Abstract: Tensor approximation is necessary to obtain compact multilinear models for multi-dimensional visual datasets. Traditionally, each multi-dimensional data item is represented as a vector. Such a scheme attens the data and partially destroys the internal structures established throughout the multiple dimensions. In this paper, we retain the original dimensionality of the data items to more effectively exploit existing spatial redundancy and allow more ef cient computation. Since the size of visual datasets can easily exceed the memory capacity of a single machine, we also present an outofcore algorithm for higher-order tensor approximation. The basic idea is to partition a tensor into smaller blocks and perform tensorrelated operations blockwise. We have successfully applied our techniques to three graphics-related data-driven models, including 6D bidirectional texture functions, 7D dynamic BTFs and 4D volume simulation sequences. Experimental results indicate that our techniques can not only process out-of-core data, but also achieve higher compression ratios and quality than previous methods.