title: Shape anomaly detection under strong measurement noise: An analytical approach to adaptive thresholding.
abstract: We suggest an analytical approach to the adaptive thresholding in a shape anomaly detection problem. We find an analytical expression for the distribution of the cosine similarity score between a reference shape and an observational shape hindered by strong measurement noise that depends solely on the noise level and is independent of the particular shape analyzed. The analytical treatment is also confirmed by computer simulations and shows nearly perfect agreement. Using this analytical solution, we suggest an improved shape anomaly detection approach based on adaptive thresholding. We validate the noise robustness of our approach using typical shapes of normal and pathological electrocardiogram cycles hindered by additive white noise. We show explicitly that under high noise levels our approach considerably outperforms the conventional tactic that does not take into account variations in the noise level.
authors.affiliation: St. Petersburg Electrotechnical University, 5 Professor Popov Street, St. Petersburg 197376, Russia.
authors.forename: Alexander S
authors.initials: AS
authors.lastname: Krasichkov
authors.affiliation: St. Petersburg Electrotechnical University, 5 Professor Popov Street, St. Petersburg 197376, Russia.
authors.forename: Eugene B
authors.initials: EB
authors.lastname: Grigoriev
authors.affiliation: St. Petersburg Electrotechnical University, 5 Professor Popov Street, St. Petersburg 197376, Russia.
authors.forename: Mikhail I
authors.initials: MI
authors.lastname: Bogachev
authors.affiliation: Pavlov First Saint Petersburg State Medical University, 6/8 Leo Tolstoy Street, St. Petersburg 197022, Russia.
authors.forename: Eugene M
authors.initials: EM
authors.lastname: Nifontov