Journal ArticleDOI
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification
Susanna Röblitz,Marcus Weber +1 more
TLDR
It is demonstrated in this paper that PCCA+ always delivers an optimal fuzzy clustering for nearly uncoupled, not necessarily reversible, Markov chains with transition states.Abstract:
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.read more
Citations
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References
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Book
Perturbation theory for linear operators
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Jianbo Shi,Jitendra Malik +1 more
TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.
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Proceedings Article
On Spectral Clustering: Analysis and an algorithm
TL;DR: 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.
Journal ArticleDOI
Laplacian Eigenmaps for dimensionality reduction and data representation
Mikhail Belkin,Partha Niyogi +1 more
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