into a sum of rank 1 terms. However, when the tensor size gets big, computing the CPD becomes a lot more challenging. Previous works proposed using random (generalized) tensor sampling or compression to alleviate this challenge. In this work, we propose using a regular tensor sampling framework instead. We show that by appropriately selecting the sampling mechanism, we can simultaneously control memory and computational complexity, while guaranteeing identifiability at the same time. Numerical experiments with synthetic and real data showcase the effectiveness of our approach.