vDSP.correlate(_:withKernel:) — meaning of output

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Created Feb ’21

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My clients are medical researchers researching methods for characterizing patients' gait from raw accelerometry by matching the data stream against a set of "templates." for the various characteristics.

Their (labyrinthine) pseudocode appears to slide a snippet ("template;" kernel?) across a data stream looking for goodness-of-fit by correlation coefficient. This is for each of several templates, so performance is at a premium.

As I read the name and the 13-word description, vDSP.correlate(_:withKernel:) does this — in some way. However, the set of numbers that emerge from my playground experiments don't make sense: Identical segments are scored 0.0 (should be 1.0, right?). Merely similar matches show values barely distinguishable from the rest, and are often well outside the range -1.0 ... 1.0.

Clearly I'm doing it wrong. Web searches don't tell me anything, but I'm naïve on the subject.

Am I mistaken in hoping this vDSP function does what I want? "Yes, you're mistaken" is an acceptable answer. Bonus if you can point me to a correct solution.
If I'm on the right track, how can I generate inputs so I can interpret the output as fits my needs?

Note: Both streams are normalized to µ = 0.0 and σ = 1.0, by vDSP, and validated by all the unit tests I've done so far.

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Answer 1

miguelfs OP

Mar ’21

Hi fritza, sorry about being a little late for answering.

Their (labyrinthine) pseudocode appears to slide a snippet ("template;" kernel?) across a data stream looking for goodness-of-fit by correlation coefficient. This is for each of several templates, so performance is at a premium.

In the way you describe it, looks like a convolution of two signals. Since you are trying to find a cross-correlation when sliding both signals, you must perform a cross-correlation.

It's similar to a convolution process. Theoretically, a cross-correlation is a convolution without reversing one of the signals before sliding it (the point is that, in my experience, there are more already-written code for convolution than for cross-correlation).

You must consider some situations:

in most algorithms, the length of both discrete-time signals must be the same, so you may need to append zeros in the end to match it.
you can reverse one of the signals and use the convolution function from vDSP.

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Answer 2

aharriscrowne OP

Mar ’22

For future viewers of this question, there is a more detailed description of the correlate method here: https://developer.apple.com/documentation/accelerate/vdsp/1d_correlation_and_convolution

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