Most of the metric learning mainly focuses on using single feature weights with L p norms, or the pair of features with Mahalanobis distances to learn the similarities between the samples, while ignoring the potential value of higher-order interactions in the feature space. In this paper, we investigate the possibility of learning weights to coalitions of features whose cardinality can be greater than two, with the help of setfunctions. With the more particular property of submodular set-function, we propose to define a metric for continuous features based on Lovasz extension of submodular functions, and then present a dedicated metric learning approach. According to the submodular constraints, it naturally leads to a higher complexity price so that we use the ξ-additive fuzzy measure to decrease this complexity, by reducing the order of interactions that are taken into account. This approach finally gives a computationally, feasible problem. Experiments on various datasets show the effectiveness of the approach.
Abstract. The vast majority of metric learning approaches are dedicated to be applied on data described by feature vectors, with some notable exceptions such as times series and trees or graphs. Many real-world networks are described by both connectivity information and features for every node. The objective of this paper is to propose better model and understand these networks. We present metric learning with Graph Information (MLGI), an algorithm for learning a Mahalanobis distance metric with the connectivity structure information of the links between nodes.
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