200
8: Stefan A. Robila, Pramod K. Varshney
based algorithm that, unlike the original one, allows the extraction of fewer
sources than the number of observations. This algorithm is known as the under
complete ICA-FE algorithm (UlCA-FE). There is a clear need for such an algorithm in the context of hyperspectral imagery, where the number of spectral
bands available far exceeds the number of independent classes contained in
the image. Designing a method that produces only these useful components
will constitute a major improvement.
In both approaches, the number of independent components to be generated
is computed based on the eigenvalue information produced in the PCA step. It
corresponds to the number of highest eigenvalues that make up approximately
99% of the variance. This criterion is frequently used in PCA for reducing data
dimensionality.
This chapter is organized as follows. In Sect. 8.2, we provide a brief assessment of the advantages of ICA over PCA when used for feature extraction.
In Sect. 8.3, we present the two ICA based feature extraction algorithms. Section 8.4 contains an assessment of the efficiency of the two methods based
on a practical experiment that uses hyperspectral data from AVIRIS sensor.
The performance metrics used are: comparative execution times, mutual information and visual inspection of the extracted features (bands) as well as the
accuracy of unsupervised classification. The results obtained by the use of PCA
are also presented. We note that the usual quantitative measures (distance between the means, distance between the distributions, etc.) have not been used
for assessing feature extraction algorithms as they employ information from
training data sets. In the case of unsupervised processing, this information is
not available.
Given the fact that in the context of hyperspectral data, the term feature is
similar to the term band, and that in ICA, the components are associated with
features, all these three terms will be used interchangeably throughout this
chapter.
8.2
PCA vs ICA for Feature Extraction
Traditionally, feature extraction algorithms focus on the increase of the separation between classes within each feature. The separation can be measured
using class information such as distance between means, distance between
probabilities, etc. Analogous to classification, depending on whether or not
prior class information is available (in the form of training pixel vectors),
feature extraction can be either supervised or unsupervised (Richards and Jia
1999) (see Chap. 2). In the case of supervised feature extraction, the availability
of training data allows the computation of the statistics and distance measures
for the classes. Feature extraction is performed, in fact, to increase the separability of the classes based on the training data. Since further processing (such
as supervised classification) is based on the same training data, the increased
separability leads to increased accuracy of the results (Richards and Jia 1999).
Unfortunately, in many cases, reference data may either not be available or
8: Stefan A. Robila, Pramod K. Varshney
based algorithm that, unlike the original one, allows the extraction of fewer
sources than the number of observations. This algorithm is known as the under
complete ICA-FE algorithm (UlCA-FE). There is a clear need for such an algorithm in the context of hyperspectral imagery, where the number of spectral
bands available far exceeds the number of independent classes contained in
the image. Designing a method that produces only these useful components
will constitute a major improvement.
In both approaches, the number of independent components to be generated
is computed based on the eigenvalue information produced in the PCA step. It
corresponds to the number of highest eigenvalues that make up approximately
99% of the variance. This criterion is frequently used in PCA for reducing data
dimensionality.
This chapter is organized as follows. In Sect. 8.2, we provide a brief assessment of the advantages of ICA over PCA when used for feature extraction.
In Sect. 8.3, we present the two ICA based feature extraction algorithms. Section 8.4 contains an assessment of the efficiency of the two methods based
on a practical experiment that uses hyperspectral data from AVIRIS sensor.
The performance metrics used are: comparative execution times, mutual information and visual inspection of the extracted features (bands) as well as the
accuracy of unsupervised classification. The results obtained by the use of PCA
are also presented. We note that the usual quantitative measures (distance between the means, distance between the distributions, etc.) have not been used
for assessing feature extraction algorithms as they employ information from
training data sets. In the case of unsupervised processing, this information is
not available.
Given the fact that in the context of hyperspectral data, the term feature is
similar to the term band, and that in ICA, the components are associated with
features, all these three terms will be used interchangeably throughout this
chapter.
8.2
PCA vs ICA for Feature Extraction
Traditionally, feature extraction algorithms focus on the increase of the separation between classes within each feature. The separation can be measured
using class information such as distance between means, distance between
probabilities, etc. Analogous to classification, depending on whether or not
prior class information is available (in the form of training pixel vectors),
feature extraction can be either supervised or unsupervised (Richards and Jia
1999) (see Chap. 2). In the case of supervised feature extraction, the availability
of training data allows the computation of the statistics and distance measures
for the classes. Feature extraction is performed, in fact, to increase the separability of the classes based on the training data. Since further processing (such
as supervised classification) is based on the same training data, the increased
separability leads to increased accuracy of the results (Richards and Jia 1999).
Unfortunately, in many cases, reference data may either not be available or