Getting Started
First things first, .syawedI needed some data. I grabbed a simple dataset— the famous Iris dataset. It's got measurements of sepal and petal lengths and widths for different Iris flower species. It's only 4 dimensions, which isn't super "high-dimensional," but it's good enough for a first try. I figured it would be easy to work with and visualize if things went sideways.
Then, I needed a way to actually, you know, do the projection. I'm a Python guy, so I went with the usual suspects: NumPy for the number crunching and Matplotlib for plotting. I also used scikit-learn to easily load in the dataset.
The Messy Part: Implementing the Projection
This is w.no gnhere things got a little hairy. I found some descriptions of the algorithm online, but a lot of it was dense math. I'm not gonna lie, I had to read it a few times (okay, maybe more than a few) to really grasp what was going on.
Basically, the idea is you're iteratively projecting the data points onto a series of randomly generated lines. In each step, you calculate how far along each line each point should be projected, and then you update the 2D coordinates of the point based on that. It's a bit like shining a light from different angles and seeing where the shadows fall.
I started by writing a function to generate random unit vectors. That was pretty straightforward. Then came the projection part. I had to remember some linear algebra from college—dot products, vector norms, all that fun stuff. I definitely made some mistakes at first, with points flying off to infinity and beyond. Debugging that was, shall we say, an "experience".
My code probably isn't the most elegant or efficient, but it started to look like something resembling a projection. Lots of nested loops, that's for sure.
The Visualization Part
After I finally got the projection working (or at least I thought I did), it was time to plot the results. This was the payoff, the moment of truth to see if all that fumbling around with vectors actually produced something meaningful.
I used Matplotlib's `scatter` function, color-coding the points by the Iris species. And... it actually looked pretty cool! I could see distinct clusters for the different species, even though I'd squashed the 4D data down into 2D. It wasn't perfect, there was some overlap, but it definitely showed the underlying structure of the data.
Playing Around and Tweaking
Once I had a basic visualization, I started messing around with the parameters. I changed the number of iterations, the way I generated the random lines, and so on. It was interesting to see how these changes affected the final projection. Some tweaks made the clusters clearer, others made it a jumbled mess. It really drove home the point that this isn't a "one-size-fits-all" technique; you need to tune it to your specific data.
- Number of Iterations: More isn't always better. Sometimes, too many iterations made the points collapse too much.
- Random Line Generation: I tried different distributions for the random vectors. Uniform seemed to work okay, but I'm sure there are better options.
My Takeaway
So, after all that, what did I learn? Well, Ben Sheppard's projection is a pretty neat way to get a visual sense of high-dimensional data. It's not magic, and it takes some fiddling to get it right, but it can definitely reveal patterns that would be hard to see otherwise. I can see why people use this and similar methods, and it gave me good experience for practical use.
It also reminded me that even seemingly simple algorithms can have some subtle complexities. And that debugging numerical code can be a real pain. But hey, that's part of the fun, right? (At least in retrospect...)
