一种自适应拟牛顿广义特征分解算法

An adaptive quasi-Newton algorithm for generalized eigen-decomposition problem

通过构造一种新的无约束损失函数,广义特征分解问题可以转化为无约束优化问题.此损失函数具有良好的特性,即具有全局极小点、无局部极值点,从而保证了迭代算法的全局收敛性.利用近似Hessian矩阵,提出了一种新的自适应拟牛顿广义特征分解算法.然后,采用随机逼近理论,严格分析了算法的收敛性.仿真结果表明,算法具有快速收敛和动态跟踪能力.

The generalized eigen-decomposition problem can be reinterpreted into an unconstrained optimization problem by constructing appropriate cost function. The global convergence is guaranteed when one seeks the solution via iterative methods, since the cost function has a unique global minimum, and no other local minima or maxima. A novel robust adaptive quasi-Newton algorithm for generalized eigen-deeompositon problem was proposed by making use of an approximation of its Hessian matrix. Using the stochastic approximation theory, a rigorous analysis of the convergence properties of the algorithm was presented. Simulation results show that the proposed algorithm has fast convergence and dynamic tracking capability.