Semi-supervised learning through adaptive Laplacian graph trimming

Zongsheng Yue, Deyu Meng, Juan He, Gemeng Zhang

Abstract: Highlights • A method which can adaptively fit a proper Laplacian weighted graph from data. • A penalty helping cut inter-cluster shortcuts and enhance intra-cluster connections. • A graph-based SSL model is less sensitive to neighborhood size by integrating ALGT. • Superiority of ALGT is verified by experimental results on synthetic and UCI data. Abstract Graph-based semi-supervised learning (GSSL) attracts considerable attention in recent years. The performance of a general GSSL method relies on the quality of Laplacian weighted graph (LWR) composed of the similarity imposed on input examples. A key for constructing an effective LWR is on the proper selection of the neighborhood size K or ε on the construction of KNN graph or ε-neighbor graph on training samples, which constitutes the fundamental elements in LWR. Specifically, too large K or ε will result in “shortcut” phenomenon while too small ones cannot guarantee to represent a complete manifold structure underlying data. To this issue, this study attempts to propose a method, called adaptive Laplacian graph trimming (ALGT), to make an automatic tuning to cut improper inter-cluster shortcut edges while enhance the connection between intra-cluster samples, so as to adaptively fit a proper LWR from data. The superiority of the proposed method is substantiated by experimental results implemented on synthetic and UCI data sets.