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9: Chintan A. Shah
order statistics. Chang et. al. (2002) have considered an application of ICA
to linear spectral mixture analysis, referred to as ICA-based linear spectral
random mixture analysis (LSRMA). They model an image pixel as a random
source resulting from a random composition of multiple spectral signatures
of distinct materials (or classes) in the image. Their experimental results have
demonstrated that the proposed LSRMA method is an effective unsupervised
approach for feature extraction and hence for classification and target detection problems. However, in these research efforts, the application of ICA has
been limited to being a feature extraction algorithm.
It is important to note that it may be inappropriate to apply a classification
or a target detection algorithm based on second order statistics on the features
extracted by ICA. This is due to the fact that these algorithms do not possess
the statistical properties that they can complement the enhancement of the
information content of the features (extracted based on higher order statistics
as is done in ICA).
The work presented in this chapter is the application of a relatively new approach, the ICA mixture model (ICAMM) algorithm (Lee et al. 2000), derived
from ICA, for an unsupervised classification of non-Gaussian classes from remote sensing data. So far, to the best of our knowledge, the ICAMM algorithm
has been employed for unsupervised classification problems in other applications such as speech signals (Lee et al. 2000), learning efficient codes of images
(Lee and Lewicki 2002) and blind signal separation in teleconferencing (Bae et
al. 2000) but not for the classification of remote sensing data.
In the proposed approach, we model each pixel of a hyperspectral image as
a random vector of intensity values that can be described by the ICA mixture
model. Unlike the approach adopted by Robila and Varshney (2002a,b), Chang
et. al. (2002) and many others who have employed the ICA model for feature
extraction, we employ K ICA model to explain the data generation properties
and propose an ICAMM algorithm for unsupervised classification. Here, K is
the prespecified number of spectral classes.
The ICAMM algorithm views the observed hyperspectral data as a mixture
of several mutually exclusive classes. Each of these classes is described by a linear combination of independent components with non-Gaussian (leptokurtic
or platykurtic) probability density functions (see Sect. 4.2 in Chap. 4). The
ICAMM algorithm finds independent components and the mixing matrix for
each class using an extended information-maximization learning algorithm
and computes the class membership probabilities for each pixel. The pixel is
allocated to the class with the highest posterior class probability to produce
a classification map.
This chapter is organized in the following manner. In Sect. 9.2, we formulate the ICAMM algorithm for unsupervised classification of non-Gaussian
classes. The steps involved in the ICAMM algorithm are also provided in this
section. In Sect. 9.3, we describe the proposed experimental methodology.
The performance of the algorithm is evaluated by conducting experiments
on a hyperspectral dataset in Sect. 9.4. Finally, we provide summary of the
experimental results.
9: Chintan A. Shah
order statistics. Chang et. al. (2002) have considered an application of ICA
to linear spectral mixture analysis, referred to as ICA-based linear spectral
random mixture analysis (LSRMA). They model an image pixel as a random
source resulting from a random composition of multiple spectral signatures
of distinct materials (or classes) in the image. Their experimental results have
demonstrated that the proposed LSRMA method is an effective unsupervised
approach for feature extraction and hence for classification and target detection problems. However, in these research efforts, the application of ICA has
been limited to being a feature extraction algorithm.
It is important to note that it may be inappropriate to apply a classification
or a target detection algorithm based on second order statistics on the features
extracted by ICA. This is due to the fact that these algorithms do not possess
the statistical properties that they can complement the enhancement of the
information content of the features (extracted based on higher order statistics
as is done in ICA).
The work presented in this chapter is the application of a relatively new approach, the ICA mixture model (ICAMM) algorithm (Lee et al. 2000), derived
from ICA, for an unsupervised classification of non-Gaussian classes from remote sensing data. So far, to the best of our knowledge, the ICAMM algorithm
has been employed for unsupervised classification problems in other applications such as speech signals (Lee et al. 2000), learning efficient codes of images
(Lee and Lewicki 2002) and blind signal separation in teleconferencing (Bae et
al. 2000) but not for the classification of remote sensing data.
In the proposed approach, we model each pixel of a hyperspectral image as
a random vector of intensity values that can be described by the ICA mixture
model. Unlike the approach adopted by Robila and Varshney (2002a,b), Chang
et. al. (2002) and many others who have employed the ICA model for feature
extraction, we employ K ICA model to explain the data generation properties
and propose an ICAMM algorithm for unsupervised classification. Here, K is
the prespecified number of spectral classes.
The ICAMM algorithm views the observed hyperspectral data as a mixture
of several mutually exclusive classes. Each of these classes is described by a linear combination of independent components with non-Gaussian (leptokurtic
or platykurtic) probability density functions (see Sect. 4.2 in Chap. 4). The
ICAMM algorithm finds independent components and the mixing matrix for
each class using an extended information-maximization learning algorithm
and computes the class membership probabilities for each pixel. The pixel is
allocated to the class with the highest posterior class probability to produce
a classification map.
This chapter is organized in the following manner. In Sect. 9.2, we formulate the ICAMM algorithm for unsupervised classification of non-Gaussian
classes. The steps involved in the ICAMM algorithm are also provided in this
section. In Sect. 9.3, we describe the proposed experimental methodology.
The performance of the algorithm is evaluated by conducting experiments
on a hyperspectral dataset in Sect. 9.4. Finally, we provide summary of the
experimental results.