Visualizing Multiclass Classification Results
Introduction Visualizing the results of a binary classifier is already a challenge, but having more than two classes aggravates the matter considerably.
Let’s say we have $k$ classes. Then for each observation, there is one correct prediction and $k-1$ possible incorrect prediction. Instead of a $2 \times 2$ confusion matrix, we have a $k^2$ possibilities. Instead of having two kinds of error, false positives and false negatives, we have $k(k-1)$ kinds of errors.
Complex Numbers in R, Part II
This post is part of a series on complex number functionality in the
R programming language. You may want to read Part I before continuing if
you are not already comfortable with the basics.
In Part I of this series, we dipped our toes in the water by explicitly
creating some complex numbers and showing how they worked with the most basic
mathematical operators, functions, and plots.
In this second part, we’ll take a more in-depth look at some scenarios where
complex numbers arise naturally – where they are less of a choice an more
of a necessity.
Complex Numbers in R, Part I
R, like many scientific programming languages, has first-class support for
complex numbers. And, just as in most other programming languages, this
functionality is ignored by the vast majority of users.
Yet complex numbers can often offer surprisingly elegant formulations and
solutions to problems. I want to convince you that familiarizing yourself with
R’s excellent complex number functionality is well worth the effort and will
pay off in two different ways: first by showing you how they are so
amazingly useful you’ll want to go out of your way to use them, and then by
showing you how they are so common and fundamental to modern analysis that you
couldn’t avoid them if you wanted to.