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# Distance Metric Learning with Application to Clustering with Side-Information

NIPS, pp.505-512, (2003)

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摘要

Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as K-means initially fails to find one that is meaningful to a user, the only recourse may be for the user to manually tweak the metric until sufficiently go...更多

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简介

- The performance of many learning and datamining algorithms depend critically on their being given a good metric over the input space.
- K-means, nearest-neighbors classifiers and kernel algorithms such as SVMs all need to be given good metrics that reflect reasonably well the important relationships between the data
- This problem is acute in unsupervised settings such as clustering, and is related to the perennial problem of there often being no “right” answer for clustering: If three algorithms are used to cluster a set of documents, and one clusters according to the authorship, another clusters according to topic, and a third clusters according to writing style, who is to say which is the “right” answer?
- This includes algorithms such as Multidimensional Scaling (MDS) [2], and Locally Linear Embedding

重点内容

- The performance of many learning and datamining algorithms depend critically on their being given a good metric over the input space
- K-means, nearest-neighbors classifiers and kernel algorithms such as SVMs all need to be given good metrics that reflect reasonably well the important relationships between the data. This problem is acute in unsupervised settings such as clustering, and is related to the perennial problem of there often being no “right” answer for clustering: If three algorithms are used to cluster a set of documents, and one clusters according to the authorship, another clusters according to topic, and a third clusters according to writing style, who is to say which is the “right” answer? Worse, if an algorithm were to have clustered by topic, and if we instead wanted it to cluster by writing style, there are relatively few systematic mechanisms for us to convey this to a clustering algorithm, and we are often left tweaking distance metrics by hand
- We are interested in the following problem: Suppose a user indicates that certain points in an input space are considered by them to be “similar.” Can we automatically learn a distance metric over ¢¤£ that respects these relationships, i.e., one that assigns small distances between the similar pairs? For instance, in the documents example, we might hope that, by giving it pairs of documents judged to be written in similar styles, it would learn to recognize the critical features for determining style
- We have presented an algorithm that, given examples of similar pairs of points in ¢ £, learns a distance metric that respects these relationships
- Our method is based on posing metric learning as a convex optimization problem, which allowed us to derive efficient, localoptima free algorithms

方法

**Experiments and Examples**

The authors begin by giving some examples of distance metrics learned on artificial data, and show how the methods can be used to improve clustering performance.

3.1 Examples of learned distance metrics

Consider the data shown in Figure 2(a), which is divided into two classes.- The authors begin by giving some examples of distance metrics learned on artificial data, and show how the methods can be used to improve clustering performance.
- 3.1 Examples of learned distance metrics.
- Consider the data shown in Figure 2(a), which is divided into two classes.
- Suppose that points in each class are “sim-.
- BDB "BDB 8gf § S %egf To visualize this, the authors can use the fact discussed earlier that learning is equivalent to finding a rescaling of the data

结论

- The authors have presented an algorithm that, given examples of similar pairs of points in ¢ £ , learns a distance metric that respects these relationships.
- The authors' method is based on posing metric learning as a convex optimization problem, which allowed them to derive efficient, localoptima free algorithms.
- The authors showed examples of diagonal and full metrics learned from simple artificial examples, and demonstrated on artificial and on UCI datasets how the methods can be used to improve clustering performance

引用论文

- C. Atkeson, A. Moore, and S. Schaal. Locally weighted learning. AI Review, 1996.
- T. Cox and M. Cox. Multidimensional Scaling. Chapman & Hall, London, 1994.
- C. Domeniconi and D. Gunopulos. Adaptive nearest neighbor classification using support vector machines. In Advances in Neural Information Processing Systems 14. MIT Press, 2002.
- G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins Univ. Press, 1996.
- T. Hastie and R. Tibshirani. Discriminant adaptive nearest neighbor classification. IEEE Transactions on Pattern Analysis and Machine Learning, 18:607–616, 1996.
- T.S. Jaakkola and D. Haussler. Exploiting generative models in discriminaive classifier. In Proc. of Tenth Conference on Advances in Neural Information Processing Systems, 1999.
- I.T. Jolliffe. Principal Component Analysis. Springer-Verlag, New York, 1989.
- R. Rockafellar. Convex Analysis. Princeton Univ. Press, 1970.
- S.T. Roweis and L.K. Saul. Nonlinear dimensionality reduction by locally linear embedding.
- B. Scholkopf and A. Smola. Learning with Kernels. In Press, 2001.
- N. Tishby, F. Pereira, and W. Bialek. The information bottleneck method. In Proc. of the 37th Allerton Conference on Communication, Control and Computing, 1999.
- K. Wagstaff, C. Cardie, S. Rogers, and S. Schroedl. Constrained k-means clustering with background knowledge. In Proc. 18th International Conference on Machine Learning, 2001.

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