Abstract
The irecent development of more sophisticated sensors for remote sensing systems enables the measurement of radiation in many more spectral intervals than previous possible. An example of this technology is the AVlRlS system., which collects image data in 220 bands. The increased dimensionality of such hyperspectral data provides a challenge to the current techniques for analyzing such data. Our experience in three dimensional space tends to rr~isleado ur intuition of geometrical and statistical properties in high dimensional space, properties that must guide our choices in the data analysis process. Using Euclidean and Cartesian geometry, high dimensional space properties are investigated and their implication for high dimensional data and its analysis are studied in order to illuminate the differences between conventional spaces and hyperdimensional space. Supervised classification techniques use labeled samples in order to train the classifier. Usually the number of such samples is limited, and as the number of bands available increases, this limitation becomes more severe, and can become dominate over the projected added value of having the additional bands 'available. This suggests the need for reducing the dimensionality via a preprocessing method which takes into consideration high dimensional space properties. Such reduction should enable th'e estimation of feature extraction parameters to be niore accurate. Using a technique referred to as Projection Pursuit, two parametric pro'jection pursuit algorithms have been developed: Parallel Parametric Projection Pursuit and Sequential Parametric Projection Pursuit. In the present work both methods are presented, and an iterative procedure of the Sequential Approach that mitigates the computation time problem is shown. Parametric Projection Pursuit' methods requires the use ,of a numerical optimization algorithm. A method to estimate an initial value that can rrlore quickly lead to the global maximum is presented for projection pursuit using Bhattacharyya distance ;3s the Projection Index. This method leads also to a high dimensional version of a feature selection algorithm, which requires significantly less computation than the normal procedure.
Date of this Version
April 1996