Conference Paper

# Rates of convergence for the cluster tree.

In proceeding of: Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010. Proceedings of a meeting held 6-9 December 2010, Vancouver, British Columbia, Canada.

Source: DBLP

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**ABSTRACT:**The level set tree approach of Hartigan (1975) provides a probabilistically based and highly interpretable encoding of the clustering behavior of a dataset. By representing the hierarchy of data modes as a dendrogram of the level sets of a density estimator, this approach offers many advantages for exploratory analysis and clustering, especially for complex and high-dimensional data. Several R packages exist for level set tree estimation, but their practical usefulness is limited by computational inefficiency, absence of interactive graphical capabilities and, from a theoretical perspective, reliance on asymptotic approximations. To make it easier for practitioners to capture the advantages of level set trees, we have written the Python package DeBaCl for DEnsity-BAsed CLustering. In this article we illustrate how DeBaCl's level set tree estimates can be used for difficult clustering tasks and interactive graphical data analysis. The package is intended to promote the practical use of level set trees through improvements in computational efficiency and a high degree of user customization. In addition, the flexible algorithms implemented in DeBaCl enjoy finite sample accuracy, as demonstrated in recent literature on density clustering. Finally, we show the level set tree framework can be easily extended to deal with functional data.07/2013; - [Show abstract] [Hide abstract]

**ABSTRACT:**Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees-which provide a concise representation of the hierarchical mode structure of probability density functions-offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N = 30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber pathways and an efficient segmentation of the pathways that had empirical accuracy comparable to standard nonparametric clustering techniques. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output.PLoS ONE 01/2014; 9(4):e93344. · 3.73 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The large amount of molecular dynamics simulation data produced by modern computational models brings big opportunities and challenges to researchers. Clustering algorithms play an important role in understanding biomolecular kinetics from the simulation data, especially under the Markov state model framework. However, the ruggedness of the free energy landscape in a biomolecular system makes common clustering algorithms very sensitive to perturbations of the data. Here, we introduce a data-exploratory tool which provides an overview of the clustering structure under different parameters. The proposed Multi-Persistent Clustering analysis combines insights from recent studies on the dynamics of systems with dominant metastable states with the concept of multi-dimensional persistence in computational topology. We propose to explore the clustering structure of the data based on its persistence on scale and density. The analysis provides a systematic way to discover clusters that are robust to perturbations of the data. The dominant states of the system can be chosen with confidence. For the clusters on the borderline, the user can choose to do more simulation or make a decision based on their structural characteristics. Furthermore, our multi-resolution analysis gives users information about the relative potential of the clusters and their hierarchical relationship. The effectiveness of the proposed method is illustrated in three biomolecules: alanine dipeptide, Villin headpiece, and the FiP35 WW domain.PLoS ONE 01/2013; 8(4):e58699. · 3.73 Impact Factor

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