Question: Locating Trends in Data

RWTodd (rwtodd@aol.com)
Mon, 10 Aug 1998 02:32:53 +0200 (MET DST)

As part of my research (see my web page if you're interested) I find myself
needing to locate certain trends in streams of data. I'll describe exactly
what I mean by trend in a moment. I think a fuzzy logic approach would help a
great deal since:

1) the trends I want recognized can be represented by category in fuzzy
terms. For instance, volume would have categories ranging from SILENT to LOUD.
I can make each a fuzzy set and categorize any sampled volume this way.
2) I can take the union of a set of these single-sample decisions and
determine the confidence that any subset of the data fits a certain category.

These seem like two good first steps.

Now what I'd eventually like to have is, for a stream of volume data, an output
that says samples 1 to 100 are LOUD, samples 101 to 200 are VERY LOUD and
samples 200 to 1000 are SOFT. Of course, not every sample in the first range
is actually in the category LOUD, but the trend in 1-100 is loudness. The
samples never stray from LOUD enough or for a long enough amount of time.
Perhaps an enhancement would be to also get output like: samples 100-107 go
from SOFT to LOUD (in other words, recognize states of transition).

So how do I locate the places where one trend ends and another emerges? Would
it be some function of the avg. and std. deviation? Ideally, this would be
done with a variable tolerance for change, so that I can only look for large
changes if I want. I'm thinking of some mechanism where I scan through it and
somehow notice that I am definitely in a another region--then I backtrack until
I find the first sample that fits better in the new category than the old one.
That's how the dividing line will be drawn. But that's as far as I get
conceptually--and is it maybe the wrong approach?

The data is discrete and the data points don't fall at even intervals (they are
musical notes, so I think each sample will have to be weighted by the amount of
time it is in effect before it'll have usefull meaning in an average...).

Sorry this ran a little long for a question...any advice would be greatly
appreciated.

-------------------------------------
Richard Todd
rwtodd@aol.com
See my computer music research at:
http://members.aol.com/rwtodd/

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