What Makes Objects Similar: A Unified Multi-Metric Learning Approach
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. Semantic linkages, however, can come from even more properties, such as different physical meanings behind social relations. Many existing metric learning models focus on spatial linkages but leave the <italic>rich</italic> semantic factors unconsidered. We propose a Unified Multi-Metric Learning (<sc>Um</sc><inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="ye-ieq1-2829192.gif"/></alternatives></inline-formula><sc>l</sc>) framework to exploit <italic>multiple types</italic> of metrics with respect to overdetermined similarities between linkages. In <sc>Um</sc><inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="ye-ieq2-2829192.gif"/></alternatives></inline-formula><sc>l</sc>, types of combination operators are 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 <sc>Um</sc><inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="ye-ieq3-2829192.gif"/></alternatives></inline-formula><sc>l</sc>, and the theoretical analysis reflects the generalization ability of <sc>Um</sc><inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="ye-ieq4-2829192.gif"/></alternatives></inline-formula><sc>l</sc> as well. Extensive experiments on diverse applications exhibit the superior classification performance and comprehensibility of <sc>Um</sc><inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="ye-ieq5-2829192.gif"/></alternatives></inline-formula><sc>l</sc>. Visualization results also validate its ability to physical meanings discovery.