Independent component analysis P13

Practical Considerations In the preceding chapters, we presented several approaches for the estimation of the independent component analysis (ICA) model. In particular, several algorithms were proposed for the estimation of the basic version of the model, which has a square mixing matrix and no noise. Now we are, in principle, ready to apply those algorithms on real data sets. Many such applications will be discussed in Part IV. However, when applying the ICA algorithms to real data, some practical considerations arise and need to be taken into account. In this chapter, we discuss different problems that may arise, in particular, overlearning. | 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 13 Practical Considerations In the preceding chapters we presented several approaches for the estimation of the independent component analysis ICA model. In particular several algorithms were proposed for the estimation of the basic version of the model which has a square mixing matrix and no noise. Now we are in principle ready to apply those algorithms on real data sets. Many such applications will be discussed in Part IV. However when applying the ICA algorithms to real data some practical considerations arise and need to be taken into account. In this chapter we discuss different problems that may arise in particular overlearning and noise in the data. We also propose some preprocessing techniques dimension reduction by principal component analysis time filtering that may be useful and even necessary before the application of the ICA algorithms in practice. PREPROCESSING BY TIME FILTERING The success of ICA for a given data set may depend crucially on performing some application-dependent preprocessing steps. In the basic methods discussed in the previous chapters we always used centering in preprocessing and often whitening was done as well. Here we discuss further preprocessing methods that are not necessary in theory but are often very useful in practice. 263 264 PRACTICAL CONSIDERATIONS Why time filtering is possible In many cases the observed random variables are in fact time signals or time series which means that they describe the time course of some phenomenon or system. Thus the sample index in Xi t is a time index. In such a case it may be very useful to filter the signals. In other words this means taking moving averages of the time series. Of course in the ICA model no time structure is assumed so filtering is not always possible If the sample points x t cannot be ordered in any

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