Linkages are essentially determined by similarity measures that may be derived from multiple perspectives. For example, spatial linkages are usually generated based on localities of heterogeneous data, whereas semantic linkages can come from various properties, such as different physical meanings behind social relations. Many existing metric learning models focus on spatial linkages, but leave the rich semantic factors unconsidered. Similarities based on these models are usually overdetermined on linkages. We propose a Unified Multi-Metric Learning (UM2L) framework to exploit multiple types of metrics. In UM2L, a type of combination operator is introduced for distance characterization from multiple perspectives, and thus can introduce flexibilities for representing and utilizing both spatial and semantic linkages. Besides, we propose a uniform solver for UM2L which is guaranteed to converge.

The main contribution of this paper is to introduce the interesting idea of "activator" (or integrator) operating on multiple metrics. Depending on how this activator (kappa) is picked, one may recover some previously proposed multiple metric learning approaches or create new relevant ones such as those discussed in Section 2.1. The proposed algorithm/analysis is an application of stochastic proximal (sub)gradient descent and is thus not a significant contribution from the optimization point of view (and the presentation of the algorithm is actually quite confusing, see below). My main problem with the paper is the experimental section. I was expecting some experiments showing how the choice of kappa influences the type of metrics that are learned, with an analysis of why some choices are better suited to some kind of problems / datasets / networks.

Linkages are essentially determined by similarity measures that may be derived from multiple perspectives. For example, spatial linkages are usually generated based on localities of heterogeneous data, whereas semantic linkages can come from various properties, such as different physical meanings behind social relations. Many existing metric learning models focus on spatial linkages, but leave the rich semantic factors unconsidered. Similarities based on these models are usually overdetermined on linkages. We propose a Unified Multi-Metric Learning (UM2L) framework to exploit multiple types of metrics.