Unsupervised Feature Selection Using Geometrical Measures in Prototype Space for Hyperspectral Imagery

Feature/band selection is a common technique to overcome the “curse of dimensionality” posed by the high dimensionality of hyperspectral imagery. When the image is characterized by unknown phenomena, an unsupervised approach can be utilized to select the most distinctive and informative bands. The efficiency of an unsupervised feature selection (FS) depends on the criteria to be optimized and the space (e.g., feature space, pixel space, spectral space, etc.) in which the data are represented. Moreover, the determination of the initial feature and the determination of the optimal feature size (the optimal number of distinct bands to be selected) are other challenges faced in unsupervised approaches. In this paper, we propose two unsupervised FS methods by representing bands in the prototype space (PS). The first method proposes a way for selecting the initial feature based on the orthogonal distance from the PS diagonal and determines the optimal feature size by employing the HySime algorithm in the PS. The second method uses two criteria defined by the tangent of the angles between the band vectors in the PS in order to select the initial feature and to describe the band correlations. Meanwhile, the determination of the optimal feature size is embedded in this method. The experimental results on real and synthetic data sets show that our methods are more reliable and can yield a better result in terms of class separability and Friedman test than other widely used techniques.