An improved EM algorithm for remote sensing classification

Abstract

The use of a general EM (expectation-maximization) algorithm in multi-spectral image classification is known to cause two problems: singularity of the variance-covariance matrix and sensitivity of randomly selected initial values. The former causes computation failure; the latter produces unstable classification results. This paper proposes a modified approach to resolve these defects. First, a modification is proposed to determine reliable parameters for the EM algorithm based on a k-means algorithm with initial centers obtained from the density function of the first principal component, which avoids the selection of initial centers at random. A second modification uses the principal component transformation of the image to obtain a set of uncorrelated data. The number of principal components as the input of the EM algorithm is determined by the principal contribution rate. In this way, the modification can not only remove singularity but also weaken noise. Experimental results obtained from two sets of remote sensing images acquired by two different sensors confirm the validity of the proposed approach. . The Gaussian mixture model is a weighted sum of Gaussian probability density functions (referred to as Gaussian components) of the mixture model describing a class, and it has been widely used in pattern recognition and classification [15][16][17][18]. In remote sensing classification, a unimodal assumption for class conditional distribution is unsuitable for remote sensing images, particularly for high spatial resolution images. It is appropriate to describe the class conditional distribution as a Gaussian mixture model. Without a model or a classification label, it would be difficult to determine the parameters of a Gaussian mixture model in classification applications. Newton-Raphson and scoring algorithms in parameter solutions are very complex and difficult [19,20]. The EM algorithm-constructed maximum likelihood has good properties because of effective model labels [1,21]. However, the EM algorithm is very sensitive to initializations and easily gets trapped in local minima. In practice, the algorithm runs many times with different initial parameters, and various local search heuristics are used to find better parameters near convergences. Moreover, significant difficulty is encountered in estimating parameters of the Gaussian mixture models with creasing dimensions. Multi-spectral and hyper-spectral images with high correlations can lead to a singular variance-covariance matrix that terminates in an iteration of the EM algorithm without a reliable result [8,22,23]. Furthermore, in the case of a large component overlap, the EM algorithm suffers from slow convergence [24]. Finally, the EM algorithm fails when the covariance matrix corresponding to one or more components becomes ill-conditioned (singular or nearly singular). Gaussian mixture model, EM algorithm, Kernel density estimation, principal component transformation

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