Distance-Preserving Vector Space Embedding for Consensus Learning

Learning a prototype from a set of given objects is a core problem in machine learning and pattern recognition. A commonly used approach for consensus learning is to formulate it as an optimization problem in terms of generalized median computation. Recently, a prototype-embedding approach has been proposed to transform the objects into a vector space, compute the geometric median, and then inversely transform back into the original space. This vector space embedding approach has been successfully applied in several domains, where the generalized median problem has inherent high-computational complexity (typically NP-hard) and thus approximate solutions are required. Generally, it can be expected that the embedding should be done in a distance-preserving manner. However, the previous work based on the prototype-embedding approach did not take this embedding aspect into account. In this paper, we discuss the drawbacks of the current prototype-embedding approach and present an extensive empirical study that provides strong evidence of significantly improved quality of generalized median computation using distance-preserving embedding (DPE) methods. We also give concrete suggestions about suitable DPE methods. Moreover, we show that this framework can be used to effectively compute other consensus objects like the closest string. Finally, a MATLAB toolbox resulting from this paper is made publically available in order to encourage other researchers to explore the embedding-based consensus computation.