An Interactive PCA visualizer

In this example, we randomly sample from a multivariate (many-variable) normal (continuous, linear) distribution. In order to not just get random noise, I added the option to input a covariance matrix. This means that each row represents how each variable depends on the other two variables. For each sample point, three independent uniformly-distributed variables from -1 to 1 are first put through the Mersenne Twister algorithm to generate normally-distributed samples, and then correlated via the Cholesky decomposition of the covariance matrix to form a linear multivariate distribution. That is to say, the three-dimensional sample points are stretched and rotated according to whatever you put into the matrix. I made this app using browser javascript, but it’s pretty computationally efficient. Feel free to give it a go! You can left-click and drag to pan around the axis center, and right-click drag to move the camera’s center.