Time series on Riemannian manifolds

---

Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Mühendislik Fakültesi, Elektrik ve Elektronik Mühendisliği Bölümü, Türkiye

Tezin Onay Tarihi: 2017

Öğrenci: HAMZA ERGEZER

Danışman: MEHMET KEMAL LEBLEBİCİOĞLU

Özet:

In this thesis, feature covariance matrices are utilized to solve several problems related to time series. In the first part of the thesis, a novel representation is proposed to represent the time series using feature covariance matrices. By this representation, time series are carried onto Riemannian manifold space. The proposed representation is firstly applied to trajectories which are essentially 2D time series. Anomaly detection and activity perception problems in crowded visual scenes are studied by using the trajectories. The second utilization of the proposed representation is for classification of 1D time series. The feature covariance matrices of overlapping subsequences are extracted and fed into two well-known classifiers as the input. The last contribution of the thesis is a rank-based distance measure for high dimensional covariance matrices. The distance measure is utilized to solve skeletal action recognition problem. Unlike classical distance measures, the rank-based distance measure enables us to learn the manifold structure. For this reason, essentially, it can be asserted that the proposed approach is about manifold learning. Performances of the approaches proposed in this thesis have been compared to most of the state-of-the-art techniques on publicly available well-known datasets. For all of the studied problems, we achieve comparable or outperforming results compared to the state-of-the-art techniques.