Mining the relationship structures among the investors plays a vital role in promoting economic development as well as preventing financial risks, especially in the context of big data. This article proposes fast networking approaches from investment big data to explore three underlying structures, namely, investment pedigrees, investment groups, and structural holes. Inspired by disjoint sets and path compression, we first present a pedigree classification algorithm to identify investment pedigrees. Second, through introducing a pruning strategy and a data structure termed as ``2-tuple list,'' we develop a novel linear-time structure mining algorithm in network (SMAN) for investigating investment groups and structural holes from the investment pedigree. Finally, we show that our SMAN has higher clustering accuracy and \nobreak efficiency than other existing algorithms on a variety of real-world tasks in terms of normalized mutual information (NMI) values. Our method is particularly well suited for mining the underlying structures from investment big data.

Social recommendations typically utilize social relationships and past behaviors to predict users’ preferences. In real-world scenarios, the connections between users and items often extend beyond simple pairwise relationships. Leveraging hypergraphs to capture high-order relationships provides a novel perspective to social recommendation. However, effectively modeling these high-order relationships is challenging due to limited external knowledge and noisy feedback. To tackle these challenges, we propose a novel framework called self-supervised hypergraph learning for knowledge-aware social recommendation (SHLKR). In SHLKR, we incorporated three main types of connections: behavior, social, and attribute context relationships. These dependencies serve as the basis for defining hyperedges in the hypergraphs. A dual-channel hypergraph structure is created based on these relationships. Then, the hypergraph convolution is applied to model the high-order interactions between users and items. Additionally, we adopted a self-supervised learning task to maximize the consistency between different views. It helps to mitigate the model’s sensitivity to noisy feedback. We evaluated the performance of SHLKR through extensive experiments on publicly available datasets. The results demonstrate that leveraging hypergraphs for modeling can better capture the complexity and diversity of user preferences and interactions.

Temporal link prediction is one of the most important tasks for predicting time-varying links by capturing dynamics within complex networks. However, it suffers from difficulties such as vulnerability to adversarial attacks and inadaptation to distinct evolutionary patterns. In this article, we propose a robust temporal link prediction architecture via stable gated models with reinforcement learning (SAGE-RL) consisting of a state encoding network (SEN) and a self-adaptive policy network (SPN). The former is utilized to capture network dynamics, while the latter helps the former adapt to distinct evolutionary patterns across various time periods. Within the SEN, a novel stable gate is introduced to ensure multiple spatiotemporal dependency paths and defend against adversarial attacks. An SPN is proposed to select different SEN instances by approximating the optimal action function, thereby adapting to various evolutionary patterns to learn the robust temporal and structural features from dynamic complex networks. It is proven that SAGE-LR with integral Lipschitz graph convolution is stable to relative perturbations in dynamic complex networks. With the aid of extensive experiments on five real-world graph benchmarks, SAGE-LR is shown to substantially outperform current state-of-the-art approaches in terms of precision and stability of temporal link prediction and ability to successfully defend against various attacks. We also implement the temporal link prediction in shipping transaction networks, which forecast effectively its potential transaction risks.

This study provides new equivalent descriptions of the Bounded Lower Oscillation ($\mathrm{BLO}$) space through Luxemburg-type $L^{\phi }$ integrability conditions, where $\phi$ is a nonnegative function with either convexity or concavity. The framework accommodates various representative forms of $\phi$, such as the power function $\phi \left(t\right)=t^p$, exponential-type functions $\phi \left(t\right)=e^{pt}-1$, and logarithmic functions $\phi \left(t\right)={log}_{+}^{k}t$, with parameters $p\in (0,\infty )$ and $k\in \mathbb{N}$. These results unify and extend existing characterizations of $\mathrm{BLO}$ by encompassing a broad class of generating functions.