Fantope regularization in metric learning
Proceedings of the IEEE conference on computer vision and …, 2014•openaccess.thecvf.com
This paper introduces a regularization method to explicitly control the rank of a learned
symmetric positive semidefinite distance matrix in distance metric learning. To this end, we
propose to incorporate in the objective function a linear regularization term that minimizes
the k smallest eigenvalues of the distance matrix. It is equivalent to minimizing the trace of
the product of the distance matrix with a matrix in the convex hull of rank-k projection
matrices, called a Fantope. Based on this new regularization method, we derive an …
symmetric positive semidefinite distance matrix in distance metric learning. To this end, we
propose to incorporate in the objective function a linear regularization term that minimizes
the k smallest eigenvalues of the distance matrix. It is equivalent to minimizing the trace of
the product of the distance matrix with a matrix in the convex hull of rank-k projection
matrices, called a Fantope. Based on this new regularization method, we derive an …
Abstract
This paper introduces a regularization method to explicitly control the rank of a learned symmetric positive semidefinite distance matrix in distance metric learning. To this end, we propose to incorporate in the objective function a linear regularization term that minimizes the k smallest eigenvalues of the distance matrix. It is equivalent to minimizing the trace of the product of the distance matrix with a matrix in the convex hull of rank-k projection matrices, called a Fantope. Based on this new regularization method, we derive an optimization scheme to efficiently learn the distance matrix. We demonstrate the effectiveness of the method on synthetic and challenging real datasets of face verification and image classification with relative attributes, on which our method outperforms state-of-the-art metric learning algorithms.
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