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Locally Defined Principal Curves and Surfaces
TLDR
A novel theoretical understanding of principal curves and surfaces, practical algorithms as general purpose machine learning tools, and applications of these algorithms to several practical problems are presented. Expand
Mean shift spectral clustering
TLDR
A spectral clustering based mode merging method for mean shift as a theoretically well-founded approach that enables a probabilistic interpretation of affinity based clustering through kernel density estimation and allows principled kernel optimization and enables the use of anisotropic variable-size kernels to match local data structures. Expand
Second-Order Volterra System Identification With Noisy Input–Output Measurements
TLDR
The main contribution of this letter is a statistical criterion that can be utilized to identify analytically the true parameters of an order-2 Volterra model from noisy input-output data. Expand
Recursive Generalized Eigendecomposition for Independent Component Analysis
TLDR
A recursive generalized eigendecomposition algorithm is proposed that tracks the optimal solution that one would obtain using all the data observed, using the stochastic gradient concept. Expand
Nonlinear Coordinate Unfolding Via Principal Curve Projections with Application to Nonlinear BSS
TLDR
A technique is presented that tackles nonlinear blind source separation (NBSS) as a nonlinear invertible coordinate unfolding problem utilizing a recently developed definition of maximum-likelihood principal curves, applicable most conveniently to independent unimodal source distributions with mixtures that have diminishing second order derivatives along the source axes. Expand
Automatic Brain Image Segmentation for Evaluation of Experimental Ischemic Stroke Using Gradient vector flow and kernel annealing
TLDR
A method that uses active contours combined with a kernel annealing approach to automatically segment the brain organs of interest, as well as a simple feature that highlights the contrast between normal and infarct brain tissue for automated analysis is demonstrated. Expand
Piecewise smooth signal denoising via principal curve projections
One common problem in signal denoising is that if the signal has a blocky, in other words a piecewise-smooth structure, the denoised signal may suffer from oversmoothed discontinuities or exhibitExpand
Principal graphs and piecewise linear subspace constrained mean-shift
Principal curves have been defined as self-consistent smooth curves that pass through the middle of data. One of the important problems with most existing principal curve algorithms is that they areExpand
Information Regularized Sensor Fusion: Application to Localization With Distributed Motion Sensors
TLDR
Simulations confirm that the introduction of information regularization significantly improves localization accuracy of both maximum likelihood and particle filter approaches compared to their baseline implementations. Expand
Self-Consistent Locally Defined Principal Surfaces
TLDR
The concept of principal sets is introduced, which are the union of all principal surfaces with a particular dimensionality with rigorous conditions for a point to satisfy that can be evaluated using only the gradient and Hessian of the probability density at the point of interest. Expand
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