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RE: Encoding Model Basics (1/?)
If we were studying visual processing, the matrix x could be implemented as an m x n 2-D matrix, where each element of the matrix corresponds to a grayscale value in a digital photograph of the object that the subject brain is observing. The size of the photograph is m values by n values.You are correct, but in practice such a matrix is usually flattened into a vector. This makes the math easier.
To capture color, we could create three such matrices, where each contains the values from one channel in an RGB image. So the first matrix contains the red values, the second contains the green values, and the third represents the blue values.For right now, I'm just dealing with black and white pixels. If we want to use colour in the future one option would to just concatenate three vectors into one. I don't know if this is the best option though.
The matrix a would capture neural activation values for those populations of neurons relevant to visual processing.Yes, but keep in mind that a is probably more useful as a theoretical construct, as we have no way of measuring it directly and depending on how we define these populations we could get something completely different. In this post I described a as a way to obtain the feature space, but depending on the encoding model we could create a completely different feature space. See chapter 4 in the paper for more details. (also, a is a vector as well)
Is that a correct assumption? So if the subject started to smell the aromas of a heated lunch wafting in from a nearby break room, this should theoretically have no impact to the values in a. Is that right? If not, how would you handle that?Well that aroma, along with millions of other things going on inside someones head, would just be considered noise and we would just have to deal with it when decoding. I'm only interested in encoding models because they are important for decoding as well, but I would assume that an encoding model would choose its a with entries only from relevant populations.
The fMRI that gives rise to the values in matrix y is a three dimensional picture of the brain. How would you propose to represent those values? Would each slice of an MRI scan (a 2D image) populate pixel values in separate matrices, y1, y2, y3, et cetera?I'm not actually sure how fMRI data is represented in hardware, except that its based on voxels. The thing about tensors is that you can always flatten them to vectors though. :) The thing about flattening is that the structure gets lost, but if your model doesn't exploit that any way it doesn't really matter. That would definately be another thing to look into.
It takes a long time to take an fMRI of the entire brain (let's say something like 10 minutes). I'm assuming that the timestamps of each MRI slice are not what you had in mind for the t time parameters for a, or are they?Well fMRI is pretty crappy, but it isn't THAT crappy. https://en.wikipedia.org/wiki/Functional_magnetic_resonance_imaging#Temporal_resolution
Is there any way to mask the fMRI data such that it excludes neural activations not relevant to visual processing (e.g., smelling cooked food, feeling pain from arthritis in one's neck or back while laying on the lab table, auditory cues from the MRI machine making noise)?Thats called removing noise and its a pretty difficult task. That said, a neural network is pretty good at just looking at the interesting bits.
Thank you for these questions! They motivate me the write more.
Thanks. I hope some of it was beneficial. The devil is usually in the details on projects like this, so the sooner you can confront potential traps, the better.
Re: matrices versus vectors: I tend to use the term "matrix" more since I always keep the numbers in that form until a matrix multiplication operation is required, then I unroll and roll the matrix as needed to use the optimized multiplication algorithm.
Re: colors: If the inputs to the CNN are photos of real world objects, I would go with the multi-channel approach, because it's the closest thing to be inspired from biology. We have separate cones in the eyes for reds, greens, and blues, while other living organisms have even more diversity, adding cones from UV light and polarized light (useful for seeing underwater). If the retinal neural cells combine the inputs from the different cones, that's one thing, but I don't think they do. That said, I think the situation changes if the inputs to the CNN are fMRI images. Don't they basically contain false colors to indicate some level of intensity? If that's the case, I would expect grayscale encoding to work.
Re: temporal characteristic of fMRI data: I was just going by personal experience. I underwent a brain MRI scan once, and it took 10 minutes. But the stats on the Wikipedia page you cited doesn't give me much confidence. I suspect that current techniques are not capturing a large amount of neural activations.
Re: filtering out neural activations in the fMRI image that represent undesired sensory inputs: I understand your response, but just be aware that this might be a matter of relevance, not noise. If the noise follows a particular pattern, the CNN may wrongly incorporate that pattern into its predictions. Think of the old experiment that classified tanks from cars, and failed, because all the photos of cars were taken on sunny days, and all the photos of tanks were taken on cloudy days. The CNN in that experiment started focusing on the sky color as a feature, rather than treating it as irrelevant data. It wasn't noise from the classic sense (from information theory and communication channels), because it was deterministic and not random (although that was an unfortunate coincidence). From another perspective, this problem seems a lot like an NLP experiment that attempts to separate simultaneous conversations at a party where a number of microphones scattered among the crowd are recording voices.
Incidentally, a Kaggle competition from a while ago used brain fMRI data. It might be useful to track down the winner of that competition and ask about the approach he or she took.