Domain Adaptation under Data Misalignment: An Application to Cepheid Variable Star Classification

We address a particular scenario within the area of domain adaptation, where a predictive model obtained from a source domain can be applied directly to a target domain. Both source and target domains share the same input or feature space, but we do not impose any restrictions on the marginal and class posterior distributions (both distributions can differ). Our main assumption is that the difference between the source and target domains can be traced to a systematic change caused by some modification in the sensing device, or environment surrounding the phenomenon under analysis, as for example when the training and testing samples correspond to stars (i.e., to light curves) that belong to different galaxies. We demonstrate how such systematic change can be reversed by shifting the target data towards the source data until both distributions are aligned. Our approach uses maximum likelihood to compute the right amount of displacement along each variable under analysis. We test our methodology on the classification of Cepheid variable stars according to their pulsation mode: fundamental and first-overtone. Experimental results with three galaxy datasets (Large Magellanic Cloud, Small Magellanic Cloud, and M33), show the effectiveness of our approach.