Boston University · M.A. Statistics · MA 751 · Machine Learning · 2022 · Team of four
Anomaly Detection with Karhunen–Loève Expansions
A graduate machine-learning project re-implementing and extending a Karhunen–Loève approach to anomaly detection — train an eigenspace on one class, then feed the energy outside it into an SVM.
Collaborators: Yulin Li, Travis Yang, Luke Zheng
This project tackles a recurring machine-learning problem: spotting anomalous signals — data that doesn’t belong to a known reference class. The idea borrows from functional analysis. A Karhunen–Loève expansion (the function-space generalization of PCA) is trained on a single reference class to estimate its eigenspace; new observations are then projected onto the subspaces outside that eigenspace, and the energy in those projections becomes a feature vector for a support-vector-machine classifier.
Our team re-derived the framework from Castrillón-Candás et al. and wrote it up with a deliberate pedagogical build-up — from ordinary PCA, to KL expansions, to the anomaly-detection application — so a reader without a functional-analysis background could follow it. We then proposed a Greedy Tree Multiclass SVM to extend the originally two-class method to three or more classes, and demonstrated the full pipeline on cancer-diagnosis data, separating tumor from healthy tissue.
Implemented in MATLAB, with the report doubling as a teaching document for the method. A four-person team project.