[With help from David Weiss]
I spent much of my PhD working on algorithms for making sense of gigabytes of brain data from fMRI scanners, especially on a fairly new approach called Multi-variate Pattern Analysis (MVPA). I want to show you how the MVPA approach is useful for tackling certain kinds of questions.
Think of the brain as a kind of orchestra. You have lots of separate instruments playing at the same time, and you can subdivide them in lots of different ways, e.g.
- You can subdivide the orchestra into parts by location – the 1st violins, the brass, the percussion etc.
- Or you could organize them by what they’re doing. Say the 2nd violins, the oboes and the trumpets have the melody, while the clarinets and the tubas have the harmony. [The harps are doing their own thing and the bassoonist is drunk.]
Likewise, there are all kinds of things going on at once in the brain.
- You can subdivide the brain by location – frontal, temporal, parietal, occipital lobes.
- Or you could organize the sub-parts by what they’re doing – vision, language, executive control, motor etc.
Let’s go back to thinking about how the multivariate approach differs in the kinds of questions it can address.
Standard univariate analysis is useful if you want to tell which instruments are involved in one case rather than another, e.g.
- violins are more active in Beethoven than Mozart, but for trumpets it’s the other way around
- one part of the brain is more active when looking at houses than faces, but for another part it’s the other way around
In contrast, a multivariate analysis might be useful if you want to know:
- is this Mozart or Beethoven?
- is this the brain of someone looking at faces or houses?
Now, let’s introduce one more concept: dimensionality reduction is an attempt to boil down many instruments (or brain regions) into a few key themes/groups:
Take the famous da-da-da-dum of Beethoven’s Fifth, where the entire orchestra is one voice – one could more or less describe the entire orchestra’s activity in terms of just one theme/process. In contrast, for Bach or something more complex and interwoven, it might be very hard to summarize what’s going in with less than 10 themes.
Likewise, maybe it’s straightforward to summarize the brain’s activity with just one or two processes when you’re doing a very simple task like looking at faces vs houses, but if you’re doing something more complicated (like watching a movie) then multiple processes are interacting in complex ways.
David Weiss‘s PACA algorithm boils down the brain’s activity over time into just a few themes. Once you’ve summarized the 50,000 readouts we get from fMRI every few seconds into 50, it’s much more feasible to try and compare different cognitive processes – just as it’s much easier to compare Mozart and Beethoven by looking at the scores of a few key instruments than looking at the full orchestral scores.
PACA was inspired by a bunch of existing dimensionality reduction algorithms that could equally be applied to problems like voice, face or handwriting recognition.
But its magic involves adding a few constraints that are particularly relevant to the brain. Here’s one example of a constraint: it doesn’t allow its estimate of a theme’s presence at a given moment to go below zero. Think of it like this – when was the last time you heard an anti-violin? Or had an anti-thought? In other words, PACA breaks the manifold streams of activity in the brain down to just a few that are all present to a greater or lesser degree at each moment.
P.S. If you hated this, you might also hate How to beat an fMRI lie detector.