Semi-Supervised Classification via Local Spline Regression

Abstract--This paper presents local spline regression for semisupervised classification. The core idea in our approach is to introduce splines developed in Sobolev space to map the data points directly to be class labels. The spline is composed of polynomials and Green's functions. It is smooth, nonlinear and able to interpolate the scattered data points with high accuracy. Specifically, in each neighborhood, an optimal spline is estimated via regularized least squares regression. With this spline, each of the neighboring data points is mapped to be a class label. Then, the regularized loss is evaluated and further formulated in terms of class label vector. Finally, all the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on the labeled and unlabeled data. To achieve the goal of semi-supervised classification, an objective function is constructed, by combining together the global loss of the local spline regressions and the squared...

• Type: Journal
• Year: 2010
• Where: PAMI
• Authors: Shiming Xiang, Feiping Nie, Changshui Zhang
• Keywords: Class Labels, Data Points, Intelligent Agents, Local Spline Regressions, PAMI 2010