Aligned Graph Classification with Regularized Logistic Regression

Data with intrinsic feature relationships are becoming abundant in many applications including bioinformatics and sensor network analysis. In this paper we consider a classification problem where there is a fixed and known binary relation defined on the features of a set of multivariate random variables. We formalize such a problem as an aligned graph classification problem. By incorporating this feature relationship in the learning process we aim to obtain improved classification performance over conventional learning that does not consider the additional information of the feature relationship. To incorporate the feature relationship, we extend logistic regression and use a regularization term that includes the normalized Laplacian of the graph, similar to the L2 regularization, deriving a modified optimization problem and solution. We demonstrate the effectiveness of our method and compare it to other methods using simulated and real data sets.