Unit:
Κατεύθυνση / ειδίκευση Επεξεργασία-Μάθηση Σήματος και Πληροφορίας (ΕΜΠ)Πληροφορική
Author:
Giannopoulos Michail
Supervisors info:
Θεοδωρίδης Σέργιος, Καθηγητής, Πληροφορικής και Τηλεπικοινωνιών, Ε.Κ.Π.Α.
Original Title:
ROBUST PRINCIPAL COMPONENT ANALYSIS: THEORETICAL ASPECTS AND ALGORITHMIC COMPARATIVE EVALUATION FOR DIMENSIONALITY REDUCTION
Translated title:
ROBUST PRINCIPAL COMPONENT ANALYSIS: THEORETICAL ASPECTS AND ALGORITHMIC COMPARATIVE EVALUATION FOR DIMENSIONALITY REDUCTION
Summary:
In the present master thesis we examine the question of whether the PCA method for dimensionality reduction could become robust vis-à-vis gross errors, and if so which algorithmic scheme from the literature would be the best choice.
In the beginning, we present the classical PCA method, its main ideas, those key properties that have made it so popular, its advantages and its disadvantages.
Afterwards, we state the main theoretical results concerning the possibility of robustyfying the PCA method, as well as some interesting applications of real life in which a robust PCA method could prove extremely useful.
Subsequently, a detailed presentation of the most popular algorithmic schemes designed to tackle this problem takes place, followed by a respective comparative analysis among them based on widely used quality metrics used in this scientific field.
Finally, a case-study inspired by the field of image processing is examined, in order on the one hand to evaluate the performance of the algorithmic schemes studied in the present thesis under tougher experimental circumstances, as well as on the other hand to examine their practical use in realistic applications.
Main subject category:
Technology - Computer science
Keywords:
Principal Component Analysis, sparsity, low-rank matrices, convex optimization, image processing
