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Type: Report × Subject: Adaptive weights ×

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    Adaptive manifold clustering
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Besold, Franz; Spokoiny, Vladimir
    Clustering methods seek to partition data such that elements are more similar to elements in the same cluster than to elements in different clusters. The main challenge in this task is the lack of a unified definition of a cluster, especially for high dimensional data. Different methods and approaches have been proposed to address this problem. This paper continues the study originated by [6] where a novel approach to adaptive nonparametric clustering called Adaptive Weights Clustering (AWC) was offered. The method allows analyzing high-dimensional data with an unknown number of unbalanced clusters of arbitrary shape under very weak modeling as-sumptions. The procedure demonstrates a state-of-the-art performance and is very efficient even for large data dimension D. However, the theoretical study in [6] is very limited and did not re-ally address the question of efficiency. This paper makes a significant step in understanding the remarkable performance of the AWC procedure, particularly in high dimension. The approach is based on combining the ideas of adaptive clustering and manifold learning. The manifold hypoth-esis means that high dimensional data can be well approximated by a d-dimensional manifold for small d helping to overcome the curse of dimensionality problem and to get sharp bounds on the cluster separation which only depend on the intrinsic dimension d. We also address the problem of parameter tuning. Our general theoretical results are illustrated by some numerical experiments.
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    Analysing fMRI experiments with the fmri package in R. version 1.0 : a user's guide
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Polzehl, Jörg; Tabelow, Karsten
    This document describes the usage of the R package fmri to analyse functional Magnetic Resonance Imaging (fMRI) data with structure adaptive smoothing procedures (Propagation-Separation (PS) approach) as described in [7].
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    Structural adaptive smoothing for single-subject analysis in SPM: the aws4SPM-toolbox
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Hoffmann, Devy; Tabelow, Karsten
    There exists a variety of software tools for analyzing functional Magnetic Resonance Imaging data. A very popular one is the freely available SPM package by the Functional Imaging Laboratory at the Wellcome Department of Imaging Neuroscience. In order to enhance the signal-to-noise ratio it provides the possibility to smooth the data in a pre-processing step by a Gaussian filter. However, this comes at the cost of reducing the effective resolution. In a series of recent papers it has been shown, that using a structural adaptive smoothing algorithm based on the Propagation-Separation method allows for enhanced signal detection while preserving the shape and spatial extent of the activation areas. Here, we describe our implementation of this algorithm as a toolbox for SPM.