A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Understanding Molecular Simulation
Understanding Molecular Simulation
On the Approximation of Complicated Dynamical Behavior
SIAM Journal on Numerical Analysis
On the Structure of Nearly Uncoupled Markov Chains
Proceedings of the International Workshop on Computer Performance and Reliability
Path Based Pairwise Data Clustering with Application to Texture Segmentation
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Data Resampling for Path Based Clustering
Proceedings of the 24th DAGM Symposium on Pattern Recognition
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
On clusterings: Good, bad and spectral
Journal of the ACM (JACM)
A tutorial on spectral clustering
Statistics and Computing
Spectral clustering with fuzzy similarity measure
Digital Signal Processing
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Given a row-stochastic matrix describing pairwise similarities between data objects, spectral clustering makes use of the eigenvectors of this matrix to perform dimensionality reduction for clustering in fewer dimensions. One example from this class of algorithms is the Robust Perron Cluster Analysis (PCCA+), which delivers a fuzzy clustering. Originally developed for clustering the state space of Markov chains, the method became popular as a versatile tool for general data classification problems. The robustness of PCCA+, however, cannot be explained by previous perturbation results, because the matrices in typical applications do not comply with the two main requirements: reversibility and nearly decomposability. We therefore demonstrate in this paper that PCCA+ always delivers an optimal fuzzy clustering for nearly uncoupled, not necessarily reversible, Markov chains with transition states.