Abstract
The theoretical limit of link prediction is a fundamental problem in this field. Taking the network structure as object to research this problem is the mainstream method. This paper proposes a new viewpoint that link prediction methods can be divided into single or combination methods, based on the way they derive the similarity matrix, and investigates whether there a theoretical limit exists for combination methods. We propose and prove necessary and sufficient conditions for the combination method to reach the theoretical limit. The limit theorem reveals the essence of combination method that is to estimate probability density functions of existing links and nonexistent links. Based on limit theorem, a new combination method, theoretical limit fusion (TLF) method, is proposed. Simulations and experiments on real networks demonstrated that TLF method can achieve higher prediction accuracy.
Highlights
Limit theory is a basic theoretical issue and has attracted wide interest across many fields
Single methods, such as Resource Allocation index (RA) index [15], which defines the relation of common neighbors and degree of nodes directly; and classification based methods, index fusion methods, fusion of structure and attribute information methods belong to link prediction combination methods
Link prediction method based on the choquet fuzzy integral [7] uses fuzzy measures to measure the importance of each similarity index in the fusion process and the interaction between them
Summary
Limit theory is a basic theoretical issue and has attracted wide interest across many fields. Considering structure or attribute features, link prediction methods based on classification have been proposed by computer science community [4,5]. This paper proposes the mathematic description of combination methods, and obtains the necessary and sufficient conditions for theoretical limit. Sci. 2018, 8, 32 limit theorem has important practical application value It reveals the ultimate goal of combination methods that is to estimate probability density functions of existing links and nonexistent links. Based on the limit theorem, a new combination method, theoretical limit fusion (TLF). The theoretical limit of combination methods prediction method based on limit theorem (TLF method).
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