Dimensionality Reduction

Dimensionality reduction is something I deal with in math, statistics, and engineering. It comes up in my research. The idea is that when data is complicated, because there are a lot of different kinds of information in it, we can make our lives easier by considering fewer variables. Sometimes we pick from the variables that are already there. Sometimes we smush several variables together and create new ones out of the results, then pick from those. Either way, it can be useful to reduce the number of variables, the number of dimensions, that we need to deal with in a complicated pile of data.

However, we lose information when we do so. Like everything else engineers need to do, there are trade-offs involved, and we need to recognize that. Dimensionality reduction means simplification, which can make large amounts of information easier to deal with. But over-simplification makes information less useful.

Using disability and access needs as an example:

I use a much more complicated thought process to decide what I can and can't do on any given day than people who know me might use to guess what I might and might not be able to do. This includes deciding when I'm just done for the day.

My major professor works with me in an environment (our lab) where my losing speech is most likely due to sensory triggers. If I lose speech due to sensory triggers, I'm leaving the environment where it happened. She knows that if I can't talk I'm probably going home. This is an appropriate simplification for the context.

However, when I was a graduate student in math, I most frequently lost speech in classes where I was a student because I'd already taught that day and I'd essentially run out of mouth-words. Nothing bad was happening, and nothing bad was going to happen because I stuck around and kept doing math without speech. My classmates and professors knew that if I couldn't talk, I was probably going to grab a whiteboard marker and start writing on the board instead. This was an appropriate simplification for the context.

Those are both examples of appropriate dimensionality reduction. In the lab, "can speak" vs. "arrived non-speaking" vs. "lost speech in the lab" was a 3-possibility variable that made a decent proxy for how I was feeling and how well I could work. In the math classroom, whether or not I can speak wasn't an important variable. 

Ignoring the variable of whether or not I can speak in the lab would mean ignoring useful information. Using the variable of whether or not I can speak in the math classroom might mislead people into finding patterns that aren't really there. So it's important to choose the right variables to focus on!



And yes, this applies to functioning levels. In addition to being ableist and grading against a neurotypical standard (which is its own, major issue), functioning levels attempt to reduce all the complex information about a persons abilities and needs over time and across a variety of contexts down to one dimension. That's always going to be inappropriate dimensionality reduction, simplifying what we know to the point that it's useless. Talking about low, medium, or high support needs isn't going to fix this problem. Neither will talking about low vs. high masking as if either of those means a single thing. Those still use a single dimension, and you can't shove enough information about what those support needs actually are, or what the specific effects of masking are into a single dimension for it to ever work.