Locality Preserving Projection for Domain Adaptation with Multi-Objective Learning

In many practical cases, we need to generalize a model trained in a source domain to a new target domain. However, the distribution of these two domains may differ very significantly, especially sometimes some crucial target features may not have support in the source domain. This paper proposes a novel locality preserving projection method for domain adaptation task, which can find a linear mapping preserving the ’intrinsic structure’ for both source and target domains. We first construct two graphs encoding the neighborhood information for source and target domains separately. We then find linear projection coefficients which have the property of locality preserving for each graph. Instead of combing the two objective terms under compatibility assumption and requiring the user to decide the importance of each objective function, we propose a multiobjective formulation for this problem and solve it simultaneously using Pareto optimization. The Pareto frontier captures all possible good linear projection coefficients that are preferred by one or more objectives. The effectiveness of our approach is justified by both theoretical analysis and empirical results on real world data sets. The new feature representation shows better prediction accuracy as our experiments demonstrate.