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As long as there is a very active discussion about the methods
for the averaging of time series, I thought I might address an old
worry of mine with respect to the averaging of curves.
As far as I can tell, in the averaging of curves taken from
various trials there is the inherent danger of producing a multimodal
average curve from a series of unimodal curves whose "peaks" and
"valleys" do not coincide in time (neither in real time nor in time
expressed as a percent of the total duration of the event). In fact,
since the "peaks" and the "valleys" of the curves of the different
trials will practically never coincide exactly in time, the resulting
"average" curve will generally tend to have "plateaus of moderately
high elevation" instead of "sharp mountain peaks of very high
elevation": The peak of the highest mountain in the average curve will
almost always (always?) be lower than the average of the peaks of the
highest mountains in the individual curves. An equivalent problem will
occur in the valleys. I don't know of a good solution to this problem,
but it seems to me that anyone averaging several curves to produce a
single "representative" curve has to be very wary of this potential
problem.
I don't know if some of the methods discussed in the recent flurry
of BIOMCH E-mail address this problem, but I have always been very
uncomfortable with the averaging of curves from different trials
because of this.
Jesus Dapena
Indiana University
================================================== ======================
Date: Fri, 9 Feb 90 14:52:00 MET
Reply-To: "Lambert Schomaker "
Sender: Biomechanics and Movement Science listserver
Comments: Sent using PMDF-822 V3.0, routing is done by KUNRC1
From: "Lambert Schomaker "
Subject: Re: Averaging of time series (jitter of peak positions)
>From: DAPENA@IUBACS
> As far as I can tell, in the averaging of curves taken from
>various trials there is the inherent danger of producing a multimodal
>average curve from a series of unimodal curves whose "peaks" and
>"valleys" do not coincide in time ....
In speech recognition this problem is solved by what is called
dynamic time warping. The time axes of single trials are bended
to obtain an optimal fit between two time functions using
dynamic programming. In fact, however, one needs a model for the
origin of the temporal fluctuations to be able to do such a transform
elegantly.
Lambert Schomaker.
for the averaging of time series, I thought I might address an old
worry of mine with respect to the averaging of curves.
As far as I can tell, in the averaging of curves taken from
various trials there is the inherent danger of producing a multimodal
average curve from a series of unimodal curves whose "peaks" and
"valleys" do not coincide in time (neither in real time nor in time
expressed as a percent of the total duration of the event). In fact,
since the "peaks" and the "valleys" of the curves of the different
trials will practically never coincide exactly in time, the resulting
"average" curve will generally tend to have "plateaus of moderately
high elevation" instead of "sharp mountain peaks of very high
elevation": The peak of the highest mountain in the average curve will
almost always (always?) be lower than the average of the peaks of the
highest mountains in the individual curves. An equivalent problem will
occur in the valleys. I don't know of a good solution to this problem,
but it seems to me that anyone averaging several curves to produce a
single "representative" curve has to be very wary of this potential
problem.
I don't know if some of the methods discussed in the recent flurry
of BIOMCH E-mail address this problem, but I have always been very
uncomfortable with the averaging of curves from different trials
because of this.
Jesus Dapena
Indiana University
================================================== ======================
Date: Fri, 9 Feb 90 14:52:00 MET
Reply-To: "Lambert Schomaker "
Sender: Biomechanics and Movement Science listserver
Comments: Sent using PMDF-822 V3.0, routing is done by KUNRC1
From: "Lambert Schomaker "
Subject: Re: Averaging of time series (jitter of peak positions)
>From: DAPENA@IUBACS
> As far as I can tell, in the averaging of curves taken from
>various trials there is the inherent danger of producing a multimodal
>average curve from a series of unimodal curves whose "peaks" and
>"valleys" do not coincide in time ....
In speech recognition this problem is solved by what is called
dynamic time warping. The time axes of single trials are bended
to obtain an optimal fit between two time functions using
dynamic programming. In fact, however, one needs a model for the
origin of the temporal fluctuations to be able to do such a transform
elegantly.
Lambert Schomaker.