Transductive Regression Piloted by Inter-Manifold Relations

Transductive Regression Piloted by Inter-Manifold Relations
Huan Wang - The Chinese University of Hong Kong, China Shuicheng Yan - University of Illinois at Urbana-Champaign, USA Thomas Huang - University of Illinois at Urbana-Champaign, USA Jianzhuang Liu - The Chinese University of Hong Kong, China Xiaoou Tang - The Chinese University of Hong Kong, China
In this paper, we present a novel semisupervised regression algorithm working on multiclass data that may lie on multiple manifolds. Unlike conventional manifold regression algorithms that do not consider the class distinction of samples, our method introduces the class information to the regression process and tries to exploit the similar configurations shared by the label distribution of multi-class data. To utilize the correlations among data from diffierent classes, we develop a cross-manifold label propagation process and employ labels from diffierent classes to enhance the regression performance. The interclass relations are coded by a set of intermanifold graphs and a regularization item is introduced to impose inter-class smoothness on the possible solutions. In addition, the algorithm is further extended with the kernel trick for predicting labels of the out-ofsample data even without class information. Experiments on both synthesized data and real world problems validate the effiectiveness of the proposed framework for semisupervised regression.

Huan Wang - The Chinese University of Hong Kong, China
Shuicheng Yan - University of Illinois at Urbana-Champaign, USA
Thomas Huang - University of Illinois at Urbana-Champaign, USA
Jianzhuang Liu - The Chinese University of Hong Kong, China
Xiaoou Tang - The Chinese University of Hong Kong, China

In this paper, we present a novel semisupervised regression algorithm working on multiclass data that may lie on multiple manifolds. Unlike conventional manifold regression algorithms that do not consider the class distinction of samples, our method introduces the class information to the regression process and tries to exploit the similar configurations shared by the label distribution of multi-class data. To utilize the correlations among data from diffierent classes, we develop a cross-manifold label propagation process and employ labels from diffierent classes to enhance the regression performance. The interclass relations are coded by a set of intermanifold graphs and a regularization item is introduced to impose inter-class smoothness on the possible solutions. In addition, the algorithm is further extended with the kernel trick for predicting labels of the out-ofsample data even without class information. Experiments on both synthesized data and real world problems validate the effiectiveness of the proposed framework for semisupervised regression.