Dear Madam or Sir,
I have great experience in machine learning. As a mathematician, I am familiar with the theoretical background and as a software developer I know how to develop clear and documented code. I have implemented all the standard machine learning algorithms ((P)PCA, FA, LDA, QDA, decision trees and other mixture models, simple NN) in Matlab, Python, R from scratch.
Moreover, I have already implemented various face recognition software in Matlab. I have implemented such a simple one that is described in your document (PCA+k-means). Therefore, I know how the algorithm works, what results are expected. Therefore, I am confident that I find your error fast.
Depending on your face data and the number of different people, I expect a recognition rate of 70-95% with the best hyper-paramters.
I am looking forward to discuss all these details in the chat. You might have a look at my reviews before making you decision. Best regards