How Does Cluster Analysis Work?
For the purposes of explanation I'm going to continue with the question of EGFP-SST interneuron heterogeneity. However, I'm going to generate artificial data to better illustrate some points.
To see the data I've generated and an explanation of how I generated it click here.
I've made 30 cells each described by 7 parameters (variables) that I magically recorded from each in Excel using a random number generator.
The simplest case would be if I could describe differences between these cells using only 1 variable such as action potential half-width (APHW). If I plotted the APWHs (this is not the "real" fake data from the Excel spreadsheet but rather more idealized numbers) for all these cells on a number line I would get a 1 dimensional description of my population of cells.
Data is usually not plotted like this though, but rather as a histogram. So here's the same data plotted as a histogram.
It's pretty easy to see that there are 3 different groups of cells described here by APHW alone. Unfortunately you won't see data like this all of the time. Maybe neuron's don't like to be called 1 dimensional. More often data looks something like this:
Or as a histogram:
It's kind of hard to get any kind of information from this, but I know that I generated the data from same 3 groups as the pictures above. The only thing that is different is the S.D. of the distributions has been doubled causing them to overlap significantly.
So how can you possibly tell that there's more than 1 group of cells from this?
The answer is that you can't. You also have to remember that we don't know for sure that this isn't just one big group that can't be subclassified at all (of course I've already told you that I have at least 3 distributions of cells so we will carry on).
Just like in looking for a good girl/boyfriend you want somebody that's smart AND funny, not just one dimensional. In that spirit we're going to add another parameter (dimension) to the mix.
Click here to see what happens when we have a 2 dimensional description of these cells.