A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
Clustering algorithms based on minimum and maximum spanning trees
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Low-dimensional embedding with extra information
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Algorithm Design
Three-Dimensional Face Recognition
International Journal of Computer Vision
Approximation algorithms for low-distortion embeddings into low-dimensional spaces
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Expression-invariant 3D face recognition
AVBPA'03 Proceedings of the 4th international conference on Audio- and video-based biometric person authentication
Robust expression-invariant face recognition from partially missing data
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
On bending invariant signatures for surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sensor network localization by eigenvector synchronization over the euclidean group
ACM Transactions on Sensor Networks (TOSN)
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The distance preserving graph embedding problem is to embed the vertices of a given weighted graph onto points in d-dimensional Euclidean space for a constant d such that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if the weights are given as a full matrix, then multi-dimensional scaling [Trevor Cox, Michael Cox, Multidimensional Scaling, second ed., Chapman & Hall CRC, 2001] can minimize the sum of squared embedding errors in quadratic time. A serious disadvantage of this approach is its quadratic space requirement. In this paper we develop a linear-space algorithm for this problem for the case when the weight of any edge can be computed in constant time. A key idea is to partition a set of n objects into O(n) disjoint subsets (clusters) of size O(n) such that the minimum inter cluster distance is maximized among all possible such partitions. Experimental results are included comparing the performance of the newly developed approach to the performance of the well-established least-squares multi-dimensional scaling approach [Trevor Cox, Michael Cox, Multidimensional Scaling, second ed., Chapman & Hall CRC, 2001] using three different applications. Although least-squares multi-dimensional scaling gave slightly more accurate results than our newly developed approach, least-squares multi-dimensional scaling ran out of memory for data sets larger than 15@?000 vertices.