Tenuous subgraph finding aims to detect a subgraph with few social interactions and weak relationships among nodes. Despite significant efforts made on this task, they are mostly carried out in view of graph-structured data. These methods depend on calculating the shortest path and need to enumerate all the paths between nodes, which suffer the combinatorial explosion. Moreover, they all lack the integration of neighborhood information. To this end, we propose a novel model named Graph Neural Network with Motif-aware for tenuous subgraph finding (GNNM), a neighborhood aggregation-based GNN framework that can capture the latent relationship between nodes. We design a GNN module to project nodes into a low-dimensional vector combining the higher-order correlation within nodes based on a motif-aware module. Then we design greedy algorithms in vector space to obtain a tenuous subgraph whose size is greater than a specified constraint. Particularly, considering that existing evaluation indicators cannot capture the latent friendship between nodes, we introduce a novel Potential Friend concept to measure the tenuity of a graph from a new perspective. Experimental results on the real-world and synthetic datasets demonstrate that our proposed method GNNM outperforms existing algorithms in efficiency and subgraph quality.

Recently, causal feature selection (CFS) has attracted considerable attention due to its outstanding interpretability and predictability performance. Such a method primarily includes the Markov blanket (MB) discovery and feature selection based on Granger causality. Representatively, the max-min MB (MMMB) can mine an optimal feature subset, i.e., MB; however, it is unsuitable for streaming features. Online streaming feature selection (OSFS) via online process streaming features can determine parents and children (PC), a subset of MB; however, it cannot mine the MB of the target attribute ( T ), i.e., a given feature, thus resulting in insufficient prediction accuracy. The Granger selection method (GSM) establishes a causal matrix of all features by performing excessively time; however, it cannot achieve a high prediction accuracy and only forecasts fixed multivariate time series data. To address these issues, we proposed an online CFS for streaming features (OCFSSFs) that mine MB containing PC and spouse and adopt the interleaving PC and spouse learning method. Furthermore, it distinguishes between PC and spouse in real time and can identify children with parents online when identifying spouses. We experimentally evaluated the proposed algorithm on synthetic datasets using precision, recall, and distance. In addition, the algorithm was tested on real-world and time series datasets using classification precision, the number of selected features, and running time. The results validated the effectiveness of the proposed algorithm.