Integrating Logic Knowledge into Graph Regularization: an application to image tagging

This paper studies how prior knowledge in form of First Order Logic (FOL) clauses can be converted into a set of continuous constraints. These constraints can be directly integrated into a learning framework allowing to jointly learn from examples and semantic knowledge. In particular, in this paper we show how the constraints can be integrated into a regularization schema working over discrete domains. We consider tasks in which items are connected to each other by given relationships, thus yielding a graph, whose nodes correspond to the available objects. It is required to estimate a set of functions defined on each node of the graph, given a small set of labeled nodes for each function. The FOL constraints enforce dependencies, resulting from the FOL knowledge, among the values that the functions assume over the nodes. The experimental results evaluate the proposed technique on an image tagging task, showing how the proposed approach provides a significantly higher tagging accuracy than simple graph regularization. The experimental results show how the selection of a proper conversion process of the FOL clauses is fundamental in order to achieve good results.