CLODD BASED BAND GROUP SELECTION Muhammad A. Islam, Derek T. Anderson, John E. Ball, and Nicolas H. Younan Mississippi State University Department of Electrical and Computer Engineering Mississippi State, MS 39762 ABSTRACT Herein, we explore both a new supervised and unsupervised technique for dimensionality reduction or multispectral sen- sor design via band group selection in hyperspectral imag- ing. Specifically, we investigate two algorithms, one based on the improved visual assessment of clustering tendency (iVAT) and the other based on the automatic extraction of “block- like” structure in a dissimilarity matrix (CLODD algorithm). In particular, the iVAT algorithm allows for identification of non-contiguous band groups. Experiments are conducted on a benchmark data set and results are compared to existing al- gorithms based on hierarchical and c-means clustering. Our results demonstrate the effectiveness of the proposed method. Index Terms— band grouping, dimensionality reduction, hyperspectral, iVAT, CLODD 1. INTRODUCTION Hyperspectral imaging is a demonstrated technology for nu- merous earth and space-borne applications involving tasks such as target detection, invasive species monitoring and pre- cision agriculture. However, hyperspectral imaging suffers from the “curse of dimensionality”. Of particular interest is new theory for dimensionality reduction or identification of fewer spectral bands for multispectral versus hyperspec- tral imaging, typically relative to some specific task, which aids efficient computation, improves classification and lowers system cost. Most techniques can be divided into two broad categories—projection or clustering. Projection techniques require all bands initially (versus feature selection) and they are focused on reducing dimensionality. Approaches include principal component analysis (PCA), Fishers linear discrim- inant analysis (FLDA) and generalized discriminant analysis This effort was partially sponsored by the Engineering Research and Development Center under Cooperative Agreement number W912HZ-15-2- 0004. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Engineering Research and Development Center or the U.S. Government. Material presented in this paper is also a product of the CREATE-GV Element of the Computational Research and Engineering Acquisition Tools and Environments (CREATE) Program sponsored by the U.S. Department of Defense HPC Modernization Program Office. (GDA), random projections (RP), and kernel extensions. Some methods are unsupervised, e.g., PCA and RP, while others are supervised, e.g., FLDA and GDA. Clustering is unsupervised learning and it can be applied to hyperspectral imagery in a number of ways. While it does not automatically do dimensionality reduction, it helps to identify structure and one can take that information and use it for dimensionality re- duction or band group selection. For example, in [1] Martinez et al. used an information measure to compute dissimilarity between bands and they used hierarchical clustering with Ward’s single linkage to produce a minimum variance par- titioning of the bands. In [2], Imani and Ghassemain used (hard) c-means for supervised band grouping. Martinez’s method suffers from the limitations of vanilla hierarchical clustering, e.g., how to pick clusters from the dendogram. Imani and Ghassemain’s approach suffers from the limita- tions of the c-means clustering algorithm, e.g., initialization, selection of c, and lack of ability compared to “soft” cluster- ing (probabilistic, fuzzy or possibilistic). Herein, we explore a new band grouping approach based on the improved visual assessment of clustering tendency (iVAT) [3]. This approach is well-grounded theoretically, and it produces visual results that an expert or additional clustering algorithm, e.g., clustering on ordered dissimilarity data (CLODD) [4], can exploit. Our goal was to identify an algorithm that could reproduce the structure that an expert currently finds and also be useful in the context of classifica- tion, which might demand different structure than an expert “sees”. A common practice is to use a proximity metric like correlation to measure the similarity between bands. Of- ten, contiguous bands are highly similar and this structure “shows up” if one produces an image of the similarity ma- trix. The CLODD algorithm analyzes a dissimilarity matrix, e.g., distances between vectors in a data set or bands in hy- perspectral imaging, and it automatically finds “block-like” structure. Structure is often found in a proximity matrix ac- cording to squares of high-contrast along the matrix diagonal. The CLODD algorithm exploits two properties, “edginess” and “contrast”. CLODD obtains contiguous band groups. However, we can automatically identify non-contiguous clus- ters (band groups) if we re-order the bands according to a method like iVAT. Herein, we explore both contiguous and