Clustering of fMRI data: the elusive optimal number of clusters.
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ABSTRACT:
SUBMITTER: Seghier ML
PROVIDER: S-EPMC6173948 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Functional magnetic resonance imaging (fMRI) data have become increasingly available and are useful for describing functional connectivity (FC), the relatedness of neuronal activity in regions of the brain. This FC of the brain provides insight into certain neurodegenerative diseases and psychiatric disorders, and thus is of clinical importance. To help inform physicians regarding patient diagnoses, unsupervised clustering of subjects based on FC is desired, allowing the data to inform us of groupings of patients based on shared features of connectivity. Since heterogeneity in FC is present even between patients within the same group, it is important to allow subject-level differences in connectivity, while still pooling information across patients within each group to describe group-level FC. To this end, we propose a random covariance clustering model (RCCM) to concurrently cluster subjects based on their FC networks, estimate the unique FC networks of each subject, and to infer shared network features. Although current methods exist for estimating FC or clustering subjects using fMRI data, our novel contribution is to cluster or group subjects based on similar FC of the brain while simultaneously providing group- and subject-level FC network estimates. The competitive performance of RCCM relative to other methods is demonstrated through simulations in various settings, achieving both improved clustering of subjects and estimation of FC networks. Utility of the proposed method is demonstrated with application to a resting-state fMRI data set collected on 43 healthy controls and 61 participants diagnosed with schizophrenia.
| S-EPMC9293048 | biostudies-literature
Project description:Four of the most common limitations of the many available clustering methods are: i) the lack of a proper strategy to deal with outliers; ii) the need for a good a priori estimate of the number of clusters to obtain reasonable results; iii) the lack of a method able to detect when partitioning of a specific data set is not appropriate; and iv) the dependence of the result on the initialization. Here we propose Cross-clustering (CC), a partial clustering algorithm that overcomes these four limitations by combining the principles of two well established hierarchical clustering algorithms: Ward's minimum variance and Complete-linkage. We validated CC by comparing it with a number of existing clustering methods, including Ward's and Complete-linkage. We show on both simulated and real datasets, that CC performs better than the other methods in terms of: the identification of the correct number of clusters, the identification of outliers, and the determination of real cluster memberships. We used CC to cluster samples in order to identify disease subtypes, and on gene profiles, in order to determine groups of genes with the same behavior. Results obtained on a non-biological dataset show that the method is general enough to be successfully used in such diverse applications. The algorithm has been implemented in the statistical language R and is freely available from the CRAN contributed packages repository.
| S-EPMC4807765 | biostudies-literature
Project description:BackgroundFunctional brain imaging studies have indicated that distinct anatomical brain regions can show coherent spontaneous neuronal activity during rest. Regions that show such correlated behavior are said to form resting-state networks (RSNs). RSNs have been investigated using seed-dependent functional connectivity maps and by using a number of model-free methods. However, examining RSNs across a group of subjects is still a complex task and often involves human input in selecting meaningful networks.Methodology/principal findingsWe report on a voxel based model-free normalized cut graph clustering approach with whole brain coverage for group analysis of resting-state data, in which the number of RSNs is computed as an optimal clustering fit of the data. Inter-voxel correlations of time-series are grouped at the individual level and the consistency of the resulting networks across subjects is clustered at the group level, defining the group RSNs. We scanned a group of 26 subjects at rest with a fast BOLD sensitive fMRI scanning protocol on a 3 Tesla MR scanner.Conclusions/significanceAn optimal group clustering fit revealed 7 RSNs. The 7 RSNs included motor/visual, auditory and attention networks and the frequently reported default mode network. The found RSNs showed large overlap with recently reported resting-state results and support the idea of the formation of spatially distinct RSNs during rest in the human brain.
| S-EPMC2291558 | biostudies-literature
Project description:BACKGROUND: Previous studies using hierarchical clustering approach to analyze resting-state fMRI data were limited to a few slices or regions-of-interest (ROIs) after substantial data reduction. PURPOSE: To develop a framework that can perform voxel-wise hierarchical clustering of whole-brain resting-state fMRI data from a group of subjects. MATERIALS AND METHODS: Resting-state fMRI measurements were conducted for 86 adult subjects using a single-shot echo-planar imaging (EPI) technique. After pre-processing and co-registration to a standard template, pair-wise cross-correlation coefficients (CC) were calculated for all voxels inside the brain and translated into absolute Pearson's distances after imposing a threshold CC?0.3. The group averages of the Pearson's distances were then used to perform hierarchical clustering with the developed framework, which entails gray matter masking and an iterative scheme to analyze the dendrogram. RESULTS: With the hierarchical clustering framework, we identified most of the functional connectivity networks reported previously in the literature, such as the motor, sensory, visual, memory, and the default-mode functional networks (DMN). Furthermore, the DMN and visual system were split into their corresponding hierarchical sub-networks. CONCLUSION: It is feasible to use the proposed hierarchical clustering scheme for voxel-wise analysis of whole-brain resting-state fMRI data. The hierarchical clustering result not only confirmed generally the finding in functional connectivity networks identified previously using other data processing techniques, such as ICA, but also revealed directly the hierarchical structure within the functional connectivity networks.
| S-EPMC3799854 | biostudies-literature
Project description:BackgroundArray comparative genomic hybridization (aCGH) to detect copy number variants (CNVs) in mammalian genomes has led to a growing awareness of the potential importance of this category of sequence variation as a cause of phenotypic variation. Yet there are large discrepancies between studies, so that the extent of the genome affected by CNVs is unknown. We combined molecular and aCGH analyses of CNVs in inbred mouse strains to investigate this question.Principal findingsUsing a 2.1 million probe array we identified 1,477 deletions and 499 gains in 7 inbred mouse strains. Molecular characterization indicated that approximately one third of the CNVs detected by the array were false positives and we estimate the false negative rate to be more than 50%. We show that low concordance between studies is largely due to the molecular nature of CNVs, many of which consist of a series of smaller deletions and gains interspersed by regions where the DNA copy number is normal.ConclusionsOur results indicate that CNVs detected by arrays may be the coincidental co-localization of smaller CNVs, whose presence is more likely to perturb an aCGH hybridization profile than the effect of an isolated, small, copy number alteration. Our findings help explain the hitherto unexplored discrepancies between array-based studies of copy number variation in the mouse genome.
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Project description:Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point processes and characterizing a Bayes clusterer that minimizes the number of misclustered points. The Bayes clusterer is analogous to the Bayes classifier. Whereas determining a Bayes classifier requires full knowledge of the feature-label distribution, deriving a Bayes clusterer requires full knowledge of the point process. When uncertain of the point process, one would like to find a robust clusterer that is optimal over the uncertainty, just as one may find optimal robust classifiers with uncertain feature-label distributions. Herein, we derive an optimal robust clusterer by first finding an effective random point process that incorporates all randomness within its own probabilistic structure and from which a Bayes clusterer can be derived that provides an optimal robust clusterer relative to the uncertainty. This is analogous to the use of effective class-conditional distributions in robust classification. After evaluating the performance of robust clusterers in synthetic mixtures of Gaussians models, we apply the framework to granular imaging, where we make use of the asymptotic granulometric moment theory for granular images to relate robust clustering theory to the application.
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Project description:This paper presents a novel multilook SAR image segmentation algorithm with an unknown number of clusters. Firstly, the marginal probability distribution for a given SAR image is defined by a Gamma mixture model (GaMM), in which the number of components corresponds to the number of homogeneous regions needed to segment and the spatial relationship among neighboring pixels is characterized by a Markov Random Field (MRF) defined by the weighting coefficients of components in GaMM. During the algorithm iteration procedure, the number of clusters is gradually reduced by merging two components until they are equal to one. For each fixed number of clusters, the parameters of GaMM are estimated and the optimal segmentation result corresponding to the number is obtained by maximizing the marginal probability. Finally, the number of clusters with minimum global energy defined as the negative logarithm of marginal probability is indicated as the expected number of clusters with the homogeneous regions needed to be segmented, and the corresponding segmentation result is considered as the final optimal one. The experimental results from the proposed and comparing algorithms for simulated and real multilook SAR images show that the proposed algorithm can find the real number of clusters and obtain more accurate segmentation results simultaneously.
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Project description:BackgroundClustering techniques are routinely used in gene expression data analysis to organize the massive data. Clustering techniques arrange a large number of genes or assays into a few clusters while maximizing the intra-cluster similarity and inter-cluster separation. While clustering of genes facilitates learning the functions of un-characterized genes using their association with known genes, clustering of assays reveals the disease stages and subtypes. Many clustering algorithms require the user to specify the number of clusters a priori. A wrong specification of number of clusters generally leads to either failure to detect novel clusters (disease subtypes) or unnecessary splitting of natural clusters.ResultsWe have developed a novel method to find the number of clusters in gene expression data. Our procedure evaluates different partitions (each with different number of clusters) from the clustering algorithm and finds the partition that best describes the data. In contrast to the existing methods that evaluate the partitions independently, our procedure considers the dynamic rearrangement of cluster members when a new cluster is added. Partition quality is measured based on a new index called Net InFormation Transfer Index (NIFTI) that measures the information change when an additional cluster is introduced. Information content of a partition increases when clusters do not intersect and decreases if they are not clearly separated. A partition with the highest Total Information Content (TIC) is selected as the optimal one. We illustrate our method using four publicly available microarray datasets.ConclusionIn all four case studies, the proposed method correctly identified the number of clusters and performs better than other well known methods. Our method also showed invariance to the clustering techniques.
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Project description:Identifying co-expressed gene clusters can provide evidence for genetic or physical interactions. Thus, co-expression clustering is a routine step in large-scale analyses of gene expression data. We show that commonly used clustering methods produce results that substantially disagree and that do not match the biological expectations of co-expressed gene clusters. We present clust, a method that solves these problems by extracting clusters matching the biological expectations of co-expressed genes and outperforms widely used methods. Additionally, clust can simultaneously cluster multiple datasets, enabling users to leverage the large quantity of public expression data for novel comparative analysis. Clust is available at https://github.com/BaselAbujamous/clust .
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Project description:In cluster-randomized trials, investigators randomize clusters of individuals such as households, medical practices, schools or classrooms despite the unit of interest are the individuals. It results in the loss of efficiency in terms of the estimation of the unknown parameters as well as the power of the test for testing the treatment effects. To recoup this efficiency loss, some studies pair similar clusters and randomize treatment within pairs. However, the clusters within a treatment arm might be heterogeneous in nature. In this article, we propose a locally optimal design that accounts the clusters heterogeneity and optimally allocates the subjects within each cluster. To address the dependency of design on the unknown parameters, we also discuss Bayesian optimal designs. Performances of proposed designs are investigated numerically through some data examples.
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