Sparse Inverse Covariance Estimates for Hyperspectral Image Classification

Classification of remotely sensed hyperspectral images calls for a classifier that gracefully handles high-dimensional data, where the amount of samples available for training might be very low relative to the dimension. Even when using simple parametric classifiers such as the Gaussian maximum-likelihood rule, the large number of bands leads to copious amounts of parameters to estimate. Most of these parameters are measures of correlations between features. The covariance structure of a multivariate normal population can be simplified by setting elements of the inverse covariance matrix to zero. Well-known results from time series analysis relates the estimation of the inverse covariance matrix to a sequence of regressions by using the Cholesky decomposition. We observe that discriminant analysis can be performed without inverting the covariance matrix. We propose defining a sparsity pattern on the lower triangular matrix resulting from the Cholesky decomposition, and develop a simple search algorithm for choosing this sparsity. The resulting classifier is used on four different hyperspectral images, and compared with conventional approaches such as support vector machines, with encouraging results