## On clustering of fMRI time series (1997)

Citations: | 45 - 3 self |

### BibTeX

@MISC{Toft97onclustering,

author = {Peter Toft and Lars Kai Hansen and Finn Årup Nielsen and L. K. Hansen and Nick Lange and Niels Mørch and F. A. Nielsen and Olaf B. Paulson and Robert Savoy and Bruce Rosen and Egill Rostrup and Peter Born and Stephen C. Strother and N. Lange and N. Mrch and Claus Svarer and O. B. Paulson},

title = {On clustering of fMRI time series},

year = {1997}

}

### Years of Citing Articles

### OpenURL

### Abstract

Introduction. The spatio-temporal fMRI signal is a combination of several interacting components: The locally correlated hemodynamic response, the network of neuronal activations, and global components such as the cardiac cycle, breathing etc. A priori this implies that the signal is correlated in time and space, and that these correlations have both short and long range components. Clustering is a classical non-parametric approach to explorative analysis data. By clustering we can group signals according to a given objective function. Clustering of waveforms has already been used in fMRI signal analysis, see e.g. (1). Clustering of stochastic data, however, is hard optimization problem with many potential pitfalls. The "optimal" cluster configuration depends on the particular choice of clustering scheme (e.g. k-means, k-medians, hierachical clustering) examples are legio (2), but just as importantly on the choice of distance metr

### Citations

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Citation Context ...trivial partition of N clusters containing one point each. K-means The above considerations provide a natural introduction to one of the most widely used clustering techniques: the K-means algorithm (=-=MacQueen, 1967-=-; Hartigan and Wong, 1979). For a given number K of clusters, the within-class inertia is iteratively minimised by assigning data to the nearest center and recalculating each centre as the average of ... |

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Citation Context ...o fMRI analysis. Several flavors of statistical tests have been used (Xiong et al., 1996). The t test implemented in SPM (Worsley and Friston, 1995), derived from the well-known general linear model (=-=McCullagh and Nelder, 1989-=-), and the nonparametric Kolmogorov–Smirnov test (Baker et al., 1994) are the most widespread examples. The correlation between the fMRI signal and the activation paradigm has also been used in differ... |

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Citation Context ... 50 values, x j (\Gamma24) to x j (25), of the cross-correlation between the fMRI time series and the activation paradigm. In one deterministic pass, the hierarchical algorithm provides a dendrogram (=-=Ripley, 1996-=-, p. 320), ie a binary tree representing the way each cluster is composed of clusters obtained in previous steps. The tree can be cut at several levels in order to obtain an arbitrary number of cluste... |

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Citation Context ... P-dimensional space. The resulting partition is potentially highly dependent on the particular choice of metric. A fairly broad class of metrics can be obtained by defining the generalised distance (=-=Mahalanobis, 1936-=-) between two vectors a and b in IR P as: d 2 (a; b) = (a \Gamma b) ? D(a \Gamma b) (3) where D is a P \ThetaP symmetric positive definite matrix that uniquely defines the metric. For D = I P (the ide... |

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Citation Context ...parametric Kolmogorov-Smirnov test (Baker et al., 1994) are the most widespread examples. The correlation between the fMRI signal and the activation paradigm has also been used in different contexts (=-=Bandettini et al., 1993-=-; Golay et al., 1997), while linear filters, like the finite input response (FIR) filter, are slowly emerging as a possible alternative (Lange and Zeger, 1997; Nielsen et al., 1997). The above methods... |

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Citation Context ...odels and techniques from signal processing and statistics have been applied to fMRI analysis. Several flavors of statistical tests have been used (Xiong et al., 1996). The t test implemented in SPM (=-=Worsley and Friston, 1995-=-), derived from the well-known general linear model (McCullagh and Nelder, 1989), and the nonparametric Kolmogorov–Smirnov test (Baker et al., 1994) are the most widespread examples. The correlation b... |

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Citation Context ...dels and techniques from signal processing and statistics have been applied to fMRI analysis. Several flavours of statistical tests have been used (Xiong et al., 1996). The t-test implemented in SPM (=-=Worsley and Friston, 1995-=-), derived from the well-known general linear model (McCullagh and Nelder, 1989), and the non-parametric Kolmogorov-Smirnov test (Baker et al., 1994) are the most widespread examples. The correlation ... |

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Citation Context ...s also been used in different contexts (Bandettini et al., 1993; Golay et al., 1997), while linear filters, like the finite input response (FIR) filter, are slowly emerging as a possible alternative (=-=Lange and Zeger, 1997-=-; Nielsen et al., 1997). The above methods focus solely (at least in a first stage) on estimating either the probability or the strength of activation on a voxel by voxel basis. In this contribution w... |

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Citation Context ...nd go to step 2 until the partition is stable. Both steps 2 and 3 decrease the within-class inertia, so that the algorithm converges in a finite number of steps. The convergence is usually very fast (=-=Bottou and Bengio, 1995-=-) and the algorithm requires to store and consider only K \Theta N distances between the data and the centres. For fMRI clustering, each data vector z j could be the time series measured in voxel j. T... |

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Citation Context ...t al., 1997, 1998; McIntyre et al., 1996; Moser et al., 1997; Scarth et al., 1996). These contributions performed a clustering directly on the fMRI time series, using the fuzzy K-means algorithm (see =-=Dav'e and Krishnapuram, 1997-=-, for a general review). Due to the high noise level in fMRI experiments, the results of clustering on the raw time series is often unsatisfactory and does not necessarily group data according to the ... |

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Citation Context ...ontains 50 values, x j(�24) to x j(25), of the cross-correlation between the fMRI time series and the activation paradigm. In one deterministic pass, the hierarchical algorithm provides a dendrogram (=-=Ripley, 1996-=-, p. 320), i.e., a binary tree representing the way each cluster is composed of clusters obtained in previous steps. The tree can be cut at several levels in order to obtain an arbitrary number of clu... |

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Citation Context ...ll as to see whether two given voxels have similar behaviour. Clustering methods have been previously used in neuroimaging for similar purposes (Baumgartner et al., 1997, 1998; McIntyre et al., 1996; =-=Moser et al., 1997-=-; Scarth et al., 1996). These contributions performed a clustering directly on the fMRI time series, using the fuzzy K-means algorithm (see Dav'e and Krishnapuram, 1997, for a general review). Due to ... |

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Citation Context ...possible to isolate zones with similar activation, as well as to see whether two given voxels have similar behavior. Clustering methods have been previously used in neuroimaging for similar purposes (=-=Baumgartner et al., 1997-=-, 1998; McIntyre et al., 1996; Moser et al., 1997; Scarth et al., 1996). These contributions performed a clustering directly on the fMRI time series, using the fuzzy K-means algorithm (see Davé and Kr... |

14 | Unsupervised learning and generalization
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Citation Context ...tual activation. We have insisted on the crucial choice of the number of clusters. Choosing the optimal number is a typical capacity control problem, and few principled approaches have been proposed (=-=Hansen and Larsen, 1996-=-). Some alternatives address this problem, eg the classical Isodata algorithm (Tou and Gonzalez, 1974, p. 97) is a popular method relying on K-means and a set of clever heuristics. Unfortunately, many... |

9 |
Comparison of Two Convolution Models for fMRI Time Series
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Citation Context ...ferent contexts (Bandettini et al., 1993; Golay et al., 1997), while linear filters, like the finite input response (FIR) filter, are slowly emerging as a possible alternative (Lange and Zeger, 1997; =-=Nielsen et al., 1997-=-). The above methods focus solely (at least in a first stage) on estimating either the probability or the strength of activation on a voxel by voxel basis. In this contribution we consider an alternat... |

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Citation Context ...et al., 1996). The t test implemented in SPM (Worsley and Friston, 1995), derived from the well-known general linear model (McCullagh and Nelder, 1989), and the nonparametric Kolmogorov–Smirnov test (=-=Baker et al., 1994-=-) are the most widespread examples. The correlation between the fMRI signal and the activation paradigm has also been used in different contexts (Bandettini et al., 1993; Golay et al., 1997), while li... |

4 |
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Citation Context ...en isolated. Finally, let us mention the possibility of the 20 presence of an inverse BOLD signal in response to an activation. To our knowledge, this effect has so far only been observed in infants (=-=Born et al., 1996-=-). Statistical aspects Let us first insist again on the fact that these experiments are of an exploratory, rather than inferential, nature. We have given guidelines as to how significance levels can b... |

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Citation Context ...hat clustering provides a general tool to perform post-processing with a number of methods. It can be applied, among other possibilities, on low-dimensional features extracted from the original data (=-=Goutte et al., 1998-=-b), statistical tests results or FIR coefficients after a linear filtering. In the following section, we present the dataset used in this study, introduce the necessary concepts and methods and insist... |

3 |
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Citation Context ... fMRI analysis. Several flavours of statistical tests have been used (Xiong et al., 1996). The t-test implemented in SPM (Worsley and Friston, 1995), derived from the well-known general linear model (=-=McCullagh and Nelder, 1989-=-), and the non-parametric Kolmogorov-Smirnov test (Baker et al., 1994) are the most widespread examples. The correlation between the fMRI signal and the activation paradigm has also been used in diffe... |

3 |
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Citation Context ...milar activation, as well as to see whether two given voxels have similar behaviour. Clustering methods have been previously used in neuroimaging for similar purposes (Baumgartner et al., 1997, 1998; =-=McIntyre et al., 1996-=-; Moser et al., 1997; Scarth et al., 1996). These contributions performed a clustering directly on the fMRI time series, using the fuzzy K-means algorithm (see Dav'e and Krishnapuram, 1997, for a gene... |

3 |
The Utility of Fuzzy Clustering in Identifying Diverse Activations in fMRI
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Citation Context ... two given voxels have similar behaviour. Clustering methods have been previously used in neuroimaging for similar purposes (Baumgartner et al., 1997, 1998; McIntyre et al., 1996; Moser et al., 1997; =-=Scarth et al., 1996-=-). These contributions performed a clustering directly on the fMRI time series, using the fuzzy K-means algorithm (see Dav'e and Krishnapuram, 1997, for a general review). Due to the high noise level ... |

2 |
Fuzzy Membership vs. Probability in Cross Correlation Based Fuzzy Clustering of fMRI Data
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Citation Context ...rnov test (Baker et al., 1994) are the most widespread examples. The correlation between the fMRI signal and the activation paradigm has also been used in different contexts (Bandettini et al., 1993; =-=Golay et al., 1997-=-), while linear filters, like the finite input response (FIR) filter, are slowly emerging as a possible alternative (Lange and Zeger, 1997; Nielsen et al., 1997). The above methods focus solely (at le... |

2 |
Statistical Models and Experimental Design. SPM course notes, chapter 3
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Citation Context ...e strategy in which we first use a loose statistical test to discard voxels that are almost surely non-activated, then cluster the remaining data. A possible strategy would be to use a simple F-test (=-=Holmes and Friston, 1997-=-, section 6.3) or other statistical tests along the same lines, and threshold at a given level. It should be noted that the traditional use of statistical testing in neuroimaging puts the emphasis on ... |

1 |
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Citation Context ...hat clustering provides a general tool to perform post-processing with a number of methods. It can be applied, among other possibilities, on low-dimensional features extracted from the original data (=-=Goutte et al., 1998-=-b), statistical tests results or FIR coefficients after a linear filtering. In the following section, we present the dataset used in this study, introduce the necessary concepts and methods and insist... |

1 |
Algorithm AS136. A K-means algorithm
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(Show Context)
Citation Context ...n of N clusters containing one point each. K-means The above considerations provide a natural introduction to one of the most widely used clustering techniques: the K-means algorithm (MacQueen, 1967; =-=Hartigan and Wong, 1979-=-). For a given number K of clusters, the within-class inertia is iteratively minimised by assigning data to the nearest center and recalculating each centre as the average of its members (minimising e... |

1 | 7(6): 1094–1101 (see also Moser et al - Imag - 1997 |