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  Back to [[NA-MIC_Internal_Collaborations:fMRIAnalysis|NA-MIC Collaborations]], [[Algorithm:MIT|MIT Algorithms]]
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__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. 
  
In the classical functional connectivity analysis, networks of interest are
+
= Clustering for Discovering Structure in the Space of Functional Selectivity =
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.
 
  
Currently, we are investigating the application of such clustering algorithms in detection of functional connectivity in high-level  
+
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.
  
= Description =
+
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.
  
We formulate the problem of characterizing connectivity as a partition of voxels into subsets
 
Spatial Activation Patterns in fMRI that are well characterized by Ns representative hypotheses, or time courses,
 
m1; : : : mNs based on the similarity of their time courses to each hypothesis.
 
We model the fMRI signal Y at each voxel as generated by the mixture pY(y) =
 
PNs
 
s=1 �spYjS(yjs) over Ns conditional likelihoods pYjS(yjs) [15]. �s is the prior
 
probability that a voxel belongs to system s 2 f1; : : : ;Nsg. Following a commonly
 
used approach in fMRI analysis, we model the class-conditional densities
 
as normal distributions centered around the system mean time course, i.e.,
 
pYjS(yjs) = N(y;ms;�s). The high dimensionality of the fMRI data makes modeling
 
a full covariance matrix impractical. Instead, most methods either limit the
 
modeling to estimating variance elements, or model the time course dynamics as
 
an auto-regressive (AR) process. At this stage, we take the simpler approach of
 
modeling variance and note that the mixture model estimation can be straightforwardly
 
extended to include an AR model. Unlike separate dimensionality reduction
 
procedures, this approach follows closely the notions of functional similarity
 
used by the detection methods in fMRI. In other words, we keep the notion of
 
co-activation consistent with the standard analysis and instead rede�ne how the
 
co-activation patterns are represented and extracted from images.
 
This unsupervised technique generalizes
 
connectivity analysis to situations where candidate seeds are difficult to
 
identify reliably or are unknown.
 
  
 +
{|
 +
|+ '''Fig 1. Categories learned from 8 subjects'''
 +
|align="center"|[[Image:Category_singlefile1.png |thumb|800px]]
 +
|}
  
 
+
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.
Recently, we have applied this method to the cingulum bundle, as shown in the following images:
 
  
 
{|
 
{|
|+ '''Fig 1. 2-System Parcellation'''
+
|+ '''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.'''
|valign="top"|[[Image:Case24-coronal-tensors-edit.png |thumb|250px|Detailed View of the Cingulum Bundle Anchor Tract]]
+
|align="center"|[[Image:Hdpprofs_all_1.png |thumb|800px]]
|valign="top"|[[Image:Case25-sagstream-tensors-edit.png|thumb|250px|Streamline Comparison]]
 
|-
 
|valign="top"|[[Image:Case26-anterior.png |thumb|250px|Anterior View of the Cingulum Bundle Anchor Tract]]
 
|valign="top"|[[Image:Case26-posterior.png|thumb|250px|Posterior View of the Cingulum Bundle Anchor Tract]]
 
 
|}
 
|}
  
''Fiber Bundle Segmentation''
+
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.'''
 +
|align="center"|[[Image:Sys_2_9_12_subj1.png |thumb|800px]]
 +
|}
  
 
{|
 
{|
|+ '''Fig 2. Cingulum Bundle Volumetric Fiber Bundles Segmentation Results'''
+
|+ '''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:ResultZoomedOut.png |thumb|250px|Zoomed Out View]]
+
|align="center"|[[Image:Sys_2_9_12_subj1.png |thumb|800px]]
|valign="top"|[[Image:ZoomedResultWithModel.png |thumb|250px|Zoomed In View]]
 
 
|}
 
|}
 +
 +
'''''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 3. Cingulum Bundle Volumetric Fiber Bundles Surface Evolution'''
+
|+ '''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.'''
|valign="top"|[[Image:PriorFiberResultOverBaseline001.png |thumb|250px|Result from Priors Only (t=1)]]
+
|align="center"|[[Image:mit_fmri_clustering_mapffacompare.PNG |thumb|800px]]
|valign="top"|[[Image:PriorFiberResultOverBaseline003.png |thumb|250px|Result from Priors Only (t=3)]]
 
|valign="top"|[[Image:PriorFiberResultOverBaseline008.png |thumb|250px|Result from Priors Only (t=8)]]
 
|-
 
|valign="top"|[[Image:LikelihoodsFiberResultOverBaseline001.png |thumb|250px|Result from Likelihoods Only (t=1)]]
 
|valign="top"|[[Image:LikelihoodsFiberResultOverBaseline003.png |thumb|250px|Result from Likelihoods Only (t=3)]]
 
|valign="top"|[[Image:LikelihoodsFiberResultOverBaseline008.png |thumb|250px|Result from Likelihoods Only (t=8)]]
 
|-
 
|valign="top"|[[Image:FinalFiberResultOverBaseline001.png |thumb|250px|Result from Combined Likelihoods and Priors (t=1)]]
 
|valign="top"|[[Image:FinalFiberResultOverBaseline003.png |thumb|250px|Result from Combined Likelihoods and Priors (t=3)]]
 
|valign="top"|[[Image:FinalFiberResultOverBaseline008.png |thumb|250px|Result from Combined Likelihoods and Priors (t=8)]]
 
 
|}
 
|}
  
''Experimental Result''
+
'''''Hierarchical Model for Exploratory fMRI Analysis without Spatial Normalization'''''
  
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
+
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.  
baseline activation) and smoothed (8mm kernel).
 
  
''Project Status''
+
<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>
  
*Working 3D implementation in Matlab using the C-based Mex functions.
 
*Currently porting to ITK.  (last updated 18/Apr/2007)
 
  
 
= Key Investigators =
 
= Key Investigators =
  
* MIT: Danial Lashkari, Polina Golland, Nancy Kanwisher
+
* MIT: Danial Lashkari, Archana Venkataraman, Ramesh Sridharan, Ed Vul, Nancy Kanwisher, Polina Golland.
 +
* 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]
 
 
* P. Golland, Y. Golland, R. Malach. Detection of Spatial Activation Patterns As Unsupervised Segmentation of fMRI Data. In Proceedings of MICCAI: International Conference on Medical Image Computing and Computer Assisted Intervention, 110-118, 2007.
 
 
 
''In press''
 
  
* D. Lashkari, P. Golland. Convex Clustering with Exemplar-Based Models. In NIPS: Advances in Neural Information Processing Systems, 2007.
+
Project Week Results: [[2008_Summer_Project_Week:fMRIconnectivity|June 2008]]
  
= Links =
+
[[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