Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural Computation
GTM: the generative topographic mapping
Neural Computation
Mode-Finding for Mixtures of Gaussian Distributions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering by Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean Shift: A Robust Approach Toward Feature Space Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Mean Shift, Mode Seeking, and Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Training products of experts by minimizing contrastive divergence
Neural Computation
The Relevance of Non-generic Events in Scale Space Models
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Adaptive mixtures of local experts
Neural Computation
Scale-based clustering using the radial basis function network
IEEE Transactions on Neural Networks
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
Fast nonparametric clustering with Gaussian blurring mean-shift
ICML '06 Proceedings of the 23rd international conference on Machine learning
Gaussian Mean-Shift Is an EM Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean shift spectral clustering
Pattern Recognition
Critical Scale for Unsupervised Cluster Discovery
MLDM '07 Proceedings of the 5th international conference on Machine Learning and Data Mining in Pattern Recognition
Unsupervised cluster discovery using statistics in scale space
Engineering Applications of Artificial Intelligence
Deformable Model Fitting by Regularized Landmark Mean-Shift
International Journal of Computer Vision
On the upper bound of the number of modes of a multivariate normal mixture
Journal of Multivariate Analysis
Add isotropic Gaussian kernels at own risk: more and more resilient modes in higher dimensions
Proceedings of the twenty-eighth annual symposium on Computational geometry
An analysis of a spatial EA parallel boosting algorithm
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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We consider a problem intimately related to the creation of maxima under Gaussian blurring: the number of modes of a Gaussian mixture in D dimensions. To our knowledge, a general answer to this question is not known. We conjecture that if the components of the mixture have the same covariance matrix (or the same covariance matrix up to a scaling factor), then the number of modes cannot exceed the number of components. We demonstrate that the number of modes can exceed the number of components when the components are allowed to have arbitrary and different covariance matrices. We will review related results from scale-space theory, statistics and machine learning, including a proof of the conjecture in 1D. We present a convergent, EM-like algorithm for mode finding and compare results of searching for all modes starting from the centers of the mixture components with a brute-force search. We also discuss applications to data reconstruction and clustering.