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An Efficient Sparse Metric Learning in High-Dimensional Space via L1-Penalized Log-Determinant Regularization

An Efficient Sparse Metric Learning in High-Dimensional Space via L1-Penalized Log-Determinant Regularization

This video was recorded at 26th International Conference on Machine Learning (ICML), Montreal 2009. This paper proposes an efficient sparse metric learning algorithm in high dimensional space via an $\ell_1$-penalized log-determinant regularization. Compare to the most existing distance metric learning algorithms, the proposed algorithm exploits the sparsity nature underlying the intrinsic high dimensional feature space. This sparsity prior of learning distance metric serves to regularize the complexity of the distance model especially in the ``less example number $p$ and high dimension $d$" setting. Theoretically, by analogy to the covariance estimation problem, we find the proposed distance learning algorithm has a consistent result at rate $\mathcal O\left(\sqrt{\left( {m^2 \log d}... Show More
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