Dimensionality reduction (mixing the rational and irrational)

[rodrigo.constanzo]

@weefuzzy

Depends what you mean by making sense. The output ‘units’ of the PCA will still be in terms of standard deviations, so won’t bear much resemblence to the millisecond input.

Ah right. Yeah, I misunderstood that.

@weefuzzy

Yes. You can think of it as using PCA to make the job of MDS easier by stripping out some redundnacy / correlation in the input. So if you wanted to go from, say, 300 input dimensions to 2, it might be worth PCA-ing down to (say) 50 or something.

This makes sense, and I’ll have a play to see. For the purposes of this example the starting dimensions will probably be more more than 10ish (overall stats like duration and time centroid, then multiple time scales of loudness derivatives and maybe deviations?). So for these kind of “meta-descriptors”, I wouldn’t have such a massive set of dimensions to start off with, but they are likely related to each other in a more linear-esque manner (e.g. time centroid will always be shorter than duration, the ratio of time centroid to duration may(?) correlate with the derivative of loudness, etc…).

@weefuzzy

In this imaginary two-item data set, normalising would give you two points [0,0] and [1,1], so definitely not similar values). Standardsing would give you two points [1,1] and [-1,-1]. In both cases, the difference is scale is accounted for (quite drastically)

So if I understand you correctly, both standardizing and normalizing those examples would happen in a way where the it would be impossible to tell which one of the two was “longer” in terms of realworld milliseconds. the 2500ms would become either a 0 or -1 and the 5000ms would become either a 1 or a 1, and the same would happen for the 400/200 version.

Maybe this kind of approach would be better suited for vanilla number crunching where I take these numbers and feed them into a function with relative weighting taken into consideration, and it spits out a ‘timeness’ value that way(?).

I still want to push further along this dimensionality reduction approach as it’s a useful vector of getting my head around it, and it may very well be a good approach to do this, but it’s a funky bugger!