# Eigen-faces

**Languages:** For this project I used Python 2.7 and the
scipy stack.
I specifically used numpy to handle matrices and the calculations on those matrices
and matplotlib to plot the reconstructed faces.

**Overview:** In this project, I was given an image of a grayscale face.
My task was to first reduce the dimensions of the face using singular value
decomposition (SVD). I then used principal components analysis (PCA) to reconstruct
a face in this lowered dimension using the first K principal directions.

**Results:**When taking the first

*K = [5,10,50]*principal directions on two randomly chosen faces, we can achieve a pretty good reconstruction result when

*k = 50*. Below are the results when using the first K principal directions.