Khoo, YLu, JYing, L2017-11-302017-11-302017-11-30https://hdl.handle.net/10161/15779In this note we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least-squares (ALS). Since the function has size exponential in $d$ where $d$ is the number of dimensions, we propose efficient sampling scheme to obtain $O(d)$ important samples in order to learn the tensor ring. Furthermore, we devise an initialization method for ALS that allows fast convergence in practice. Numerical examples show that to approximate a function with similar accuracy, the tensor ring format provided by the proposed method has less parameters than tensor-train format and also better respects the structure of the original function.math.NAmath.NA65D15, 33F05, 15A69G.1.3; G.1.10Journal article