Chaotic Behaviors Arising from Learning Algorithms

In the previous chapters, we have discussed the convergence of some subspace learning algorithms by mainly using the DDT method. Some invariant sets of these algorithms will be obtained under certain conditions. The convergence conditions of these algorithms will be derived. However, some learning algorithms exhibit some chaotic behaviors in practical applications. In [123], Xu’s LMSER algorithm can produce chaotic behaviors when the learning rate is chosen in certain range. The article [122] also explores chaotic behaviors of the Douglas’s MCA learning algorithm [60].