Many traditional indexing methods perform poorly in high dimensional vector space.The Vector Approximation File approach overcomes some of the difficulties of dimensionality curse

but it can't support the quadratic form metric.A novel VA-File approach for quadratic form distance is introduced in this paper.By the SVD of similarity matrix

the quadratic form distance can be converted to the Euclidean distance

and the approximation vector can be obtained. The low-dimensional filter algorithm is also applied during the nearest neighbor search.The vectors are first filtered with the low-dimensional approximate distance measure

and then the candidate results are re-computed with high-dimensional distance measure.The experimental results show that it can save the computational time significantly because only a small set of vectors is computed on the high-dimensional distance measure.