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Counting Temporal Classes in a RS-fMRI Data Exploring Volumes Organization

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Alberto Arturo Vergani at University of Pavia
Alberto Arturo Vergani
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Abstract

The poster represents a RS-fMRI analysis of one subject by using fuzzy c-means clustering algorithm. The goal was to establish the optimal number of temporal classes, that range from 2 to 5.
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Counting Temporal Classes in a RS- fMRI Data
Exploring Volumes Organization
Alberto Arturo Vergani
Middlesex University London, Department of Computer Science
a.vergani@mdc.ac.uk
Highlights
•The RS-fMRI data is about one subject (Female, 31 years-old, healthy, [3]).
•Fuzzy C-Means clustering algorithm [1] is evaluated by the Fuzzy Partition Coefficient [4]
•There is the assumption that a fMRI sequence of volumes has classes.
•The number of optimal temporal classes is within 2-5 range.
Key-words
•RS-fMRI is a functional passive paradigm in which subject does nothing in the scanner [2].
•Temporal clustering is the partition of the fMRI volumes in classes [5].
•The fMRI temporal class is a set of clustered volumes.
•Fuzzy C-Means clustering algorithm finds classes by using many-values logic framework [1].
Some formalities ...
The FCM minimizes the following objective function Jm:
Jm=
N
X
i=1
C
X
j=1
um
ij ||xi−cj||2with 1 ≤m≤ ∞ (1)
where uij and cjare:
uij =1
PC
k=1 ||xi−cj||
||xi−ck||
2
m−1
and cj=PN
i=1 um
ij ·xi
PN
i=1 um
ij
(2)
The Functional Connectivity is computed with CCP earson =COV (X,Y )
SD(X)·SD(Y)
References
[1] James C Bezdek, Robert Ehrlich, and William Full. Fcm: The fuzzy c-means clustering algo-
rithm. Computers & Geosciences, 10(2-3):191–203, 1984.
[2] BB Biswal, M Mennes, X Zuo, S Gohel, C Kelly, Steve M Smith, Christian F Beckman, J S
Adelstein, RL Buckner, S Colcombe, et al. Toward discovery science of human brain function.
Proceedings of the National Academy of Sciences, 107(10):4734–4739, 2010.
[3] David N Kennedy, Christian Haselgrove, Jon Riehl, Nina Preuss, and Robert Buccigrossi. The
nitrc image repository. Neuroimage, 124:1069–1073, 2016.
[4] E Trauwaert. On the meaning of dunn’s partition coefficient for fuzzy clusters. Fuzzy sets and
systems, 25(2):217–242, 1988.
[5] AA Vergani, S Martinelli, and E Binaghi. Clustering functional mri patterns with fuzzy and
competitive algorithms. In International Symposium Computational Modeling of Objects Rep-
resented in Images, pages 129–144. Springer, 2018.
ResearchGate has not been able to resolve any citations for this publication.
FCM—the Fuzzy C-Means clustering-algorithm
Article
Full-text available
  • Dec 1984
  • COMPUT GEOSCI-UK
This paper transmits a FORTRAN-IV coding of the fuzzy c-means (FCM) clustering program. The FCM program is applicable to a wide variety of geostatistical data analysis problems. This program generates fuzzy partitions and prototypes for any set of numerical data. These partitions are useful for corroborating known substructures or suggesting substructure in unexplored data. The clustering criterion used to aggregate subsets is a generalized least-squares objective function. Features of this program include a choice of three norms (Euclidean, Diagonal, or Mahalonobis), an adjustable weighting factor that essentially controls sensitivity to noise, acceptance of variable numbers of clusters, and outputs that include several measures of cluster validity.
View
Toward discovery science of human brain function
Article
Full-text available
  • Mar 2010
  • P NATL ACAD SCI USA
Although it is being successfully implemented for exploration of the genome, discovery science has eluded the functional neuroimaging community. The core challenge remains the development of common paradigms for interrogating the myriad functional systems in the brain without the constraints of a priori hypotheses. Resting-state functional MRI (R-fMRI) constitutes a candidate approach capable of addressing this challenge. Imaging the brain during rest reveals large-amplitude spontaneous low-frequency (<0.1 Hz) fluctuations in the fMRI signal that are temporally correlated across functionally related areas. Referred to as functional connectivity, these correlations yield detailed maps of complex neural systems, collectively constituting an individual's "functional connectome." Reproducibility across datasets and individuals suggests the functional connectome has a common architecture, yet each individual's functional connectome exhibits unique features, with stable, meaningful interindividual differences in connectivity patterns and strengths. Comprehensive mapping of the functional connectome, and its subsequent exploitation to discern genetic influences and brain-behavior relationships, will require multicenter collaborative datasets. Here we initiate this endeavor by gathering R-fMRI data from 1,414 volunteers collected independently at 35 international centers. We demonstrate a universal architecture of positive and negative functional connections, as well as consistent loci of inter-individual variability. Age and sex emerged as significant determinants. These results demonstrate that independent R-fMRI datasets can be aggregated and shared. High-throughput R-fMRI can provide quantitative phenotypes for molecular genetic studies and biomarkers of developmental and pathological processes in the brain. To initiate discovery science of brain function, the 1000 Functional Connectomes Project dataset is freely accessible at www.nitrc.org/projects/fcon_1000/.
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The NITRC image repository
Article
  • Jun 2015
  • NEUROIMAGE
The Neuroimaging Informatics Tools and Resources Clearinghouse (NITRC - www.nitrc.org) suite of services include a resources registry, image repository and a cloud computational environment to meet the needs of the neuroimaging researcher. NITRC provides image-sharing functionality through both the NITRC Resource Registry (NITRC-R), where bulk data files can be released through the file release system (FRS), and the NITRC Image Repository (NITRC-IR), a XNAT-based image data management system. Currently hosting 14 projects, 6845 subjects, and 8285 MRI imaging sessions, NITRC-IR provides a large array of structural, diffusion and resting state MRI data. Designed to be flexible about management of data access policy, NITRC provides a simple, free, NIH-funded service to support resource sharing in general, and image sharing in particular. Copyright © 2015. Published by Elsevier Inc.
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On the meaning of Dunn's partition coefficient for fuzzy clusters
Article
  • Feb 1988
  • FUZZY SET SYST
A constantly recurring problem in cluster analysis is that of evaluating the number of clusters that are present in a data set. The development of fuzzy clustering has brought no definite answer to this question, although some new means have been provided offering new ways to tackle this problem.One of the promising approaches was Dunn's partition coefficient Fk(U) that has been shown to vary between 1, for hard clusters, and 1/k, for completely fuzzy sets of objects: hence the idea that Fk(U) expresses a measure of how far a given fuzzy partition is from a hard one. Assuming moreover that an optimal partition in an optimal number of clusters will have a ‘harder’ look than any other partition, Fk(U) could be considered as a cluster validity index.That this procedure is unjustified is shown by the study of the (D, F)-diagram in which, by analogy to the partition coefficient F, a fuzziness coefficient D is defined.An important result of this study is that a higher Fk(U) value does not always correspond to a better allocation than a partition with a lower value: this observation contradicts the role of the partition coefficient as cluster validity measurement.These results are emply confirmed by various artificial and classical numerical examples.
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Clustering functional mri patterns with fuzzy and competitive algorithms
  • Jan 2018
  • 129-144
  • Aa Vergani
  • E Martinelli
  • Binaghi
AA Vergani, S Martinelli, and E Binaghi. Clustering functional mri patterns with fuzzy and competitive algorithms. In International Symposium Computational Modeling of Objects Represented in Images, pages 129-144. Springer, 2018.