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.