Learning discriminative representation for image classification.

We introduce a new classifier for small-sample image data based on a two-dimensional discriminative regression approach. For a test example, our method estimates a discriminative representation from training examples, which accounts for discriminativeness between classes and enables accurate derivation of categorical information. Unlike existing methods that vectored image data, the learning of the representation in our method is performed with the two-dimensional features of the data, and thus inherent spatial information of the data is fully exploited. This new type of two-dimensional discriminative regression, different from existing regression models, allows for building a highly effective and robust classifier for image data through explicitly incorporating discriminative information and inherent spatial information. We compare our method with several state-of-the-art classifiers of small-sample images and experimental results show superior performance of the proposed method in classification accuracy as well as robustness to noise corruption.

Notes on attribution functions.

Let Q,Kσ be the knowledge space derived from an attribution function σ on Q. Under an assumption for σ, this paper gives some necessary and sufficient conditions such that Q,Kσ is discriminative. It also discusses the resolubility of σ when Q is an infinite set. More precisely, this paper proves that σ is not resoluble if Q is uncountable, and gives a necessary and sufficient condition such that σ is resoluble when Q,Kσ is ∞ -well-graded. By way of applications of these results, discriminativeness and resolubility are discussed around the merge of skill multimaps and the meshing of the delineated knowledge spaces.