Thanks for that excellent explanation.
Admittingly I admire the old Ortho Cytofluorograph with it's
2 family-fridge size computer attachments. They created
density plots where indeed every dot was representing a
cell, and the more cells there were per dot, the darker the
dots got. The old Tectronix printer was quite good in
bringing that out on paper. Is this a too simple way to do
it or too difficult to program for the modern computers?
The Coulter Software actually offers a reasonable compromise
to that using pixel print patterns to indicate a higher
number of cells per pixel, but above 6 levels that starts
getting difficult to interpret. Thus you can manually set
the scale to avoid that. Otherwise as I said before, I tend
to use WinMDI for easier transfer into the windows
environment. I don't know how many other programs support
density plots, but assume the new Coulter windows software
as well as the software from Applied Cytometry Systems will
do that as well.
As our eye is much better in gray scale separation than in
colour, gray (or brightness) scales should be the way to go.
In the old Ortho histograms could already be displayed with
a log counting scale, but the doubling per gray scale, using
only 16 gray levels already gives a dynamic range from 1 dot
per channel to 32768 dots per channel. No fiddling required
and very nice to explain to users too! Thus to keep the
discussion going I shall vote for density dot plots.
By the way, we have a senior board member who is colour
blind, so no way to impress him with colourful contours or
dots. Just the facts will do.
Gerhard.Nebe-von-Caron@Unilever.com
______________________________ Reply Separator _________________________________
Subject: Re: data display (contours,etc)
Author: BIGOS@Beadle.Stanford.EDU at INTERNET
Date: 05/10/97 11:17
I will make an attempt here to sort out the can of worms Alice G. called contour
maps. Hopefully we won't get any noggin clogs along the way.
Firstly, we must return to the smoothed data discussion. Assuming that one is
using a 64x64 or 128x128 grid to generate the 2D histogram to be contoured, it
is my experience that unless one has a large number of events in the histogram
(several hundred thousand) the contour lines are very messy. The noise in the
system and the relative sparceness of the data taxes most contour line
generation
algorithms. So, in order to have readable contour maps one needs to either
collect very large data sets or smooth small data sets. On unsmoothed small data
sets, other graphic presentations will probably be more informative than contour
maps.
Secondly there is the question of how to choose the interval between contour
levels. Three are currently in common use in the flow community. The most common
one can be referred to as Linear, where the interval between contour lines is a
fixed density or number of events. Choosing this interval is the can of worm
that Alice refers to - make the interval too small and the contour map turns
into a big black smudge - make the interval too large and significant features
can disappear. I have not seen a good algorithm for automatically generating
this interval.
Another method of choosing contour intervals can be called Logarithmic. The user
specifies an interval, say 50%, and the algorithm finds the highest peak, puts
the first contour at 50% of that level, the next at 25%, and so forth until the
last contour is at the one event level. This is an automatic process, and graphs
generated with this method will be consistent in showing variation in the data
that occur at low frequency but poor at showing moderate to high frequency
features.
The last method can be called Probability. This method was developed by Wayne
Moore in the early 1980s. Based on its use here for over 15 years I can
confidently say it provides an automatic way of contouring immunologic flow data
that shows all significant moderate and high level features. Combined with
outlying dots, it also allows viewing low-level features. Commercially this
method is available both in CellQuest (BD) and FlowJo (Treestar). Briefly,
here's how it works.
The user specifies a percent, which, like the Logarithmic method, determines the
number of contour levels - 10% results in nine, 5% results in 19, etc. The
algorithm picks the contour levels so that the specified percentage of events is
between each level. Note that if there are separate event populations (as there
usually is), then the number of events between corresponding contour levels on
each population will add up to the specified percentage. Mathematically this
means that given any event (at random), it has equal chance on appearing between
any two contour levels - hence the name Probability contours.
Using probability contours with outlying dots on smoothed data removes almost
all the uncertainty that Alice expressed for visualizing immunologic flow data.
For data that has populations with narrow sharp peaks, such as chromosomes,
Linear levels work much better.
Lastly, what is important is not contours per say, but the method of choosing
the contour line levels and the smoothness of the underlying distribution.
Having chosen the levels, other renderings of the data such as the pseudo-color
plots on probability levels in FlowJo, can be just as informative as a contour
lines. Nothing, however, will substitute for the experience and insight of the
researcher analyzing the data.
-Marty Bigos
Stanford Shared FACS Facility
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