Varying similarity metrics in indexing and retrieving high dimensional data

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Many applications require varying distance metrics by putting a weight on different dimensions. Taking an example in visual information retrieval, due to the subjective nature of similarity measurements, the distance metrics can vary between different users. The main problem with k nearest neighbour (k-nn) searches using weighted metrics in a high dimensional space is whether the searches can be done efficiently, since in an arbitrary distance metric the intersection between the k-nn sphere and the bounding envelopes of nodes in an index tree cannot be easily calculated. This project aims to seek a novel solution. It will create a great impact on and have many applications in high dimensional visual information retrieval, instance-based learning, complex analysis, non-parametric density estimation, etc.