Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Journal of Machine Learning Research
Stability-based validation of clustering solutions
Neural Computation
A tutorial on spectral clustering
Statistics and Computing
Stability Based Sparse LSI/PCA: Incorporating Feature Selection in LSI and PCA
ECML '07 Proceedings of the 18th European conference on Machine Learning
Improving clustering stability with combinatorial MRFs
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Multi-core parallelization in Clojure: a case study
Proceedings of the 6th European Lisp Workshop
Unsupervised Stability-Based Ensembles to Discover Reliable Structures in Complex Bio-molecular Data
Computational Intelligence Methods for Bioinformatics and Biostatistics
Proceedings of the 18th ACM conference on Information and knowledge management
A stability based validity method for fuzzy clustering
Pattern Recognition
Stability of k-means clustering
COLT'07 Proceedings of the 20th annual conference on Learning theory
Clustering Stability: An Overview
Foundations and Trends® in Machine Learning
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Group detection in mobility traces
Proceedings of the 6th International Wireless Communications and Mobile Computing Conference
Characterization, Stability and Convergence of Hierarchical Clustering Methods
The Journal of Machine Learning Research
Penalized cluster analysis with applications to family data
Computational Statistics & Data Analysis
The Journal of Machine Learning Research
Optimality and stability of the K-hyperline clustering algorithm
Pattern Recognition Letters
Clustering for semi-supervised spam filtering
Proceedings of the 8th Annual Collaboration, Electronic messaging, Anti-Abuse and Spam Conference
Center-based clustering under perturbation stability
Information Processing Letters
Selection of the number of clusters via the bootstrap method
Computational Statistics & Data Analysis
SIAM Journal on Computing
Some connectivity based cluster validity indices
Applied Soft Computing
GANC: Greedy agglomerative normalized cut for graph clustering
Pattern Recognition
An effective unsupervised network anomaly detection method
Proceedings of the International Conference on Advances in Computing, Communications and Informatics
SOHAC: efficient storage of tick data that supports search and analysis
ICDM'12 Proceedings of the 12th Industrial conference on Advances in Data Mining: applications and theoretical aspects
Stability-based model selection for high throughput genomic data: an algorithmic paradigm
ICARIS'12 Proceedings of the 11th international conference on Artificial Immune Systems
Stability of density-based clustering
The Journal of Machine Learning Research
A non-parametric method to estimate the number of clusters
Computational Statistics & Data Analysis
A statistical view of clustering performance through the theory of U-processes
Journal of Multivariate Analysis
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Stability is a common tool to verify the validity of sample based algorithms. In clustering it is widely used to tune the parameters of the algorithm, such as the number k of clusters. In spite of the popularity of stability in practical applications, there has been very little theoretical analysis of this notion. In this paper we provide a formal definition of stability and analyze some of its basic properties. Quite surprisingly, the conclusion of our analysis is that for large sample size, stability is fully determined by the behavior of the objective function which the clustering algorithm is aiming to minimize. If the objective function has a unique global minimizer, the algorithm is stable, otherwise it is unstable. In particular we conclude that stability is not a well-suited tool to determine the number of clusters – it is determined by the symmetries of the data which may be unrelated to clustering parameters. We prove our results for center-based clusterings and for spectral clustering, and support our conclusions by many examples in which the behavior of stability is counter-intuitive.