Weakness:
1. The real applications that the proposed method can be applied to seem to be rather restricted. It seems the proposed algorithm can only be used as a fast evaluation of residual error for 'guessing' or 'predetermining' the range of Tucker ranks, not the real ranks.
2. Since the sampling size 's' depends on the exponential term 2^[1/(e^2K-2)] (in Theorem 3.4), it could be very large if one requires the error tolerance 'e' to be relatively small and the order of tensor 'K' to be high. In that situation, there won't be much benefits to use this algorithm. Question:
1. In the Fig.1, why blue curve with large sample size 's=80' achieves the worst error compared with that of red curve with small sample size 's=20'?
Overall, although proposed algorithm is theoretically sound, but appears be limited in applications for practical propose.
2. Since the sampling size 's' depends on the exponential term 2^[1/(e^2K-2)] (in Theorem 3.4), it could be very large if one requires the error tolerance 'e' to be relatively small and the order of tensor 'K' to be high. In that situation, there won't be much benefits to use this algorithm. Question: