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A (very) brief introduction to multivoxel analysis “stuff”

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### A (very) brief introduction to multivoxel analysis “stuff”

Jo Etzel, Social Brain Lab

Mass univariate (spm)

Test every voxel separately

Fit a linear model to each voxel

Look for brain structures where the blobs occur

Obtain a p-value for each voxel

Use parametric (or permutation) statistics to evaluate significance

Multivariate

Test groups of voxels (ROIs) at once

Use machine learning algorithms

Structures first (no blobs)

Obtain a classification accuracy for each ROI

Evaluate significance of accuracy by permutation testing and perhaps subsetting (parametric statistics also possible)

Classification

- What sort of flower is this?
- Is this example type 1 or type 2?

from www.cac.science.ru.nl/people/ustun/index.html

from http://spect.yale.edu/displaying_results.html

listening to hand action sounds

listening to mouth action sounds

Is the brain activity in this ROI different while listening to hand and mouth action sounds?

Can the activity in the right premotor cortex classify the volumes into hand and mouth action sounds?

- or -

www.cs.sunysb.edu/~mueller/research/brainMiner/

to classifiers

temporal compression; extract GLM parameter estimates

for each ROI in each volume (or summary volume)

- classify each subject separately, average accuracy across subjects
- subjects can have their own patterns
- classify subjects together, test left-out subject
- subjects need the same patterns

all data

2nd test: mouth vs. hand?

1st train: mouth vs. hand?

classifier

training set

accuracy (from test set)

* P < 0. 0042, permutation test

(Bonferroni correction) of 0.05 for

12 ROIs.

ROIs

So, have which ROIs allowed significant classification accuracy for separating mouth and hand action sounds: preML, preMR, M1L, S2R, audL, audR.

What?

null hypothesis is arbitrary labeling

If labeling is arbitrary (random), then there is no relationship between the labels and the activity, so classification should not be possible.

real data classified about the same as arbitrary data: no evidence for a relationship between the labels and the activity: not significant.

real data is classified better than the arbitrary data: it is “unusual:” significant.

How?

classify the real data

make many randomized-label data sets (arbitrary or “fake” data).

classify each fake data set in the same way as the real data

proportion of fake data sets classified better than the real data is the p-value

Permutation Test1. Analyze the real data (get accuracy).

M1 L = 0.6000

2. Make lots of permuted-label data sets (all if possible, at least 1,000).

3. Analyze the fake data sets (get accuracies).

0.4944 0.510 0.499 0.5211 0.480 0.5002 0.498 0.519 0.5720 0.4789 …

4. Count how many of the fake data sets were classified more accurately than the real data.

Of 1000 fake data sets, none had accuracy higher than 0.60.

5. Divide and get the p-value.

(50/1001 = 0.0499)

1/1001 = 0.000999, so

M1 L p = 0.001

Done!

Permutation test results, showing true results with uncorrected p-value cutoff lines. True mean accuracy lines that fall above the range of the permuted lines are highly significant (p= 0.002).

Random Forests (RFs)

first fMRI use, I think

algorithm makes 10,000 CARTs, all try to classify, majority vote final class

algorithm makes random variable selections for the “forest” of “trees”

support vector machines (svms)

previously used with fMRI data

algorithm converts data to a higher dimension to try to find a linear separating line (hyperplane) between the classes.

Black box?classifier

k-nearest neighbor

Linear discriminant analysis

Gaussian Naïve Bayes

Hidden Markov Models

Partial Least Squares

For more info/review:

Mitchell, Machine Learning, 2004, 145-175;

O’toole, Journal of Cognitive Neuroscience, 2007, 1735-1753.

classifier

Other classification-type algorithms

Neural Networks

- A generalization of linear regression functions; many variations.
- Each node calculates a weighted sum, and does a binary input to the next layer, so simple networks can be expressed as (long) equations.
- Training the network for each person involves setting the weights on each voxel.

Idea: brain activity pattern during remembering an item should be similar to the pattern when learning the item.

- Subjects learned 3 lists of 10 items each; items were labeled pictures of famous people, famous locations, and everyday objects.
- After learning, subjects tried to remember all of the items; saying them aloud as they remembered them.

volumes when recalling

1: training

volumes when learning items in each category

classifier

(neural network)

3: accuracy

(sort of)

“For each brain scan, the classifier produced an estimate of the match between the current testing pattern and each of the three study contexts.”

“However, follow-up analyses indicated that voxels outside of peak category-selective areas are also important for establishing this result.”

Take-Home Message

- Classification (multivariate methods) can answer questions and find patterns not available with spm-type methods.
- spm is still useful, though!
- Method is (for me) ROI-focused: start with hypotheses about which ROIs can classify (or not) which stimuli.
- Differences in activation to stimuli can be restated as classification predictions.

Permutation vs. t-test p-values

The permutation and t-test p-values are very highly correlated, though not always identical.

Calculated correlation line in solid, perfect in dotted.

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