L2 norm regularized feature kernel regression for graph data

Abstract

Features in many real world applications such as Cheminformatics, Bioinformatics and Information Retrieval have complex internal structure. For example, frequent patterns mined from graph data are graphs. Such graph features have different number of nodes and edges and usually overlap with each other. In conventional data mining and machine learning applications, the internal structure of features are usually ignored. In this paper we consider a supervised learning problem where the features of the data set have intrinsic complexity, and we further assume that the feature intrinsic complexity may be measured by a kernel function. We hypothesize that by regularizing model parameters using the information of feature complexity, we can construct simple yet high quality model that captures the intrinsic structure of the data. Towards the end of testing this hypothesis, we focus on a regression task and have designed an algorithm that incorporate the feature complexity in the learning process, using a kernel matrix weighted L2 norm for regularization, to obtain improved regression performance over conventional learning methods that does not consider the additional information of the feature. We have tested our algorithm using 5 different real-world data sets and have demonstrate the effectiveness of our method.