Log-like transforms
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From: C. Bruce Bagwell <cbb@[EMAIL PROTECTED]
>
Date: Tue Mar 21 2006 - 12:01:08 EST
Hello all,
Log-like transforms such as the "Logicle" and "HyperLog" serve as a
means of
representing data that may have negative, zero, and positive values.
The
Log transform's im****tance to cytometry is that it allows us to
visualize
populations with vastly different intensities and standard deviations.
The
im****tance of both of these normalizations cannot be overstated. If
not for
the Log transform, cytometry would never have gained a foothold in the
late
70's and early 80's and we all would probably have different jobs now.
Unfortunately, there are processes in cytometry that can produce
negative
numbers in our data, compensation being the best known. Since the Log
transform is undefined at zero and negative numbers, historically we
had to
trim our data to be able to display it in the Log domain. Thus, an
im****tant point to make is that the "Logicle" and "HyperLog"
transforms
really preserve the real underlying data since our data no longer need
to be
limited to the positive scale.
V
Since these transforms faithfully represent our real-valued data,
properly
compensated data are now visually evident; whereas, in the past with
Log
transforms, our data could appear to be under-compensated. Of all the
advantages of these transforms, showing properly compensated data in a
non-biased manner is most im****tant.
There is another aspect to these transforms that is very subtle but
im****tant to be aware of. Because of binning effects, the Log
transform
could transform a single negative population into two distinct
clusters: one
that was piled up on the axis and the other that appeared as a broad
low-intensity distribution. If one sorted the higher-intensity
cluster and
then reran the cells through the cytometer, the two distinct clusters
would
appear unchanged. Our log amplifiers were noisy enough to blur this
effect,
but it was always there to some degree. In my paper, HyperLog - A
Flexible
Log-like Transform for Negative, Zero, and Positive Valued Data
(Cytometry
Part A 64A: 34-42, 2005) I show this effect in Fig 1.
If you create a Log-like transform by creating a spline between the
log
transform and a line as was suggested in one of the responses to this
topic,
there is a serious danger of creating false populations due to binning
artifacts, much like those formed with the Log transform. Both the
"Logicle" and "HyperLog" have the im****tant ability to flatten the
linear
slope through the origin to eliminate these false populations from
occurring.
In Verity's implementation of the "HyperLog" we chose to take the "set
it
and leave it" approach to "tweaking" the transform. Our default
handles
over 95% of all the cases that typically come up. In the "Logicle"
transform, they chose to have it optimize the transform for each data
set.
The advantage of the former is that the axes always appear the same
and
thus, different graphics can be compared since their axes are uniform.
The
advantage of the latter is that the negative population will never
appear
split and will always have a consistent variance.
If there is an interesting point to discuss it is whether axes should
change
with the data or should remain consistent for comparison purposes.
Bruce
C. Bruce Bagwell MD, Ph.D.
President
Verity Software House
45A Augusta Road
PO Box 247
Topsham, ME 04086
Email: cbb@[EMAIL PROTECTED]
on Tue Mar 21 15:18:00 2006
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