1. ## Analyzing multidimensional input

Hi,

In a recent experiment that I am performing, I have three independent parameters and one outcome that depends on this set of parameters. So from my understanding, I can map these three parameters into a three dimensional space. What I am trying to do is to map the change of these values to a particular probability value i.e. if a point in the space lies above a particular plane, then I have certain probability of that outcome occurring. But because this is a complex task, I was wondering if it is possible to transform this data into a 2 dimensional space and then do a similar thing. Does anyone have any suggestions for me please?

Thanks

2. ## Projection

What you are looking for is a mapping $\displaystyle \phi:\mathbb{R}^3\to\mathbb{R}^2$ so that the function in question can be visualized in three dimensions? There are plenty of such mappings available. The one that is most useful invariably depends on what function you are using in the first place. Just like drawing the image of a cube on two-dimensional paper can give you an idea what it looks like, but not describe it perfectly.

Can you give us more specific details about the experiment, including your function $\displaystyle f(x,y,z)$ and sample data?