This is a project that Kristen Bystrom and Alice Roberts completed for Math 496 - Special Topics in Mathematics of Data Science.
Project Description: Presentations 2 (Week 4) Eigenfaces and PCA (Alice & Kristen) Suppose you have a database of face images arranged into a data matrix A (here each column is an image). The eigenfaces are the principal components of this dataset. Your objective in this presentation is consider the use and application of PCA in for face images, including as a tool for face recognition. Your first two tasks are:
Read the wikipedia page (Links to an external site.)Links to an external site. and reimplement the code there for the Yale dataset (see here (Links to an external site.)Links to an external site. - I suggest you use the 32x32 Data File). Compute and plot the first few eigenfaces. (Warning: the code on wikipedia may need some debugging). Explain the connection between PCA and singular values, and modify the code to avoid forming the covariance matrix. Your third task is to use eigenfaces as a facial recognition tool. Following the description given on wikipedia, write a code that takes a new image and classifies it according to the database. How successful is your approach? Discuss.
This project was assigned to Alice and I by Professor Ben Adcock, Department of Mathematics, SFU.