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That's why we developed the "Boundary Forest" algorithm which is a fast nearest-neighbor type algorithm with generalization at least as good as K-NN, while being able to respond to queries very quickly.

It maintains trees of examples that let it train and respond to test queries in logarithmic time with the number of stored examples, which can be much less than the overall number of training samples. It thus maintains k-NN's property of very fast training time, and is also an online algorithm, and can be used for regression problems as well as classification.

See our paper that was presented at AAAI 2015 here: http://www.disneyresearch.com/publication/the-boundary-fores...

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