CUADRO DE RECURSOS Y/O GASTOS ADMINISTRATIVOS Y SUSTANTIVOS Con el desglose de cada uno de los conceptos

It is important to know the variability of the AEP component estimates because one of the objectives of this research is to objectively select the AEP estimated components in children with CIs. To evaluate the variability of the estimates, 20 repetitions were realized in the calculation of the ICs for the three ICA algorithms already mentioned. The SIR index was calculated, using a convenient signal reference, for each of the 20 repetition for all the estimates; the histograms of the maximal SIR indexes for the three algorithms are shown in this section.

Figure 6.8 shows the histograms of the maximal SIR indices for four different recordings from children with CIs (I: S3-St1, II: S5-St1, III: S4-St1 and IV: S4-St2), calculated for the estimates of both (a) the CI artifact and (b) the AEP. In all the cases,

FastICA shows a larger spread of the SIR values than Ext-Infomax and TDSEP-ICA.

In most of the recordings, TDSEP-ICA shows the higher values of the AEP SIR index. The range of values of the SIR index for the estimation of the CI artifact, using

FastICA and Ext-Infomax, are similar in all the recordings shown in this figure. The

ranges of values of the SIR index for the estimation of the AEP for the three algorithms are similar in recordings I and IV; in recordings II and III TDSEP-ICA shows the higher values of the AEP SIR index.

(a) (b)

Figure 6.8 Comparison between, Ext-Infomax, FastICA, and TDSEP-ICA for (a) CI artifact

With these results, it is possible to conclude that TDSEP-ICA is the algorithm with the smallest variability in the estimate of the ICs; this algorithm is the one that best estimates the AEPs as well as the artifact. Both FastICA and Ext-Infomax recover efficiently the components related to the CI artifact; however, only TDSEP-ICA successfully recovers the AEPs in all the subjects with CIs. In conclusion, the performance of the TDSEP-ICA algorithm is better and more optimal for the dataset analyzed in this research.

6.4 Summary

Although FastICA and Infomax are maybe the most popular ICA algorithms used to estimate the components of the AEP in normal hearing subjects, here it was found that the algorithm with the more stable IC estimates is TDSEP-ICA with =0, 1, 2, ..., 20. In normal hearing children, although TDSEP-ICA does not have the lowest separability matrix values, the block structure of this matrix is always clearer than

FastICA and Ext-Infomax. One-dimensional ICs can be related with both the AEP and

noise.

In children with CIs, FastICA and Ext-Infomax have problems in recovering a clear AEP (without the CI artifact), especially when the recordings have low SNR.

TDSEP-ICA recovers the AEP in one- or two-dimensional ICs. All the algorithms

estimate the CI artifact reasonable well, although only TDSEP-ICA recovers it in one- dimensional ICs. TDSEP-ICA is the algorithm with the best separation of noise in these recordings.

The average value of the AEP SIR index is higher with FastICA than with Ext-

Infomax and TDSEP-ICA than in recordings from normal hearing children. In

children with CIs, TDSEP-ICA is the algorithm with the highest AEP SIR index values whilst FastICA is the algorithm with the highest CI SIR index.

It can be seen that using the SIR index, the variability of the estimation of three ICA algorithms, Infomax, FastICA and TDSEP-ICA, can be estimated. In both recordings, from normal hearing children and children with CIs; TDSEP-ICA is the

algorithm with the smallest variability in the AEP component estimates. This permits to conclude that TDSEP-ICA has the most robust and efficient estimate of the AEPs and this is to be expected over shorter window sizes and for a technique that makes use of the inherent information available in the time-series itself.

On the other hand, standard implementation of the ICA algorithm results in the number of ICs being equal to or less than the number of measurements, although it is generally the case that some of the components do not have a physiological significance; for this reason it is fundamental to know the number of sources to be estimated. It is convenient to have an objective method to select the ICs with physiological meaning.

In the next chapter, a procedure to select objectively ICs with physiological and physical meaning, using the concepts of Mutual Information and clustering is described.

Chapter 7.

Selection of Independent Components

using Mutual Information and

Clustering

A crucial part of applying ICA to any neurophysiological data is the selection of relevant ICs; in other words, to decide which ICs have neurophysiological meaning (in our case the auditory response). Standard ICA implementation supposes a square mixing matrix; this results in as many ICs as EEG channels (19 in our case). Responses to repetitive stimuli are the most important signals here; so the ICs of interest should be repetitive and time-locked with the stimuli. In this chapter a novel procedure for the selection of ICs using MI and cluster analysis is presented (an introduction of MI is included in Section 4.1).

Section 7.1 explains the basic theory of Cluster Analysis including the basic terminology used in hierarchical clustering, used in the procedure proposed in this chapter. Section 7.2 includes the description of this procedure to identify robust ICs associated with the AEP and the CI artifact, using MI combined with cluster analysis theory. This procedure is a modification of the method implemented by Kraskov et al [86]. The authors utilize MI between the ICs as a similarity measure and recursively using the grouping property of the MI, they cluster the output of ICA of biomedical signals. Section 7.3 shows the results of hierarchical agglomerative clustering of the ICs recovered by TDSEP-ICA from children with CIs. The dendrograms produced by the agglomeration of the ICs are showed together with the most robust clusters in four different recordings.