Information Processing Letters
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Matrix computations (3rd ed.)
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Constrained K-means Clustering with Background Knowledge
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
Feature Selection via Concave Minimization and Support Vector Machines
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
A Column Generation Algorithm For Boosting
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
The Journal of Machine Learning Research
Privacy-preserving cox regression for survival analysis
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Learning a Mahalanobis distance metric for data clustering and classification
Pattern Recognition
Semi-definite Manifold Alignment
ECML '07 Proceedings of the 18th European conference on Machine Learning
Feature selection and kernel design via linear programming
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Large Scale Online Learning of Image Similarity Through Ranking
The Journal of Machine Learning Research
Semi-supervised sparse metric learning using alternating linearization optimization
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Scalable large-margin Mahalanobis distance metric learning
IEEE Transactions on Neural Networks
Multi-task low-rank metric learning based on common subspace
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
Distance metric learning with eigenvalue optimization
The Journal of Machine Learning Research
Positive semidefinite metric learning using boosting-like algorithms
The Journal of Machine Learning Research
Kernel regression with sparse metric learning
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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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.