Hyperspectral Classification Using ICA Based Mixture Model
225
have made an assumption that the number of sources is equal to the number
of sensor observations (N = M). This simplification is justified due to the fact
that if N > M, the dimensions of the sensor observation vector Xt can always
be reduced so that N = M. Such a reduction in dimensionality can be achieved
by all of the preprocessing or feature extraction techniques discussed above.
However, a detailed review of these feature extraction techniques reveals that,
other than PCA, none of the above mentioned feature extraction techniques
have a well-established theory on estimating the optimal number of ranked
features to be retained. In the case of PCA, the criterion for feature selection
can be stated as - sum of the variance of the retained principal components
should exceed 99% of the total data variance. Hence, we consider PCA as
a technique for estimating the intrinsic dimensionality of the hyperspectral
data. PCA, though optimal in the mean square sense, suffers from various
limitations (Duda et al. 2000), and therefore, there is a need to investigate
the performance of other feature extraction techniques for hyperspectral data.
Thus, in addition to PCA, we consider SPCA, OSP and PP as feature extraction
techniques.
9.3.4
Unsupervised Classification
The features obtained by a particular feature extraction technique are employed by the ICAMM algorithm as well as by the most widely used K-means
algorithm for classification. The accuracy of the ICAMM algorithm derived
classification is then compared with that obtained from the K-means classification algorithm.
In the next section, we apply and evaluate the performance of the ICAMM
algorithm for classification of data acquired from AVIRIS hyperspectral sensor.
9.4
Experimental Results and Analysis
To comparatively evaluate the classification performance we utilize the measure, overall accuracy that is computed as the percentage of correctly classified
pixels among all the pixels. The overall accuracy, obtained by the ICAMM
algorithm, varies for each run. This is due to the random initialization of
the mixing matrix and the bias vectors for the classes. Hence, we present the
results averaged over 100 runs of the ICAMM algorithm. We also provide further insight into the ICAMM derived classification obtained from one run by
critically analyzing the classification map and its corresponding error matrix.
Individual class accuracies have been assessed through producer's and user's
accuracy measures (see Sect. 2.6.5 of Chap. 2 for details on accuracy measures).
Data from the AVIRIS sensor, has been used for this experiment (see
Sect. 4.4.3 of Chap. 4 for details on this dataset). For computational efficiency,
a sub-image of size 80 x 40 pixels has been selected here. Some of the bands
(centered at 0.48 11m, 1.59 11m, and 2.1611 m) are depicted in Fig. 9.2a-c. The
225
have made an assumption that the number of sources is equal to the number
of sensor observations (N = M). This simplification is justified due to the fact
that if N > M, the dimensions of the sensor observation vector Xt can always
be reduced so that N = M. Such a reduction in dimensionality can be achieved
by all of the preprocessing or feature extraction techniques discussed above.
However, a detailed review of these feature extraction techniques reveals that,
other than PCA, none of the above mentioned feature extraction techniques
have a well-established theory on estimating the optimal number of ranked
features to be retained. In the case of PCA, the criterion for feature selection
can be stated as - sum of the variance of the retained principal components
should exceed 99% of the total data variance. Hence, we consider PCA as
a technique for estimating the intrinsic dimensionality of the hyperspectral
data. PCA, though optimal in the mean square sense, suffers from various
limitations (Duda et al. 2000), and therefore, there is a need to investigate
the performance of other feature extraction techniques for hyperspectral data.
Thus, in addition to PCA, we consider SPCA, OSP and PP as feature extraction
techniques.
9.3.4
Unsupervised Classification
The features obtained by a particular feature extraction technique are employed by the ICAMM algorithm as well as by the most widely used K-means
algorithm for classification. The accuracy of the ICAMM algorithm derived
classification is then compared with that obtained from the K-means classification algorithm.
In the next section, we apply and evaluate the performance of the ICAMM
algorithm for classification of data acquired from AVIRIS hyperspectral sensor.
9.4
Experimental Results and Analysis
To comparatively evaluate the classification performance we utilize the measure, overall accuracy that is computed as the percentage of correctly classified
pixels among all the pixels. The overall accuracy, obtained by the ICAMM
algorithm, varies for each run. This is due to the random initialization of
the mixing matrix and the bias vectors for the classes. Hence, we present the
results averaged over 100 runs of the ICAMM algorithm. We also provide further insight into the ICAMM derived classification obtained from one run by
critically analyzing the classification map and its corresponding error matrix.
Individual class accuracies have been assessed through producer's and user's
accuracy measures (see Sect. 2.6.5 of Chap. 2 for details on accuracy measures).
Data from the AVIRIS sensor, has been used for this experiment (see
Sect. 4.4.3 of Chap. 4 for details on this dataset). For computational efficiency,
a sub-image of size 80 x 40 pixels has been selected here. Some of the bands
(centered at 0.48 11m, 1.59 11m, and 2.1611 m) are depicted in Fig. 9.2a-c. The