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This paper addresses the problem of supervised classification of remote sensing images in the presence of incomplete (nonexhaustive) training sets. The problem is analyzed according to two different perspectives: 1) description and recognition of a specific land-cover class by using single-class classifiers and 2) solution of multiclass problems with single-class classification techniques. In this framework, we analyze different one-class classifiers and introduce in the remote sensing community the support vector domain description method (SVDD). The SVDD is a kernel-based method that exhibits intrinsic regularization ability and robustness versus low numbers of high-dimensional samples. The SVDD technique is compared with other standard single-class methods both in problems focused on the recognition of a single specific land-cover class and in multiclass problems. For the latter, we properly define an easily scalable multiclass architecture capable to deal with incomplete training data. Experimental results, obtained on different kinds of data (synthetic, hyperspectral, and multisensor images), point out the effectiveness of the SVDD technique and provide important indications for driving the choice of the classification technique and architecture in the presence of incomplete training data.