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Topic: off-line change detection & clustering in a time series of multidimensional
data

Replies: 18   Last Post: May 21, 2012 1:23 PM

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 Richard Ulrich Posts: 2,795 Registered: 12/13/04
Re: off-line change detection & clustering in a time series of multidimensional data
Posted: May 15, 2012 7:10 PM

On Tue, 15 May 2012 14:26:47 -0700 (PDT), moo.marc@gmail.com wrote:

>>Thanks Rich, I've been looking for non-parametric methods since I
don't really know if my measurement error is "normal". I'll keep that
in mind though.

Here are a couple of negative comments on "nonparametric" -- in
the sense of using rank-order statistics. I like to think of it
as starting a *transformation* of the raw data, to rank-order. A
test-computation may not show you that, but that transformation
is always implicit. After the transformation, you can expect
residuals that give you pretty good ANOVA tests. Even for
samples that are pretty small, the resulting EXACT non-parametric
test is well-reproduced by a simple ANOVA on the rank-scores.
- If you violate "non-parametric assumptions," like by having ties,
the ANOVA sometimes gives a *better* test (limits that are more
accurate under Monte-carlo testing) than the text-book formulas
for non-parametric p-values.

So, think of non-parametric as starting with rank-transforms, which
yield certain residuals that may be "normal" enough that the testing
by ANOVA is pretty good; and wonder whether some continuous
transformation of your scores might be as good or better.

The rank-transform is not reversible, and it loses the anchoring
information of the actual scores.

Rank-transforming gives you, sometimes, improved tests. It
divorces you from the original means, etc.

It does not put you in any good position at all for doing the
sort of modeling that you suggest you are headed for.

>>
>>I realize there might be simpler ways to get what I want, which is

why I'm asking around. I've thought of using a "signal processing"
approach instead of clustering, but the reason I looked up clustering
is because I originally was considering few "fast" movements,
resulting in step-like time series. Filtering would smooth out those
jumps and make interval boundaries less precise. Also, noise varies
between collections, so I wouldn't know how to automatically decide on
filtering parameters. I also like the possibility of getting
justification or goodness-of-fit information using statistical methods
(I was reading on AIC today).

I haven't done that sort of thing, but I thought that folks used
simple filters to find "something" and then used fancier algorithms
to make find boundaries and make identifications.

>>
>>One of the reasons I want a "good" partition, is that I would

eventually use this motion data to apply some "motion correction"
algorithm to other data that is collected at the same time.

--
Rich Ulrich