Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Data clustering using a model granular magnet
Neural Computation
Agnostic classification of Markovian sequences
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
A randomized algorithm for pairwise clustering
Proceedings of the 1998 conference on Advances in neural information processing systems II
A New Nonparametric Pairwise Clustering Algorithm Based on Iterative Estimation of Distance Profiles
Machine Learning - Special issue: Unsupervised learning
Threshold Validity for Mutual Neighborhood Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multidimensional Scaling by Deterministic Annealing
EMMCVPR '97 Proceedings of the First International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Normalized Cuts and Image Segmentation
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
A Metric for Distributions with Applications to Image Databases
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
DEMScale: Large Scale MDS Accounting for a Ridge Operator and Demographic Variables
IDA '09 Proceedings of the 8th International Symposium on Intelligent Data Analysis: Advances in Intelligent Data Analysis VIII
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We present a novel approach for embedding general metric and nonmetric spaces into low-dimensional Euclidean spaces. As opposed to traditional multidimensional scaling techniques, which minimize the distortion of pairwise distances, our embedding algorithm seeks a low-dimensional representation of the data that preserves the structure (geometry) of the original data. The algorithm uses a hybrid criterion function that combines the pairwise distortion with what we call the geometric distortion. To assess the geometric distortion, we explore functions that reflect geometric properties. Our approach is different from the Isomap and LLE algorithms in that the discrepancy in distributional information is used to guide the embedding. We use clustering algorithms in conjunction with our embedding algorithm to direct the embedding process and improve its convergence properties.We test our method on metric and nonmetric data sets, and in the presence of noise. We demonstrate that our method preserves the structural properties of embedded data better than traditional MDS, and that its performance is robust with respect to clustering errors in the original data. Other results of the paper include accelerated algorithms for optimizing the standard MDS objective functions, and two methods for finding the most appropriate dimension in which to embed a given set of data.