Possibilistic Neighborhood Graph: A New Concept of Similarity Graph Learning

Adaptive graph-based representation and learning methods have received extensive attention due to their good performance in supervised and unsupervised learning tasks. These methods often involve probability constraint, i.e., the sum-to-one constraint, when learning a similarity graph. Whereas this constraint may degrade the ability to precisely measure the similarity between samples. In terms of clustering tasks, limited by the sum-to-one constraint, the similarity between some noisy points may tend to be large, which causes these abnormal points to be grouped into a separate cluster, and other close clusters with normal points are merged. To address this problem, this study proposes a novel notion of possibilistic neighbor graph (PNG). In PNG, the possibility of two samples being neighbors can be measured adaptively and precisely by removing the sum-to-one constraint and incorporating a new regularization term. By using the possibility rather than the probability in the similarity graph learning, the solution space is enlarged without increasing the complexity. The mathematical properties of PNG are discussed in detail, and a new graph-based clustering method (CPNG) is also developed based on the learned PNG. Extensive experimental results on several benchmark datasets demonstrate the superiority of CPNG in comparison with some state-of-the-art methods.