NNMap: A method to construct a good embedding for nearest neighbor classification

• We define a quantitative criterion of embedding quality for NN classification.
• Based on this new criterion, we propose NNMap to construct a good embedding.
• NNMap learns a fast distance to speed up nearest neighbor classification.
• NNMap is equally valid in both metric and non-metric spaces.

This paper aims to deal with the practical shortages of nearest neighbor classifier. We define a quantitative criterion of embedding quality assessment for nearest neighbor classification, and present a method called NNMap to construct a good embedding. Furthermore, an efficient distance is obtained in the embedded vector space, which could speed up nearest neighbor classification. The quantitative quality criterion is proposed as a local structure descriptor of sample data distribution. Embedding quality corresponds to the quality of the local structure. In the framework of NNMap, one-dimension embeddings act as weak classifiers with pseudo-losses defined on the amount of the local structure preserved by the embedding. Based on this property, the NNMap method reduces the problem of embedding construction to the classical boosting problem. An important property of NNMap is that the embedding optimization criterion is appropriate for both vector and non-vector data, and equally valid in both metric and non-metric spaces. The effectiveness of the new method is demonstrated by experiments conducted on the MNIST handwritten dataset, the CMU PIE face images dataset and the datasets from UCI machine learning repository.