Many data partitioning index methods perform poorly in high dimensional space and do not support relevance feedback retrieval. The vector approximation file (VA-File) approach overcomes some of the difficulties of high dimensional vector spaces, but cannot be applied to relevance feedback retrieval using kernel distances in the data measurement space. This paper introduces a novel KVA-File (kernel VA-File) that extends VA-File to kernel-based retrieval methods. A key observation is that kernel distances may be non-linear in the data measurement space but is still linear in an induced feature space. It is this linear invariance in the induced feature space that enables KVA-File to work with kernel distances. An efficient approach to approximating vectors in an induced feature space is presented with the corresponding upper and lower distance bounds. Thus an effective indexing method is provided for kernel-based relevance feedback image retrieval methods. Experimental results using large image data sets (approximately 100,000 images with 463 dimensions of measurement) validate the efficacy of our method.