Multi-Objective Optimization-Based Networked Multi-Label Active Learning

Introduction

With the fast development of network applications (Batini & Rula, 2015; Cao et al., 2016; Long & Siau, 2007), network research has attracted more attention from both academic researchers and industrial engineers (Bhagat, Cormode, & Muthukrishnan, 2011; Bu et al., 2018; Li, et al., 2016), where one of the important research directions is networked multi-label classification (Wang & Sukthankar, 2013; Wu, Zhao, & Li, 2016; Zhang, et al., 2010). Specifically, unknown labels of nodes can be inferred by the known labels of other nodes in the neighborhood, and these inferred labels can be further used in user classification, community detection, or personalized recommendation (Guo, et al., 2017; Hong, et al., 2015; Li, et al., 2015). Networked data, which is different from traditional data with simple structures (Bhagat, Cormode, & Muthukrishnan, 2011), can reflect the complex relations, such as friendship or colleagues in life, or co-authorship of an article (Guo, et al., 2017; Miller, Perlman, & Brehm, 2007), between nodes in network environments (Fakhraei, et al., 2015; Otte & Rousseau, 2002), which makes it difficult to classify labels in networks (McDowell & Aha, 2016).

Mathematically, the multi-labeled network can be represented as a graph G=(W, E, C, Y), where W={, ,..., } is a set of nodes, E is a set of edges that connect pairs of nodes, C={, ,..., } represents labels with K classes, and =()∈ denotes the multi-labels that are associated with node (if belongs to label , = 1, otherwise = 0). W is divided into two disjoint parts: S, i.e., nodes whose labels are known which are named as seed nodes, and S = nseed and U, i.e., nodes whose labels need to be classified. The networked multi-label classification problem is to use S to infer the labels for nodes in U. Our seed node selection is to actively learn the set S to satisfy some objectives under certain conditions.