BEGIN:VCALENDAR
VERSION:2.0
PRODID:ECMLPKDD-MB
BEGIN:VEVENT
DTSTAMP;TZID=Europe/Dublin:20180826T200000
UID:_ecmlpkdd_528
DTSTART;TZID="Europe/Dublin":20180913T170000
DTEND;TZID="Europe/Dublin":20180913T172000
LOCATION:Hogan
TRANSP:TRANSPARENT
SEQUENCE:1
DESCRIPTION:In domain adaptation, machine learning methods trained on a source domain, which has label information, must be modified to fit a target test domain whose feature distribution is assumed to vary from the source (e.g., ranking Amazon book reviews given labeled movie reviews). Various approaches to domain adaptation have been studied in the literature, ranging from geometric approaches to statistical approaches. One popular linear algebraic approach is based on aligning second order statistics, principally the covariances, between source and target domains. In this paper, we provide a new framework for domain adaptation, based on formulating transfer from source to target as a problem of metric learning on manifolds. Specifically, our approach is based on exploiting the Riemannian manifold geometry of symmetric positive definite (SPD) covariance matrices. We show that the domain adaptation problem of aligning source and target covariances can be reduced to solving the well-known Riccati equation, which has an exact solution on the manifold of SPD matrices involving the geometric or sharp mean. We additionally constrain the Ricatti based solution to reflect the underlying geometry of the source and target domains using diffusions on the underlying source and target manifolds. We also introduce an additional component of statistical alignment by minimizing the Maximum Mean Discrepancy (MMD) metric. A key strength of our proposed approach is that it enables integrating multiple sources of variation between source and target in a unified way, by reducing the combined objective function to a nested set of Ricatti equations. In addition to showing the theoretical optimality of our solution, we present detailed experiments using standard transfer learning testbeds from computer vision comparing our proposed algorithms to past work in domain adaptation, showing improved results over a large variety of previous methods.
SUMMARY:Domain Adaptation using Metric Learning on Manifolds
CLASS:PUBLIC
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END:VCALENDAR