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Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
 
__NOTOC__
 
__NOTOC__
 +
= Improving fMRI Analysis using Supervised and Unsupervised Learning =
  
= fMRI Clustering =
+
One of the major goals in the analysis of fMRI data is the detection of regions of the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, supervised, and unsupervised learning methods have been employed to find these networks. In this project, we develop novel learning algorithms that enable more efficient inferences from fMRI measurements. 
  
One of the major goals in analysis of fMRI data is the detection of networks in the brain with similar functional behavior. A wide variety of methods  including hypothesis-driven statistical tests, unsupervised learning methods such as PCA and ICA, and different clustering algorithms have been employed to find these networks. This project aims to particularly study application of model-based clustering algorithms in identification of functional connectivity in the brain.
+
= Clustering for Discovering Structure in the Space of Functional Selectivity =
  
= Description =
+
We are devising clustering algorithms for discovering structure in the functional organization of the high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli; we refer to these regions as /functional units/. Currently, the conventional method for detection of these regions is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.
  
 +
We formulate a model-based clustering algorithm that simultaneously
 +
finds a set of activation profiles and their spatial maps from fMRI time courses. We validate
 +
our method on data from studies of category selectivity in the visual
 +
cortex, demonstrating good agreement with findings from prior
 +
hypothesis-driven methods. This hierarchical model enables functional group analysis
 +
independent of spatial correspondence among subjects. We have also developed a co-clustering extension of this
 +
algorithm which can simultaneously find a set of clusters of voxels and categories
 +
of stimuli in experiments with diverse sets of stimulus categories. Our model is nonparametric, learning the numbers of clusters in both domains as well as the cluster parameters.
  
'''''Generative Model for Functional Connectivity'''''
+
Fig. 1 shows the categories learned by our algorithm on a study with 8 subjects. We split trials of each image into two groups of equal size and consider
 +
each group as an independent stimulus forming a total of 138
 +
stimuli. Hence, we can examine the consistency of our stimulus categorization with respect to identical trials. Stimulus pairs
 +
corresponding to the same image are generally assigned to the same
 +
category, confirming the consistency of the resuls across
 +
trials. Category 1 corresponds to the scene images and, interestingly, also includes all images of
 +
trees. This may suggest a high level category structure that is not
 +
merely driven by low level features. Such a structure is even more
 +
evident in the 4th category where images of a tiger that has a large
 +
face join human faces. Some other animals are clustered together with human bodies in categories 2 and
 +
9. Shoes and cars, which have similar shapes, are clustered together
 +
in category 3 while tools are mainly found in category 6.
  
In the classical functional connectivity analysis, networks of interest are
 
defined based on correlation with the mean time course of a user-selected
 
`seed' region. Further, the user has to also specify a subject-specific threshold at which correlation
 
values are deemed significant. In this project, we simultaneously estimate the optimal
 
representative time courses that summarize the fMRI data well and
 
the partition of the volume into a set of disjoint regions that are best
 
explained by these representative time courses. This approach to functional connectivity analysis offers two
 
advantages. First, is removes the sensitivity of the analysis to the details
 
of the seed selection. Second, it substantially simplifies group analysis
 
by eliminating the need for the subject-specific threshold. Our experimental results indicate that
 
the functional segmentation provides a robust, anatomically meaningful
 
and consistent model for functional connectivity in fMRI.
 
  
We formulate the problem of characterizing connectivity as a partition of voxels into subsets that are well characterized by a certain number of representative hypotheses, or time courses, based on the similarity of their time courses to each hypothesis. We model the fMRI signal at each voxel as generated by a mixture of Gaussian distributions whose centers are the desired representative time courses. Using the EM algorithm to solve the corresponding model-fitting problem, we alternatively estimate the representative time courses and cluster assignments to improve our random initialization.  
+
{|
 +
|+ '''Fig 1. Categories learned from 8 subjects'''
 +
|align="center"|[[Image:Category_singlefile1.png |thumb|800px]]
 +
|}
  
''' ''Experimental Results'' '''
+
Fig. 2 shows the cluster centers, or activation profiles, for the first 13 of 25 clusters learned by our method. We see salient category structure in our profiles. For instance, system 1 shows lower responses to cars, shoes, and tools compared to other stimuli. Since the images representing these three categories in our experiment are generally smaller in terms of pixel size, this system appears selective to lower level features (note that the highest probability of activation among shoes corresponds to the largest shoe 3). System 3 and system 8 seem less responsive to faces compared to all other stimuli.
  
We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the
+
{|
baseline activation) and smoothed (8mm kernel).
+
|+ '''Fig 2. System profiles of posterior probabilities of activation for each system to different stimuli. The bar heights correspond to the posterior probability of activation.'''
 +
|align="center"|[[Image:Hdpprofs_all_1.png |thumb|800px]]
 +
|}
  
Fig. 1 shows the 2-system partition extracted in each subject independently
+
Fig. 3 shows the membership maps for the systems 2, 9, and 12, selective for bodies, faces, and scenes, respectively, which our model learns in a completely unsupervised fashion from the data. For comparison, Fig. 4 shows the significance maps found by applying the conventional confirmatory t-test to the data from the same subject. While significance maps appear to be generally larger than the extent of systems identified by our method, a close inspection reveals that system membership maps include the peak voxels for their corresponding contrasts.
of all others. It also displays the boundaries of the intrinsic system determined
 
through the traditional seed selection, showing good agreement between the two
 
partitions. Fig. 2 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.  
 
  
<table>
+
{|
<tr> <th> '''Fig 1. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 2. 3-System Parcelation. Results for all 7 subjects.'''
+
|+ '''Fig 3. Membership probability maps corresponding to systems 22, 9, and 12, selective respectively for bodies (magenta), scenes (yellow), and faces (cyan) in one subject.'''
<tr> <td align="center">
+
|align="center"|[[Image:Sys_2_9_12_subj1.png |thumb|800px]]
[[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
+
|}
[[Image:mit_fmri_clustering_parcellation2_shb5_6.png |400px]]
 
[[Image:mit_fmri_clustering_parcellation2_shb7.png |400px]]
 
<td align="center">
 
[[Image:mit_fmri_clustering_parcellation3_shb1_3.png |400px]]
 
[[Image:mit_fmri_clustering_parcellation3_shb4_5.png |400px]]
 
[[Image:mit_fmri_clustering_parcellation3_shb6.png |400px]]
 
[[Image:mit_fmri_clustering_parcellation3_shb7.png |400px]]
 
</table>
 
 
 
Fig.3 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 4 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 5, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.
 
 
 
<table>
 
<tr><th> '''Fig 3. 2-System Parcellation. Group-wise result.''' <th> '''Fig 4. Validation: Parcelation of the intrinsic system.'''
 
<tr> <td align="center">
 
[[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
 
<td align="center">
 
[[Image:mit_fmri_clustering_intrinsicsystem.png |thumb|500px]]
 
</table>
 
  
 
{|
 
{|
|+ '''Fig 5. Validation: Visual system.'''
+
|+ '''Fig 4. Map representing significance values for three contrasts: bodies-objects (magenta), faces-objects (cyan), and scenes-objects (yellow) in the same subject. Lighter colors correspond to higher significance.'''
|valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
+
|align="center"|[[Image:Sys_2_9_12_subj1.png |thumb|800px]]
 
|}
 
|}
  
''' ''Clustering Study of Domain Specificity in High Level Visual Cortex'' '''
+
'''''Earlier work'''''
 
 
As a more specific application of model-based clustering algorithms, we are devising clustering algorithms for detection of functional connectivity in high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli. Currently, the conventional method for detection of these methods is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.
 
 
 
Introducing the notion of space of activation
 
profiles, we construct a representation of the data which explicitly
 
parametrizes all interesting patterns of activation. Mapping the data into
 
this space, we formulate a model-based clustering algorithm that simultaneously
 
finds a set of activation profiles and their spatial maps. We validate
 
our method on the data from studies of category selectivity in visual
 
cortex, demonstrating good agreement with the findings based on prior
 
hypothesis-driven methods. This model enables functional group analysis
 
independent of spatial correspondence among subjects. We are currently working on a co-clustering extension of this
 
algorithm which can simultaneously find a set of clusters of voxels and meta-categories
 
of stimuli in experiments with diverse sets of stimulus categories.
 
  
Fig. 6 compares the map of voxels assigned to a face-selective profile by our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.
+
Fig. 5 compares the map of voxels assigned to a face-selective profile by an earlier version of our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.
  
 
{|
 
{|
|+ '''Fig 6. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
+
|+ '''Fig 5. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.'''
 
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
 
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
 
|}
 
|}
  
 +
'''''Hierarchical Model for Exploratory fMRI Analysis without Spatial Normalization'''''
  
''' ''Comparison of Data-Driven Analysis Methods for Identification of Functional Connectivity in fMRI'' '''
+
Building on the work on the clustering model for the domain specificity, we develop a hierarchical exploratory method for simultaneous parcellation of multisub ect fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both inter-subject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to fit the model to the data. The resulting algorithm finds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several subjects. We demonstrate the application of our method on the same visual fMRI study as before. Fig. 6 shows the scene-selective parcel in 2 different subjects. Parcel-level spatial correspondence is evident in the figure between the subjects.
 +
 
 +
<table>
 +
<tr> <th> '''Fig 6. The map of the scene selective parcels in two different subjects. The rough location of the scene-selective areas PPA and TOS, identified by the expert, are shown on the maps by yellow and green circles, respectively.'''  
 +
<tr>
 +
<td align="center">
 +
[[Image:mit_fmriclustering_hierarchicalppamapsubject1.jpg |650px]]
 +
<td align="center">
 +
[[Image:mit_fmriclustering_hierarchicalppamapsubject2.jpg |650px]]
 +
</table>
  
Although ICA and clustering rely on very different assumptions on the underlying distributions, they produce surprisingly similar results for signals with large variation. Our main goal is to evaluate and compare the performance of ICA and clustering based on Gaussian mixture model (GMM) for identification of functional connectivity. Using the synthetic data with artificial activations and artifacts under various levels of length of the time course and signal-to-noise ratio of the data, we compare both spatial maps and their associated time courses estimated by ICA and GMM to each other and to the ground truth. We choose the number of sources via the model selection scheme, and compare all of the resulting components of GMM and ICA, not just the task-related components, after we match them component-wise using the Hungarian algorithm. This comparison scheme is verified in a high level visual cortex fMRI study. We find that ICA requires a smaller number of total components to extract the task-related components, but also needs a large number of total components to describe the entire data. We are currently applying ICA and clustering methods to connectivity analysis of schizophrenia patients.
 
  
 
= Key Investigators =
 
= Key Investigators =
  
* MIT Algorithms: Danial Lashkari, Y. Bryce Kim, Archana Venkataraman, Polina Golland, Nancy Kanwisher.
+
* MIT: Danial Lashkari, Archana Venkataraman, Ramesh Sridharan, Ed Vul, Nancy Kanwisher, Polina Golland.
* Harvard DBP 2: J. Oh, Marek Kubicki.
+
* Harvard: J. Oh, Marek Kubicki, Carl-Fredrik Westin.
  
 
= Publications =
 
= Publications =
  
''In print''
+
[http://www.na-mic.org/publications/pages/display?search=Projects%3AfMRIClustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database on fMRI clustering]
 
 
* [http://www.na-mic.org/pages/Special:Publications?text=fMRI+Clustering&submit=Search&words=all&title=checked&keywords=checked&authors=checked&abstract=checked&sponsors=checked&searchbytag=checked| NA-MIC Publications Database]
 
 
 
''In press''
 
 
 
  
* D. Lashkari, N. Kanwisher, P. Golland. Discovering Structure in the Space of Activation Profiles in fMRI. Accepted to MICCAI 2008.
+
  Project Week Results: [[2008_Summer_Project_Week:fMRIconnectivity|June 2008]]
  
 
[[Category:fMRI]]
 
[[Category:fMRI]]

Latest revision as of 20:06, 28 November 2012

Home < Projects:fMRIClustering
Back to NA-MIC Collaborations, MIT Algorithms

Improving fMRI Analysis using Supervised and Unsupervised Learning

One of the major goals in the analysis of fMRI data is the detection of regions of the brain with similar functional behavior. A wide variety of methods including hypothesis-driven statistical tests, supervised, and unsupervised learning methods have been employed to find these networks. In this project, we develop novel learning algorithms that enable more efficient inferences from fMRI measurements.

Clustering for Discovering Structure in the Space of Functional Selectivity

We are devising clustering algorithms for discovering structure in the functional organization of the high-level visual cortex. It is suggested that there are regions in the visual cortex with high selectivity to certain categories of visual stimuli; we refer to these regions as /functional units/. Currently, the conventional method for detection of these regions is based on statistical tests comparing response of each voxel in the brain to different visual categories to see if it shows considerably higher activation to one category. For example, the well-known FFA (Fusiform Face Area) is the set of voxels which show high activation to face images. We use a model-based clustering approach to the analysis of this type of data as a means to make this analysis automatic and further discover new structures in the high-level visual cortex.

We formulate a model-based clustering algorithm that simultaneously finds a set of activation profiles and their spatial maps from fMRI time courses. We validate our method on data from studies of category selectivity in the visual cortex, demonstrating good agreement with findings from prior hypothesis-driven methods. This hierarchical model enables functional group analysis independent of spatial correspondence among subjects. We have also developed a co-clustering extension of this algorithm which can simultaneously find a set of clusters of voxels and categories of stimuli in experiments with diverse sets of stimulus categories. Our model is nonparametric, learning the numbers of clusters in both domains as well as the cluster parameters.

Fig. 1 shows the categories learned by our algorithm on a study with 8 subjects. We split trials of each image into two groups of equal size and consider each group as an independent stimulus forming a total of 138 stimuli. Hence, we can examine the consistency of our stimulus categorization with respect to identical trials. Stimulus pairs corresponding to the same image are generally assigned to the same category, confirming the consistency of the resuls across trials. Category 1 corresponds to the scene images and, interestingly, also includes all images of trees. This may suggest a high level category structure that is not merely driven by low level features. Such a structure is even more evident in the 4th category where images of a tiger that has a large face join human faces. Some other animals are clustered together with human bodies in categories 2 and 9. Shoes and cars, which have similar shapes, are clustered together in category 3 while tools are mainly found in category 6.


Fig 1. Categories learned from 8 subjects
Category singlefile1.png

Fig. 2 shows the cluster centers, or activation profiles, for the first 13 of 25 clusters learned by our method. We see salient category structure in our profiles. For instance, system 1 shows lower responses to cars, shoes, and tools compared to other stimuli. Since the images representing these three categories in our experiment are generally smaller in terms of pixel size, this system appears selective to lower level features (note that the highest probability of activation among shoes corresponds to the largest shoe 3). System 3 and system 8 seem less responsive to faces compared to all other stimuli.

Fig 2. System profiles of posterior probabilities of activation for each system to different stimuli. The bar heights correspond to the posterior probability of activation.
Hdpprofs all 1.png

Fig. 3 shows the membership maps for the systems 2, 9, and 12, selective for bodies, faces, and scenes, respectively, which our model learns in a completely unsupervised fashion from the data. For comparison, Fig. 4 shows the significance maps found by applying the conventional confirmatory t-test to the data from the same subject. While significance maps appear to be generally larger than the extent of systems identified by our method, a close inspection reveals that system membership maps include the peak voxels for their corresponding contrasts.

Fig 3. Membership probability maps corresponding to systems 22, 9, and 12, selective respectively for bodies (magenta), scenes (yellow), and faces (cyan) in one subject.
Sys 2 9 12 subj1.png
Fig 4. Map representing significance values for three contrasts: bodies-objects (magenta), faces-objects (cyan), and scenes-objects (yellow) in the same subject. Lighter colors correspond to higher significance.
Sys 2 9 12 subj1.png

Earlier work

Fig. 5 compares the map of voxels assigned to a face-selective profile by an earlier version of our algorithm with the t-test's map of voxels with statistically significant (p<0.0001) response to faces when compared with object stimuli. Note that in contrast with the hypothesis testing method, we don't specify the existence of a face-selective region in our algorithm and the algorithm automatically discovers such a profile of activation in the data.

Fig 5. Spatial maps of the face selective regions found by the statistical test (red) and our mixture model (dark blue). Maps are presented in alternating rows for comparison. Visually responsive mask of voxels used in our experiment is illustrated in yellow and light blue.
Mit fmri clustering mapffacompare.PNG

Hierarchical Model for Exploratory fMRI Analysis without Spatial Normalization

Building on the work on the clustering model for the domain specificity, we develop a hierarchical exploratory method for simultaneous parcellation of multisub ect fMRI data into functionally coherent areas. The method is based on a solely functional representation of the fMRI data and a hierarchical probabilistic model that accounts for both inter-subject and intra-subject forms of variability in fMRI response. We employ a Variational Bayes approximation to fit the model to the data. The resulting algorithm finds a functional parcellation of the individual brains along with a set of population-level clusters, establishing correspondence between these two levels. The model eliminates the need for spatial normalization while still enabling us to fuse data from several subjects. We demonstrate the application of our method on the same visual fMRI study as before. Fig. 6 shows the scene-selective parcel in 2 different subjects. Parcel-level spatial correspondence is evident in the figure between the subjects.

Fig 6. The map of the scene selective parcels in two different subjects. The rough location of the scene-selective areas PPA and TOS, identified by the expert, are shown on the maps by yellow and green circles, respectively.

Mit fmriclustering hierarchicalppamapsubject1.jpg

Mit fmriclustering hierarchicalppamapsubject2.jpg


Key Investigators

  • MIT: Danial Lashkari, Archana Venkataraman, Ramesh Sridharan, Ed Vul, Nancy Kanwisher, Polina Golland.
  • Harvard: J. Oh, Marek Kubicki, Carl-Fredrik Westin.

Publications

NA-MIC Publications Database on fMRI clustering

Project Week Results: June 2008