On convergence of the NIC algorithm for subspace computation

The "novel information criterion" (NIC) algorithm was developed by Miao and Hua in 1998 for fast adaptive computation of the principal subspace of a vector sequence. The NIC algorithm is as efficient computationally as the PAST method, which was devised by Yang in 1995, and also has an attractive orthonormal property. Although all available evidence suggests that the NIC algorithm converges to the desired solution for any fixed leakage factor between zero and one, a complete proof (or disproof) has not been found, except for an arbitrarily small leakage factor. This paper presents this long-standing open problem with a discussion of what is known so far. The results shown in this paper provide a new insight into the orthonormal property of the NIC algorithm at convergence.