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Curvilinear Distance Metric Learning
Shuo Chen · Lei Luo · Jian Yang · Chen Gong · Jun Li · Heng Huang

Wed Dec 11 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #36

Distance Metric Learning aims to learn an appropriate metric that faithfully measures the distance between two data points. Traditional metric learning methods usually calculate the pairwise distance with fixed distance functions (\emph{e.g.,}\ Euclidean distance) in the projected feature spaces. However, they fail to learn the underlying geometries of the sample space, and thus cannot exactly predict the intrinsic distances between data points. To address this issue, we first reveal that the traditional linear distance metric is equivalent to the cumulative arc length between the data pair's nearest points on the learned straight measurer lines. After that, by extending such straight lines to general curved forms, we propose a Curvilinear Distance Metric Learning (CDML) method, which adaptively learns the nonlinear geometries of the training data. By virtue of Weierstrass theorem, the proposed CDML is equivalently parameterized with a 3-order tensor, and the optimization algorithm is designed to learn the tensor parameter. Theoretical analysis is derived to guarantee the effectiveness and soundness of CDML. Extensive experiments on the synthetic and real-world datasets validate the superiority of our method over the state-of-the-art metric learning models.

Author Information

Shuo Chen (Nanjing University of Science and Technology)
Lei Luo (Pitt)
Jian Yang (Nanjing University of Science and Technology)
Chen Gong (Nanjing University of Science and Technology)
Jun Li (MIT)
Heng Huang (University of Pittsburgh)

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