Low-Dimensional Embedding

Data reduction is a critical element in analysis. A common application of data reduction is to embed observations from a high-dimensional space into a lower-dimensional space in which analysis and interpretation are more tractable.

In this notebook, we will quickly explore some of the most basic embedding methods, beginning with PCA.

Principal Component Analysis (PCA)

$\mathbf{A} = \mathbf{X X}^T$



In [26]:

    
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt



In [27]:

    
n = 10
k = 3
X = np.concatenate((sp.rand(n,k), sp.rand(n,k), sp.rand(n,k)),0)