Temporal Network Embedding with High-Order Nonlinear Information

Abstract

Temporal network embedding, which aims to learn the low-dimensional representations of nodes in temporal networks that can capture and preserve the network structure and evolution pattern, has attracted much attention from the scientific community. However, existing methods suffer from two main disadvantages: 1) they cannot preserve the node temporal proximity that capture important properties of the network structure; and 2) they cannot represent the nonlinear structure of temporal networks. In this paper, we propose a high-order nonlinear information preserving (HNIP) embedding method to address these issues. Specifically, we define three orders of temporal proximities by exploring network historical information with a time exponential decay model to quantify the temporal proximity between nodes. Then, we propose a novel deep guided auto-encoder to capture the highly nonlinear structure. Meanwhile, the training set of the guide auto-encoder is generated by the temporal random walk (TRW) algorithm. By training the proposed deep guided auto-encoder with a specific mini-batch stochastic gradient descent algorithm, HNIP can efficiently preserves the temporal proximities and highly nonlinear structure of temporal networks. Experimental results on four real-world networks demonstrate the effectiveness of the proposed method.

Temporal Network Embedding via Tensor Factorization

“…A temporal network embedding algorithm that exploits the time-constrained temporal random walk using an extension to the node2vec [4] algorithm via the skip-gram model. • HNIP [12]. A temporal network embedding algorithm that employs the high-order non-linear information as an extension to the auto-encoder-based network embedding algorithms.…”

“…( 4) to encode sufficient temporal information (for RESCAL we use matrix product instead of t-product). For CTDNE, HNIP, and HTNE, we adopt the same hyperparameter settings as in paper [12]. For TNE, we take the embeddings of last timestamp for evaluations.…”

“…HTNE [18] extended CTDNE by generating neighbors using the Hawkes process. [12] proposed HNIP, a temporal random walk that preserves high-order proximity and used an auto-encoder to capture the nonlinearity of the network structure. All these neighborhood-based algorithms have an inherent disadvantage that their local structure inferences are heavily reliant on neighborhood relations and can overlook the global structure at large, which may incur poor performance especially when the graph is densely connected.…”

Multiscale Clustering Based Diffusion Representation Learning Method

“…where t j and t i are the time when user j and user i received message m, respectively. The design of formula is inspired by the first-order temporal proximity [15]. Different from the original formula, we take the logarithm of time interval.…”

Towards a typology of university technology transfer organizations in China: evidences from Tsinghua University

“…However, the optimal predictor trained with the training distribution may not generalize well to the test distribution when there exists a distribution shift problem. In the literature of dynamic graphs, researchers are devoted to capturing laws of network dynamics which are stable in systems [42,86,103,113,138]. Following them, we assume the conditional distribution is the same 𝑝 𝑡𝑟 (Y 𝑡 |G 1:𝑡 ) = 𝑝 𝑡𝑒 (Y 𝑡 |G 1:𝑡 ), and only consider the covariate shift problem where 𝑝 𝑡𝑟 (G 1:𝑡 ) ≠ 𝑝 𝑡𝑒 (G 1:𝑡 ).…”