9 May 2002 Fuzzy clustering of fMRI data: toward a theoretical basis for choosing the fuzziness index
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The fuzzy clustering algorithm (FCA) is a promising approach for the unsupervised analysis of complex fMRI studies with unknown input functions. Among the few parameters required by the FCA, the fuzziness index m plays an important role and the outcome of the clustering depends strongly on it. Unfortunately, there is no theoretical basis currently known for choosing the value of m and so far, empirical approaches have been carried out to find a reasonable value. The theoretical approach presented here calculates the probability distribution of the membership values uij during one iteration of the FCA and judges the regularity of this distribution, therefore indicating the degree of fuzziness of the resulting partition. This allows us to estimate the compactness of the clusters. It turns our that this probability does not only depend on the fuzziness index m, but also on the length of the time courses, a fact that was until now not noticed. Consequently, a reasonable choice of the fuzziness index depends on the signal to noise ratio and the temporal dimension of the data.
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Martin Buerki, Martin Buerki, Helmut Oswald, Helmut Oswald, Gerhard Schroth, Gerhard Schroth, } "Fuzzy clustering of fMRI data: toward a theoretical basis for choosing the fuzziness index", Proc. SPIE 4684, Medical Imaging 2002: Image Processing, (9 May 2002); doi: 10.1117/12.467054; https://doi.org/10.1117/12.467054

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