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Independent component analysis P14

Overview and Comparison of Basic ICA Methods In the preceding chapters, we introduced several different estimation principles and algorithms for independent component analysis (ICA). In this chapter, we provide an overview of these methods. First, we show that all these estimation principles are intimately connected, and the main choices are between cumulant-based vs. negentropy/likelihood-based estimation methods, and between one-unit vs. multiunit methods. In other words, one must choose the nonlinearity and the decorrelation method. We discuss the choice of the nonlinearity from the viewpoint of statistical theory. In practice, one must also choose the optimization method. We compare the algorithms experimentally,. | Independent Component Analysis. Aapo Hyvarinen Juha Karhunen Erkki Oja Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-40540-X Hardback 0-471-22131-7 Electronic 14 Overview and Comparison of Basic ICA Methods In the preceding chapters we introduced several different estimation principles and algorithms for independent component analysis ICA . In this chapter we provide an overview of these methods. First we show that all these estimation principles are intimately connected and the main choices are between cumulant-based vs. negentropy likelihood-based estimation methods and between one-unit vs. multiunit methods. In other words one must choose the nonlinearity and the decorrelation method. We discuss the choice of the nonlinearity from the viewpoint of statistical theory. In practice one must also choose the optimization method. We compare the algorithms experimentally and show that the main choice here is between on-line adaptive gradient algorithms vs. fast batch fixed-point algorithms. At the end of this chapter we provide a short summary of the whole of Part II that is of basic ICA estimation. 14.1 OBJECTIVE FUNCTIONS VS. ALGORITHMS A distinction that has been used throughout this book is between the formulation of the objective function and the algorithm used to optimize it. One might express this in the following equation ICA method objective function optimization algorithm. In the case of explicitly formulated objective functions one can use any of the classic optimization methods for example stochastic gradient methods and Newton 273 274 OVERVIEW AND COMPARISON OFBASIC ICA METHODS methods. In some cases however the algorithm and the estimation principle may be difficult to separate. The properties of the ICA method depend on both of the objective function and the optimization algorithm. In particular the statistical properties e.g. consistency asymptotic variance robustness of the ICA method depend on the choice of the objective function the algorithmic .