Clustering via Kernel Decomposition
IEEE Transactions on Neural NetworksPublished 1 January 2006Open access
A. Szymkowiak-Have, Mark Girolami, Jan Larsen
Citations27
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
In this letter, the affinity matrix is created from the elements of a nonparametric density estimator and then decomposed to obtain posterior probabilities of class membership.
Abstract
Spectral clustering methods were proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this letter, the affinity matrix is created from the elements of a nonparametric density estimator and then decomposed to obtain posterior probabilities of class membership. Hyperparameters are selected using standard cross-validation methods.
Keywords
Computer Science
Density Estimation for Statistics and Data Analysis
15,768 Citations2018B.W. Silverman
Neural ComputationNonlinear Component Analysis as a Kernel Eigenvalue Problem
8,078 Citations1998Bernhard Schölkopf, Alexander J. Smola +1 more
A new method for performing a nonlinear form of principal component analysis by the use of integral operator kernel functions is proposed and experimental results on polynomial feature extraction for pattern recognition are presented.
On Spectral Clustering: Analysis and an algorithm
7,751 Citations2001Andrew Y. Ng, Michael I. Jordan +1 more
A simple spectral clustering algorithm that can be implemented using a few lines of Matlab is presented, and tools from matrix perturbation theory are used to analyze the algorithm, and give conditions under which it can be expected to do well.
Algorithms for Non-negative Matrix Factorization
5,463 Citations2000Daniel D. Lee, H. Sebastian Seung
Two different multiplicative algorithms for non-negative matrix factorization are analyzed and one algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence.
IEEE Transactions on Neural NetworksA general regression neural network
4,415 Citations1991Donald F. Specht
The general regression neural network (GRNN) is a one-pass learning algorithm with a highly parallel structure that provides smooth transitions from one observed value to another.
Probabilistic latent semantic indexing
3,916 Citations1999Thomas Hofmann
Probabilistic Latent Semantic Indexing is a novel approach to automated document indexing which is based on a statistical latent class model for factor analysis of count data.
Using the Nyström Method to Speed Up Kernel Machines
1,522 Citations2000Christopher K. I. Williams, Matthias Seeger
It is shown that an approximation to the eigendecomposition of the Gram matrix can be computed by the Nystrom method (which is used for the numerical solution of eigenproblems) and the computational complexity of a predictor using this approximation is O(m2n).
When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts?
711 Citations2004David L. Donoho, Victoria Stodden
Theoretical results are shown to be predictive of the performance of published NMF code, by running the published algorithms on one of the synthetic image articulation databases.
Journal of the American Statistical AssociationRecent Developments in Nonparametric Density Estimation
471 Citations1991Alan Julian Izenman
A method of multivariate density estimation that did not spring from a univariate generalization is described, namely, projection pursuit density estimation, in which both dimensionality reduction and density estimation can be pursued at the same time.
UC BerkeleyLearning Spectral Clustering
431 Citations2003Francis R. Bach, Michael I. Jordan
A new cost function for spectral clustering is derived based on a measure of error between a given partition and a solution of the spectral relaxation of a minimum normalized cut problem.
On clusterings-good, bad and spectral
380 Citations2002Ramachandran Kannan, S. Vempala +1 more
Two results regarding the quality of the clustering found by a popular spectral algorithm are presented, one proffers worst case guarantees whilst the other shows that if there exists a "good" clustering then the spectral algorithm will find one close to it.
Learning Segmentation by Random Walks
370 Citations2000Marina Meilă, Jianbo Shi
This interpretation shows that spectral methods for clustering and segmentation have a probabilistic foundation and proves that the Normalized Cut method arises naturally from the framework.
Neural ComputationOrthogonal Series Density Estimation and the Kernel Eigenvalue Problem
142 Citations2002Mark Girolami
The view is presented that the eigenvalue decomposition of a kernel matrix can also provide the discrete expansion coefficients required for a nonparametric orthogonal series density estimator.
ArXiv.orgAggregate and mixed-order Markov models for statistical language processing
139 Citations1997Lawrence K. Saul, Fernando Pereira
This work considers the use of language models whose size and accuracy are intermediate between different order n-gram models and examines smoothing procedures in which these models are interposed between different orders.
Computational Statistics & Data AnalysisWebmining: learning from the world wide web
38 Citations2002Jan Larsen, Lars Kai Hansen +3 more
The use of unsupervised and supervised learning methods for user behavior modeling and content-based segmentation and classification of web pages are discussed.
Hierarchical Clustering for Datamining
22 Citations2001A. Szymkowiak, Jan Larsen +1 more
This paper presents hierarchical probabilistic clustering methods for unsupervised and supervised learning in datamining applications based on the previously suggested Generalizable Gaussian Mixture model.
Probabilistic Hierarchical Clustering with Labeled and Unlabeled Data
20 Citations2001Jan Larsen, A. Szymkowiak +2 more
This paper presents hierarchical probabilistic clustering methods for unsupervised and supervised learning in datamining applications, where supervised learning is performed using both labeled and unlabeled examples.
