Online Multi-Hop Information Based Kernel Learning Over Graphs

Abstract

With complex systems emerging in various applications, e.g., financial, biological and social networks, graphs become working horse to model and analyse these systems. Nodes within networks usually entail attributes. Due to privacy concerns and missing observations, nodal attributes may be unavailable for some nodes in real-world networks. Besides, new nodes with unknown nodal attributes may emerge at any time, which require evaluation of the corresponding attributes in real-time. In this context, the present paper reconstructs nodal attributes of unobserved ones via an estimated nodal function based on their connectivity patterns with other nodes in the graph. Unlike existing works which only consider single-hop neighbors, the present paper further explores global information and adaptively combines the effects of multi-hop neighbors together. A multikernel-based approach is developed, which is capable of leveraging global network information, and scales well with network size as well. In addition, it has the flexibility to account for different nonlinear relationship by adaptively selecting the appropriate kernel combination. Experiments on real-word datasets corroborate the merits of the proposed algorithm.

NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs

“…(2) Query2Box (Ren, Hu, and Leskovec 2020), EMQL (Sun et al 2020), HypE (Fatemi et al 2020), CQD (Arakelyan et al 2021), and PERM (Choudhary et al 2021) handle arbitrary logical queries involving disjunction(∨) in addition to ∃ and ∧, which are called existentially positive first order (EPFO) queries. (3) BetaE (Ren and Leskovec 2020), ConE (Zhang et al 2021), NewLook , Fuzz-QE (Chen, Hu, and Sun 2022), and GNN-QE (Zhu et al 2022) can handle all first-order logic (FOL) with logical operations including ∃, ∧, ∨, and negation(¬).…”

“…Traditional CQA methods obtain answers through graph database query languages such as SPARQL, for which challenges remain, such as high time complexity and missing edges. To tackle these challenges, some approaches based on query embedding (QE) (Hamilton et al 2018;Ren, Hu, and Leskovec 2020;Arakelyan et al 2021;Zhang et al 2021;Lin et al 2022;Chen, Hu, and Sun 2022) propose to embed queries and entities into the same latent space according to computational graphs, obtaining query answers by computing similarity scores. However, most QE approaches are limited to queries among bi- In modern large-scale KGs, e.g., Wikidata (Vrandecic and Krötzsch 2014) and Freebase (Bollacker et al 2008), in addition to binary relational facts, n-ary facts (n ≥ 2) are also abundant, which have a novel hyper-relational representation of one primary triple plus n-2 attribute-value qualifiers ((s, r, o), {(a i : v i )} n−2 i=1 ) (Rosso, Yang, and Cudré-Mauroux 2020).…”

Gaussian Kernel Variance For an Adaptive Learning Method on Signals Over Graphs

“…The authors of [16] have shown the impressive performance of the algorithm in terms of Normalized Mean Square Error (NMSE) and its low complexity. Authors of [17] propose a similar algorithm, Graph Kernel Least Mean Squares-Random Fourier Features (GKLMS-RFF), which contains the same model but takes graph-filtered nodal value time sequence of a node as input, instead of the adjacency vector of a node, and provide the convergence condition. Gradraker is extended to exploit multi-hop information for estimation in [17], and has the potential to be applied on multi-layer graphs.…”

“…Among many kinds of shift-invariant kernels [15], e.g., Gaussian kernels, Laplacian kernels, and Cauchy kernels, we will focus on Gaussian kernels. Noting that the kernel being used models how similarity changes with difference, and that the laws of large numbers indicate wide application of the Gaussian distribution, it is intuitive to use Gaussian kernels in most situations [16], [17], [20]. For this reason, in this paper we will discuss SKG with a Gaussian kernel in detail.…”