document: Learning sparse metrics via linear programming Calculation of object similarity , for example through a distance function , is a common part of data mining and machine learning algorithms . This calculation is crucial for efficiency since distances are usually evaluated a large number of times , the classical example being query-by-example ( find objects that are similar to a given query object ) . Moreover , the performance of these algorithms depends critically on choosing a good distance function . However , it is often the case that ( 1 ) the correct distance is unknown or chosen by hand , and ( 2 ) its calculation is computationally expensive ( e.g. , such as for large dimensional objects ) . In this paper , we propose a method for constructing relative-distance preserving low-dimensional mapping ( sparse mappings ) . This method allows learning unknown distance functions ( or approximating known functions ) with the additional property of reducing distance computation time . We present an algorithm that given examples of proximity comparisons among triples of objects ( object i is more like object j than object k ) , learns a distance function , in as few dimensions as possible , that preserves these distance relationships . The formulation is based on solving a linear programming optimization problem that finds an optimal mapping for the given dataset and distance relationships . Unlike other popular embedding algorithms , this method can easily generalize to new points , does not have local minima , and explicitly models computational efficiency by finding a mapping that is sparse , i.e. one that depends on a small subset of features or dimensions . Experimental evaluation shows that the proposed formulation compares favorably with a state-of-the art method in several publicly available datasets .
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