An alternating projection algorithm for computing the nearest euclidean distance matrix
SIAM Journal on Matrix Analysis and Applications
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust feature extraction via information theoretic learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Universal multi-dimensional scaling
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Coding Images with Local Features
International Journal of Computer Vision
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We derive a robust Euclidean embedding procedure based on semidefinite programming that may be used in place of the popular classical multidimensional scaling (cMDS) algorithm. We motivate this algorithm by arguing that cMDS is not particularly robust and has several other deficiencies. General-purpose semidefinite programming solvers are too memory intensive for medium to large sized applications, so we also describe a fast subgradient-based implementation of the robust algorithm. Additionally, since cMDS is often used for dimensionality reduction, we provide an in-depth look at reducing dimensionality with embedding procedures. In particular, we show that it is NP-hard to find optimal low-dimensional embeddings under a variety of cost functions.