Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
The Concentration of Fractional Distances
IEEE Transactions on Knowledge and Data Engineering
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Nonlinear Dimensionality Reduction
Nonlinear Dimensionality Reduction
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
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Simbed, standing for similarity-based embedding, is a new method of embedding high-dimensional data. It relies on the preservation of pairwise similarities rather than distances. In this respect, Simbed can be related to other techniques such as stochastic neighbor embedding and its variants. A connection with curvilinear component analysis is also pointed out. Simbed differs from these methods by the way similarities are defined and compared in both the data and embedding spaces. In particular, similarities in Simbed can account for the phenomenon of norm concentration that occurs in high-dimensional spaces. This feature is shown to reinforce the advantage of Simbed over other embedding techniques in experiments with a face database.