224
9: Chintan A. Shah
is represented by a reduced number of effective features, retaining most of
the intrinsic information content (Duda et al. 2000). Feature extraction from
remote sensing data relies on the ability to separate classes based on their
spectral characteristics (Richards and Jia 1999a).
In our experiments, we investigate four unsupervised feature extraction
techniques: principal component analysis (PCA) (Richards and Jia 1999a),
segmented principal component analysis (SPCA) (Richards and Jia 1999b),
orthogonal subspace projection (OSP) (Harsayani and Chang 1994), and projection pursuit (PP) (Ifarraguerri and Chang 2000), to reduce the data volume
so as to increase the efficiency of the I CAMM algorithm.
PCA, a correlation based linear transformation, seeks a projection that leads
to a representation with high data variance. It projects N-dimensional data onto
a new subspace, spanned by the principal axes, leading to principal components. SPCA, makes use of the block structure of the correlation matrix so that
PCA is conducted on data of smaller dimensionality (Richards and Jia 1999b).
For OSP, a two-step iterative process is followed, i. e., first a pixel vector with
the maximum length as a class signature Sj is selected and then the orthogonal
projections of all image pixels onto an orthogonal complement space of Sj
are found. PP, also a two-step iterative process, first searches for a projection
that maximizes a projection index, based on the information divergence of the
projection's estimated probability distribution from the Gaussian distribution.
Next, it reduces the rank by projecting the data onto the subspace orthogonal
to the previous projection.
9.3.2
Feature Ranking
Feature extraction is followed by feature ranking, where a ranking criterion is
used to rank the features extracted by a particular feature extraction technique.
The ranking criterion is established based on its ability to rank the features
in the order of significance of information content of the extracted features
(Landgrebe 2002). Features obtained by PCA and SPCA, are ranked based on
variance as a measure of information content. For OSP and PP, features are
ranked based on the order of projections.
9.3.3
Feature Selection
Once the features are ranked in the order of significance, we perform the
task of feature selection, i. e., we determine the optimal number of features
to be retained, which lead to a high compression ratio and at the same time
minimize the reconstruction error. This is indicated by the feature selection
stage in Fig. 9.1, where we selectthe firstM features from the features extracted
by each of the feature extraction techniques. Recall our discussion in Sect. 9.2,
pertaining to the assumption about the restriction on the number of sources
(M) and the number of sensor observations (N) in the ICAMM algorithm. We
9: Chintan A. Shah
is represented by a reduced number of effective features, retaining most of
the intrinsic information content (Duda et al. 2000). Feature extraction from
remote sensing data relies on the ability to separate classes based on their
spectral characteristics (Richards and Jia 1999a).
In our experiments, we investigate four unsupervised feature extraction
techniques: principal component analysis (PCA) (Richards and Jia 1999a),
segmented principal component analysis (SPCA) (Richards and Jia 1999b),
orthogonal subspace projection (OSP) (Harsayani and Chang 1994), and projection pursuit (PP) (Ifarraguerri and Chang 2000), to reduce the data volume
so as to increase the efficiency of the I CAMM algorithm.
PCA, a correlation based linear transformation, seeks a projection that leads
to a representation with high data variance. It projects N-dimensional data onto
a new subspace, spanned by the principal axes, leading to principal components. SPCA, makes use of the block structure of the correlation matrix so that
PCA is conducted on data of smaller dimensionality (Richards and Jia 1999b).
For OSP, a two-step iterative process is followed, i. e., first a pixel vector with
the maximum length as a class signature Sj is selected and then the orthogonal
projections of all image pixels onto an orthogonal complement space of Sj
are found. PP, also a two-step iterative process, first searches for a projection
that maximizes a projection index, based on the information divergence of the
projection's estimated probability distribution from the Gaussian distribution.
Next, it reduces the rank by projecting the data onto the subspace orthogonal
to the previous projection.
9.3.2
Feature Ranking
Feature extraction is followed by feature ranking, where a ranking criterion is
used to rank the features extracted by a particular feature extraction technique.
The ranking criterion is established based on its ability to rank the features
in the order of significance of information content of the extracted features
(Landgrebe 2002). Features obtained by PCA and SPCA, are ranked based on
variance as a measure of information content. For OSP and PP, features are
ranked based on the order of projections.
9.3.3
Feature Selection
Once the features are ranked in the order of significance, we perform the
task of feature selection, i. e., we determine the optimal number of features
to be retained, which lead to a high compression ratio and at the same time
minimize the reconstruction error. This is indicated by the feature selection
stage in Fig. 9.1, where we selectthe firstM features from the features extracted
by each of the feature extraction techniques. Recall our discussion in Sect. 9.2,
pertaining to the assumption about the restriction on the number of sources
(M) and the number of sensor observations (N) in the ICAMM algorithm. We