Akademik Veri Yönetim Sistemi
Tezin Türü: Yüksek Lisans
Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye
Tezin Onay Tarihi: 2022
Tezin Dili: İngilizce
Öğrenci: SELÇUK GÜRSES
Danışman: Semra Pamuk
Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
Özet:
Topological data analysis (TDA) consists of a growing collection of techniques that reveal the shape of data. These techniques may be especially useful for comprehend ing global features of high-dimensional data that are inaccessible via other methods. The usage of TDA has been constrained by the difficulties of merging the subject’s primary tool, the barcode or persistence diagram, with statistics and machine learning. The persistence landscape is a stable topological summary that is easily combinable with statistical and machine learning technologies. This new summary has various advantages: First, since it is a function, calculations are significantly more quickly than conventional TDA tools. Second, it can be seen as a random variable with values in a Banach space, so it conforms to some statistical theorems such as strong law of large numbers and central limit theorem. Third, it provides a unique average unlike persistence diagrams and barcodes. This thesis is a survey that represents how the persistence landscape is constructed and contributes to the applications.