Gaussian mixture models (GMM) are widely used for unsupervised classification applications in remote sensing. Expectation-Maximization (EM) is the standard algorithm employed to estimate the parameters of these models. However, such iterative optimization methods can easily get trapped into local maxima. Researchers use populationbased stochastic search algorithms to obtain better estimates. We present a novel particle swarm optimization-based algorithm for maximum likelihood estimation of Gaussian mixture models. The proposed approach provides solutions for important problems in effective application of populationbased algorithms to the clustering problem. We present a new parametrization for arbitrary covariance matrices that allows independent updating of individual parameters during the search process. We also describe an optimization formulation for identifying the correspondence relations between different parameter orderings of candidate solutions. Experiments on a hyperspectral image show better clustering results compared to the commonly used EM algorithm for estimating GMMs.

a b s t r a c tGaussian mixture models (GMM), commonly used in pattern recognition and machine learning, provide a flexible probabilistic model for the data. The conventional expectation-maximization (EM) algorithm for the maximum likelihood estimation of the parameters of GMMs is very sensitive to initialization and easily gets trapped in local maxima. Stochastic search algorithms have been popular alternatives for global optimization but their uses for GMM estimation have been limited to constrained models using identity or diagonal covariance matrices. Our major contributions in this paper are twofold. First, we present a novel parametrization for arbitrary covariance matrices that allow independent updating of individual parameters while retaining validity of the resultant matrices. Second, we propose an effective parameter matching technique to mitigate the issues related with the existence of multiple candidate solutions that are equivalent under permutations of the GMM components. Experiments on synthetic and real data sets show that the proposed framework has a robust performance and achieves significantly higher likelihood values than the EM algorithm.

High spectral and high spatial resolution images acquired from new generation satellites have enabled new applications. However, the increasing amount of detail in these images also necessitates new algorithms for automatic analysis. This paper describes a new approach to discover compound structures such as different types of residential, commercial, and industrial areas that are comprised of spatial arrangements of primitive objects such as buildings, roads, and trees. The proposed approach uses a robust Gaussian mixture model (GMM) where each Gaussian component models the spectral and shape content of a group of pixels corresponding to a primitive object. The algorithm can also incorporate spatial constraints on the layout of the primitive objects in terms of their relative positions. Given example structures of interest, a new learning algorithm fits a GMM to the image data, and this model can be used to detect other similar structures by grouping pixels that have high likelihoods of belonging to the Gaussian object models while satisfying the spatial layout constraints without any requirement for region segmentation. Experiments using WorldView-2 data show that the proposed method can detect high-level structures that cannot be modeled using traditional techniques.

Abstract-We present solutions to two problems that prevent the effective use of population-based algorithms in clustering problems. The first solution presents a new representation for arbitrary covariance matrices that allows independent updating of individual parameters while retaining the validity of the matrix. The second solution involves an optimization formulation for finding correspondences between different parameter orderings of candidate solutions. The effectiveness of the proposed solutions are demonstrated on a novel clustering algorithm based on particle swarm optimization for the estimation of Gaussian mixture models.

High spectral and high spatial resolution images acquired from new generation satellites have enabled new applications. However, the increasing amount of detail in these images also necessitates new algorithms for automatic analysis. This paper describes a new approach to discover compound structures such as different types of residential, commercial, and industrial areas that are comprised of spatial arrangements of primitive objects such as buildings, roads, and trees. The proposed approach uses a robust Gaussian mixture model (GMM) where each Gaussian component models the spectral and shape content of a group of pixels corresponding to a primitive object. The algorithm can also incorporate spatial constraints on the layout of the primitive objects in terms of their relative positions. Given example structures of interest, a new learning algorithm fits a GMM to the image data, and this model can be used to detect other similar structures by grouping pixels that have high likelihoods of belonging to the Gaussian object models while satisfying the spatial layout constraints without any requirement for region segmentation. Experiments using WorldView-2 data show that the proposed method can detect high-level structures that cannot be modeled using traditional techniques.