Multi-Manifold Positive and Unlabeled Learning for Visual Analysis

Abstract

Positive and Unlabeled (PU) learning has attracted intensive research interests in recent years, which is capable of training a binary classifier solely based on positive and unlabeled examples when the negative data are absent or too are diverse. However, the existing PU learning methods largely overlook the relationship between the examples when handling the unlabeled data, leading to insufficient exploitation of data structure which actually contains useful distribution information. Therefore, by following the multi-manifold assumption which is observed in many real-world vision problems, this paper proposes a novel algorithm termed “Multi-Manifold PU learning” (MMPU), which assumes that the data belonging to different classes lie on different underlying manifolds. As such, the structural information revealed by the dataset is deployed, which is helpful in deciding the labels of unlabeled examples. Our MMPU contains two main steps, namely, multi-manifold exploration and positive confidence training, where the former is accomplished by computing the local similarity, structural similarity, and semantic similarity of pairwise data, and the latter establishes a binary classifier in reproducing kernel Hilbert space based on the real-valued confidence level of each example to be positive. Experimentally, we not only test the proposed MMPU on five highly nonlinear synthetic datasets but also apply MMPU to various typical computer vision tasks, including handwritten digit recognition, violent behavior detection, and hyperspectral image classification. The results demonstrate that MMPU can obtain a superior performance compared to the state-of-the-art PU learning methodologies.