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Classification is an important problem in image document processing and is often a preliminary step towards recognition, understanding, and information extraction. In this paper, the problem is formulated in the framework of concept learning and each category corresponds to the set of image documents with similar physical structure. We propose a solution based on two algorithmic ideas. First, we obtain a structured representation of images based on labeled XY-trees (this representation informs the learner about important relationships between image sub-constituents). Second, we propose a probabilistic architecture that extends hidden Markov models for learning probability distributions defined on spaces of labeled trees. Finally, a successful application of this method to the categorization of commercial invoices is presented.

We propose a general framework to incorporate first-order logic (FOL) clauses, that are thought of as an abstract and partial representation of the environment, into kernel machines that learn within a semi-supervised scheme. We rely on a multi-task learning scheme where each task is associated with a unary predicate defined on the feature space, while higher level abstract representations consist of FOL clauses made of those predicates. We re-use the kernel machine mathematical apparatus to solve the problem as primal optimization of a function composed of the loss on the supervised examples, the regularization term, and a penalty term deriving from forcing real-valued constraints deriving from the predicates. Unlike for classic kernel machines, however, depending on the logic clauses, the overall function to be optimized is not convex anymore. An important contribution is to show that while tackling the optimization by classic numerical schemes is likely to be hopeless, a stage-based learning scheme, in which we start learning the supervised examples until convergence is reached, and then continue by forcing the logic clauses is a viable direction to attack the problem. Some promising experimental results are given on artificial learning tasks and on the automatic tagging of bibtex entries to emphasize the comparison with plain kernel machines.

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