Unsupervised Texture Segmentation in a Deterministic Annealing Framework
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Classification with Nonmetric Distances: Image Retrieval and Class Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
TalkMine: a soft computing approach to adaptive knowledge recommendation
Soft computing agents
A generalized kernel approach to dissimilarity-based classification
The Journal of Machine Learning Research
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Optimal Cluster Preserving Embedding of Nonmetric Proximity Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the information and representation of non-Euclidean pairwise data
Pattern Recognition
On the perceptual organization of image databases using cognitive discriminative biplots
EURASIP Journal on Applied Signal Processing
Linear-Time Computation of Similarity Measures for Sequential Data
The Journal of Machine Learning Research
Dealing with non-metric dissimilarities in fuzzy central clustering algorithms
International Journal of Approximate Reasoning
RECM: Relational evidential c-means algorithm
Pattern Recognition Letters
Manifold integration with Markov random walks
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Graph embedding using constant shift embedding
ICPR'10 Proceedings of the 20th International conference on Recognizing patterns in signals, speech, images, and videos
Non-Euclidean or non-metric measures can be informative
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Densifying Distance Spaces for Shape and Image Retrieval
Journal of Mathematical Imaging and Vision
Robust common spatial filters with a maxmin approach
Neural Computation
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Pairwise proximity data, given as similarity or dissimilarity matrix, can violate metricity. This occurs either due to noise, fallible estimates, or due to intrinsic non-metric features such as they arise from human judgments. So far the problem of non-metric pairwise data has been tackled by essentially omitting the negative eigenvalues or shifting the spectrum of the associated (pseudo-)covariance matrix for a subsequent embedding. However, little attention has been paid to the negative part of the spectrum itself. In particular no answer was given to whether the directions associated to the negative eigenvalues would at all code variance other than noise related. We show by a simple, exploratory analysis that the negative eigenvalues can code for relevant structure in the data, thus leading to the discovery of new features, which were lost by conventional data analysis techniques. The information hidden in the negative eigenvalue part of the spectrum is illustrated and discussed for three data sets, namely USPS handwritten digits, text-mining and data from cognitive psychology.