CHAPTER 9
Hyperspectral Classification
Using ICA Based Mixture Model
Chintan A. Shah
9.1
Introduction
Unsupervised classification of remote sensing images is typically based on
a mixture model, where the distribution of the entire data is modeled as
a weighted sum of the class-component densities (Duda et al. 2000). When
the class-component densities are assumed to be multivariate Gaussian, the
mixture model is known as the Gaussian mixture model. The K -means and the
ISODATA algorithms that are widely used in remote sensing are based on the
Gaussian mixture model. These Gaussian mixture model based classification
algorithms often perform unsatisfactorily. This stems from the Gaussian distribution assumption for the class-component densities. Gaussianity is only an
assumption, rather than a demonstrable property of natural spectral classes,
and has been widely accepted due to its analytical tractability and mathematical
simplicity. However, if a class happens to be multimodal, it is no longer appropriate to model the class with a multivariate Gaussian distribution. Therefore,
the use of the Gaussian mixture model in such cases may lead to unsatisfactory
performance.
This underlying Gaussian mixture model assumption is limited as it exploits
only the second order statistics of the observed data to estimate the posterior
densities. Limitations of using second order statistics (mean and covariance),
in characterizing multivariate data, have been discussed in Shah (2003). From
this discussion, one can identify the importance of employing higher order
statistics, to represent the data more completely (Shah et al. 2004). In fact,
it is well established that in theory, a complete description of an arbitrary
distribution can be made by the use of statistics of all orders, as in an infinite
series (Stark and Woods 1994). Independent component analysis (ICA) exploits
higher order statistics in multivariate data (e. g. Common 1994; Hyvarinen and
Oja) and has been applied to hyperspectral image analysis for feature extraction
and target detection (e. g. Robila and Varshney 2002a,b; Robila 2002; Chang et
al. 2002).
In Chap. 8, Robila and Varshney have investigated the feasibility of ICA
for unsupervised feature extraction from hyperspectral imagery. Their results
have demonstrated that ICA achieves significantly better performance in extracting features as compared to traditional PCA that is based only on second
P. K. Varshney et al., Advanced Image Processing Techniques for Remotely Sensed Hyperspectral Data
© Springer-Verlag Berlin Heidelberg 2004
Hyperspectral Classification
Using ICA Based Mixture Model
Chintan A. Shah
9.1
Introduction
Unsupervised classification of remote sensing images is typically based on
a mixture model, where the distribution of the entire data is modeled as
a weighted sum of the class-component densities (Duda et al. 2000). When
the class-component densities are assumed to be multivariate Gaussian, the
mixture model is known as the Gaussian mixture model. The K -means and the
ISODATA algorithms that are widely used in remote sensing are based on the
Gaussian mixture model. These Gaussian mixture model based classification
algorithms often perform unsatisfactorily. This stems from the Gaussian distribution assumption for the class-component densities. Gaussianity is only an
assumption, rather than a demonstrable property of natural spectral classes,
and has been widely accepted due to its analytical tractability and mathematical
simplicity. However, if a class happens to be multimodal, it is no longer appropriate to model the class with a multivariate Gaussian distribution. Therefore,
the use of the Gaussian mixture model in such cases may lead to unsatisfactory
performance.
This underlying Gaussian mixture model assumption is limited as it exploits
only the second order statistics of the observed data to estimate the posterior
densities. Limitations of using second order statistics (mean and covariance),
in characterizing multivariate data, have been discussed in Shah (2003). From
this discussion, one can identify the importance of employing higher order
statistics, to represent the data more completely (Shah et al. 2004). In fact,
it is well established that in theory, a complete description of an arbitrary
distribution can be made by the use of statistics of all orders, as in an infinite
series (Stark and Woods 1994). Independent component analysis (ICA) exploits
higher order statistics in multivariate data (e. g. Common 1994; Hyvarinen and
Oja) and has been applied to hyperspectral image analysis for feature extraction
and target detection (e. g. Robila and Varshney 2002a,b; Robila 2002; Chang et
al. 2002).
In Chap. 8, Robila and Varshney have investigated the feasibility of ICA
for unsupervised feature extraction from hyperspectral imagery. Their results
have demonstrated that ICA achieves significantly better performance in extracting features as compared to traditional PCA that is based only on second
P. K. Varshney et al., Advanced Image Processing Techniques for Remotely Sensed Hyperspectral Data
© Springer-Verlag Berlin Heidelberg 2004