Measuring the congruence of fuzzy partitions in fuzzy c -means clustering

Suleman, Abdul

doi:10.1016/j.asoc.2016.06.037

“…Our findings are in line with previous studies that compared several CV indices on different simulated datasets and found that CV indices may fail to indicate the true number of clusters in noisy data that have high number of classes (Suleman 2017;Wang & Zhang 2007;Zhou et al 2014a). It might be the case their effectiveness might even be lesser given the complex nature of noise in MRI images with significant correlations between voxels (Gudbjartsson & Patz 1995;Parrish et al 2000).…”

Section: Discussionsupporting

confidence: 92%

“…Specifically, the following 22 datasets were generated: (i) a single-cluster dataset (noted 1cluster; e.g. the 'null' case, see (Tibshirani et al 2001)) with highly similar voxels (c opt = 1; Supplementary Figure 2a); (ii) a dataset without any obvious structure (noted n-cluster data; c opt near to n; Supplementary Figure 2b), see (Suleman 2017); (iii) ten datasets with known number of clusters c opt varying from 2 to 11 and low noise level ( = 1, see illustration in Supplementary Figure 2c with c opt = 3); (iv) ten datasets with a known number of clusters c opt varying from 2 to 11 and high noise level ( = 4, see illustration in Supplementary Figure 2d with c opt = 3).…”

Section: Simulated Datamentioning

confidence: 99%

Peer Review #1 of "Clustering of fMRI data: the elusive optimal number of clusters (v0.1)"

Auer¹

2018

0

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Model-free methods are widely used for the processing of brain fMRI data collected under natural stimulations, sleep, or rest. Among them is the popular fuzzy c-mean algorithm, commonly combined with cluster validity (CV) indices to identify the 'true' number of clusters (components), in an unsupervised way. CV indices may however reveal different optimal c-partitions for the same fMRI data, and their effectiveness can be hindered by the high data dimensionality, the limited signal-to-noise ratio, the small proportion of relevant voxels, and the presence of artefacts or outliers. Here, the author investigated the behaviour of seven robust CV indices. A new CV index that incorporates both compactness and separation measures is also introduced. Using both artificial and real fMRI data, the findings highlight the importance of looking at different compactness and separation measures, defined here as building blocks of CV indices, to depict a full description of the data structure, in particular when no agreement is found between CV indices. Overall, for fMRI, it makes sense to relax the assumption that only one unique c-partition exists, and appreciate that different c-partitions (with different optimal numbers of clusters) can be useful explanations of the data, given the hierarchical organization of many brain networks.

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“…1 Two alternative objective functions are provided in [22] III. VALIDITY MEASURE The original version of our proposal is given in [19], where the reconstruction ability of the Bezdek [1] fuzzy c-means (FCM) algorithm is tested. We do not present its functional formula here, for reasons that soon will become clear.…”

Section: Archetypal Analysismentioning

confidence: 99%

“…Our proposal is analytical, and relies on information-theoretic principles. It is an adaptation of an AIC-like measure, proposed in [19], to the specifics of AA.…”

Section: Introductionmentioning

confidence: 99%

Validation of archetypal analysis

Suleman

¹

2017

2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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We use an information-theoretic criterion to assess the goodness-of-fit of the output of archetypal analysis (AA), also intended as a fuzzy clustering tool. It is an adaptation of an existing AIC-like measure to the specifics of AA. We test its effectiveness using artificial data and some data sets arising from real life problems. In most cases, the results achieved are similar to those provided by an external similarity index. The average reconstruction accuracy is about 93%.

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“…Multidimensional 292 scaling (MDS) tools were used to visualise the simulated c clusters.293 Specifically, the following 22 datasets were generated: (i) a single-cluster dataset (noted 1-294 cluster; e.g. the 'null' case, see(Tibshirani et al 2001)) with highly similar voxels (c opt = 1;295Supplementary Figure 2a); (ii) a dataset without any obvious structure (noted n-cluster data; c opt 296 near to n;Supplementary Figure 2b), see(Suleman 2017); (iii) ten datasets with known number 297 of clusters c opt varying from 2 to 11 and low noise level ( = 1, see illustration in Supplementary 298Figure 2cwith c opt = 3); (iv) ten datasets with a known number of clusters c opt varying from 2 to 299 11 and high noise level ( = 4, see illustration inSupplementary Figure 2dwith c opt = 3).…”

mentioning

confidence: 99%

Peer Review #1 of "Clustering of fMRI data: the elusive optimal number of clusters (v0.2)"

Auer¹

2018

0

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Model-free methods are widely used for the processing of brain fMRI data collected under natural stimulations, sleep, or rest. Among them is the popular fuzzy c-mean algorithm, commonly combined with cluster validity (CV) indices to identify the 'true' number of clusters (components), in an unsupervised way. CV indices may however reveal different optimal c-partitions for the same fMRI data, and their effectiveness can be hindered by the high data dimensionality, the limited signal-to-noise ratio, the small proportion of relevant voxels, and the presence of artefacts or outliers. Here, the author investigated the behaviour of seven robust CV indices. A new CV index that incorporates both compactness and separation measures is also introduced. Using both artificial and real fMRI data, the findings highlight the importance of looking at different compactness and separation measures, defined here as building blocks of CV indices, to depict a full description of the data structure, in particular when no agreement is found between CV indices. Overall, for fMRI, it makes sense to relax the assumption that only one unique c-partition exists, and appreciate that different c-partitions (with different optimal numbers of clusters) can be useful explanations of the data, given the hierarchical organization of many brain networks.PeerJ reviewing PDF | (

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Measuring the congruence of fuzzy partitions in fuzzy c -means clustering

Cited by 16 publications

References 41 publications

Peer Review #1 of "Clustering of fMRI data: the elusive optimal number of clusters (v0.1)"

Peer Review #1 of "Clustering of fMRI data: the elusive optimal number of clusters (v0.1)"

Validation of archetypal analysis

Peer Review #1 of "Clustering of fMRI data: the elusive optimal number of clusters (v0.2)"

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