SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Evaluating a class of distance-mapping algorithms for data mining and clustering
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
Learning to Classify Text Using Support Vector Machines: Methods, Theory and Algorithms
Learning to Classify Text Using Support Vector Machines: Methods, Theory and Algorithms
Fast approximations for sums of distances, clustering and the Fermat--Weber problem
Computational Geometry: Theory and Applications
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
The Journal of Machine Learning Research
Distributional clustering of English words
ACL '93 Proceedings of the 31st annual meeting on Association for Computational Linguistics
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Histograms of Oriented Gradients for Human Detection
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
ICML '06 Proceedings of the 23rd international conference on Machine learning
Improved Approximation Algorithms for Large Matrices via Random Projections
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Embeddings of surfaces, curves, and moving points in euclidean space
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
Eigensolver methods for progressive multidimensional scaling of large data
GD'06 Proceedings of the 14th international conference on Graph drawing
Texture mapping via spherical multi-dimensional scaling
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Instant approximate 1-center on road networks via embeddings
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Neurocomputing
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In this paper, we propose a unified algorithmic framework for solving many known variants of MDS. Our algorithm is a simple iterative scheme with guaranteed convergence, and is modular; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods in comparable time. Moreover, they have a small memory footprint and scale effectively for large data sets. We expect that this framework will be useful for a number of MDS variants that have not yet been studied. Our framework extends to embedding high-dimensional points lying on a sphere to points on a lower dimensional sphere, preserving geodesic distances. As a complement to this result, we also extend the Johnson-Lindenstrauss Lemma to this spherical setting, by showing that projecting to a random O((1/µ2) log n)-dimensional sphere causes only an eps-distortion in the geodesic distances.