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Fig. 7.10
Three sources in a learning style space for graduate courses with no grades
assumptions about the source signals so that they imply a given model for the
source distributions, for instance, the Extended InfoMax algorithm [ 29 ] restricts
the sources to be sub-gaussian or super-gaussian, or also classical ICA rely
exclusively on certain higher order statistics of the signals in order to measure
independence, such as [ 30 ]. Other algorithms make assumptions that only fit to
specific applications like TDSEP [ 31 ], which is based on some time-delayed
statistics and is not suited for problems without temporal correlations. The non-
parametric ICA algorithm applied is more adaptable to the data. It does not assume
any restriction on the data since the probability distributions are calculated directly
from the training set through a non-parametric kernel-based approach. This
algorithm also focuses the independence estimation among the source components
directly based on the marginal distributions.
Summarizing the results, Fig. 7.11 shows the relationship between learning
style dimensions and e-learning web activities separating interactivity from per-
sonal activity fields.
7.3 Conclusions
In this chapter, we have explored the use of the ICAMM and the SICAMM
methods in two quite different applications: sequential dependence modelling and
data mining. The parameters of the ICA mixture models were estimated using the
Mixca algorithm proposed in Chap. 3 . In the first application, we proposed an
extension of ICAMM, which allows class-transition information to be included in
the classifier. As this is equivalent to considering the sequencing of the classes, we
have called it sequential ICAMM. Essentially, SICAMM is a sequential Bayesian
processor where the underlying probability densities are mixtures of independent
component analyzers. Estimates of the model parameters (mixing matrices, cen-
troids, and probability densities of the sources) are required in both ICAMM and
SICAMM. This can be done in a supervised (true classes are known) or unsu-
pervised (true classes are estimated) manner from a training set of feature vectors.
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