Is the k-NN classifier in high dimensions affected by the curse of dimensionality?

Details Is the k-NN classifier in high dimensions affected by the curse of dimensionality? Is the k-NN classifier in high dimensions affected by the curse of dimensionality?

2011-10-19

arxiv.org/abs/1110.4347v1

Statistics

Machine Learning

17 pages, latex2e

Scientific paper

There is an increasing body of evidence suggesting that exact nearest neighbour search in high-dimensional spaces is affected by the curse of dimensionality at a fundamental level. Does it necessarily mean that the same is true for k nearest neighbours based learning algorithms such as the k-NN classifier? We analyse this question at a number of levels and show that the answer is different at every layer that we peel. As our first main result, we show the consistency of a k approximate nearest neighbour classifier. However, the performance of the classifier in very high dimensions is provably unstable. As our second major result, we point out that the existing model for statistical learning is oblivious of dimension of the domain and so every learning problem admits a universally consistent reduction to the one-dimensional case.

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