In a previous article, I introduced a vectorized method for achieving interpolation, which works quite well, and is very fast. I abandoned it because I had other things getting my attention, including, maximizing the use of vectorization in my core algorithms, because it really changes their runtimes. I’ve also proven that you can’t beat the accuracy of my algorithms for a class of datasets that I’ve rigorously defined as, “locally consistent” datasets. The gist is, if classifications don’t change much over small distances, then the dataset is locally consistent. Because my core algorithms are also have linear runtimes, that’s pretty much the end of the story for locally consistent datasets, which probably covers a significant chunk of real world datasets.

So, I’ve started to think about datasets that are not locally consistent, and what’s interesting, is that the MNIST Fashion dataset seems to have some inconsistent classes, because my algorithms have really high accuracy overall for MNIST Fashion, but have randomly horrible accuracy for certain rows (but not enough to push the overall accuracy down too much). So I’m now turning my attention to using interpolation, i.e., constructing a function that takes the features in a dataset, and calculates its class.

Before I decided to do this, I wanted to make sure that I wasn’t wasting my time, and creating something that is only superficially different from what I’ve already done, but mathematically equivalent. And it turns out, it is not the same as the distance-based clustering and prediction I’ve made use of so far. Specifically, it doesn’t require the same features to have similar values, which my current algorithms do –

It instead requires that the function returns the same value when evaluated for two elements of the same class. As a result, I’m going to spend a few days on this, because it is new, and perhaps it’s useful, and could provide a more efficient method of implementing what is a basically neural network.