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The 25th International Conference on Machine Learning (ICML 2008)

Fast Solvers and Efficient Implementations for Distance Metric Learning

author: Kilian Weinberger, Yahoo! Research, Yahoo!

Description

In this paper we study how to improve nearest neighbor classification by learning a Mahalanobis distance metric. We build on a recently proposed framework for distance metric learning known as large margin nearest neighbor (LMNN) classification. Within this framework, we focus specifically on the challenges in scalability and adaptability posed by large data sets. Our paper makes three contributions. First, we describe a highly efficient solver for the particular instance of semidefinite programming that arises in LMNN classification; our solver can handle problems with billions of large margin constraints in a few hours. Second, we show how to reduce both training and testing times using metric ball trees; the speedups from ball trees are further magnified by learning low dimensional representations of the input space. Third, we show how to learn different Mahalanobis distance metrics in different parts of the input space. For large data sets, these mixtures of locally adaptive metrics lead to even lower error rates.

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Slides
0:00 Fast Solvers and Efficient Implementations for Distance Metric Learning
0:05 Mahalanobis Distance - 1
0:34 Mahalanobis Distance - 2
0:46 Mahalanobis Distance - 3
0:51 k-NN Classification - 1
1:23 k-NN Classification - 2
1:36 Large Margin Nearest Neighbor (LMNN) - 1
1:54 Large Margin Nearest Neighbor (LMNN) - 2
2:14 Large Margin Nearest Neighbor (LMNN) - 3
2:18 Large Margin Nearest Neighbor (LMNN) - 4
2:36 Large Margin Nearest Neighbor (LMNN) - 5
2:43 Large Margin Nearest Neighbor (LMNN) - 6
3:00 Large Margin Nearest Neighbor (LMNN) - 7
3:08 Large Margin Nearest Neighbor (LMNN) - 8
3:11 Large Margin Nearest Neighbor (LMNN) - 9
3:24 Large Margin Nearest Neighbor (LMNN) - 10
3:38 Large Margin Nearest Neighbor (LMNN) - 11
3:56 Three Questions - 1
4:03 Three Questions - 2
4:16 Three Questions - 3
4:25 Three Questions - 4
4:39 How Can One Apply LMNN to Larger Data Sets?
4:49 Semidefinite Program
5:14 3 Speed-Ups
5:58 Optimization on MNIST
6:32 Three Questions - 5
6:52 How Can One Make LMNN Classification Faster?
7:03 Ball-Trees
7:31 Pruning Principle - 1
7:43 Pruning Principle - 2
7:55 Pruning Principle - 3
8:14 Catch: Dimensionality
9:02 Reduce the Dimensionality!!
9:06 LMNN-svd
10:35 LMNN-rect - 1
11:07 LMNN-rect - 2
11:16 LMNN-rect - 3
11:38 LMNN-rect - 4
11:38 LMNN-rect - 5
11:52 LMNN for Balltrees - 1
13:39 LMNN for Balltrees - 2
13:44 Three Questions - 6
14:06 How Can One Make LMNN Classification more Accurate?
14:13 Limits of a Global Linear Metric - 1
15:05 Limits of a Global Linear Metric - 2
15:28 Can We Apply LMNN Locally? - 1
15:41 Can We Apply LMNN Locally? - 2
16:12 Solution
16:26 Multiple Metrics-LMNN - 1
16:43 Multiple Metrics-LMNN - 2
16:49 Multiple Metrics-LMNN - 3
17:12 Multiple Metrics-LMNN - 4
17:32 Multiple Metrics
18:17 How Should One Divide the Training Data? - 1
19:01 How Should One Divide the Training Data? - 2
19:31 2D mnist
20:00 Comparison with LMNN
20:50 Comparison with SVMs
21:46 Three Questions - 7
22:04 Conclusion
22:35 - Questions

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