A true classic topic in ML: Facial recognition is very high-dimensional, meaning that each picture can have millions of pixels, each of which can be a single feature. It's computationally expensive to deal with all these features, and invites overfitting problems. PCA (principal components analysis) is a classic dimensionality reduction tool that compresses these many dimensions into the few that contain the most variation in the data, and those principal components are often then fed into a classic ML algorithm like and SVM. 

One of the best thing about eigenfaces is the great example code that you can find in sklearn--you can distinguish pictures of world leaders yourself in just a few minutes!

http://scikit-learn.org/stable/auto_examples/applications/face_recognition.html

Facial Recognition with Eigenfaces

Linear Digressions