Joint Approximate Diagonalization Utilizing AIC-Based Decision in the Jacobi Method

摘要

Joint approximate diagonalization is one of well-known methods for solving independent component analysis and blind source separation. It calculates an orthonormal separating matrix which diago-nalizes many cumulant matrices of given observed signals as accurately as possible. It has been known that such diagonalization can be carried out efficiently by the Jacobi method, where the optimization for each pair of signals is repeated until the convergence of the whole separating matrix. Generally, the Jacobi method decides whether the optimization is actually applied to a given pair by a convergence decision condition. Then, the whole convergence is achieved when no pair is actually optimized any more. Though this decision condition is crucial for accelerating the speed of the whole optimization, many previous works have employed simple conditions based on an arbitrarily selected threshold. In this paper, we propose a novel decision condition which is based on Akaike information criterion (AIC). It is derived by assuming each cumulant matrix to be a sample generated independently. In each pair optimization, the condition compares the reduction rate of the objective function with a constant depending on the number of cumulant matrices. It involves no thresholds (and no parameters) to be set manually. Numerical experiments verify that the proposed decision condition can accelerate the optimization speed for artificial data.