Exploratory analysis of the behavior of time-changing data using advanced linear algebra topics
Análisis exploratorio del comportamiento de datos cambiantes en el tiempo usando tópicos avanzados de álgebra lineal
Author: Omar Oña
Director: Diego Peluffo
Universidad de las Fuerzas Armadas, Sangolquí - Ecuador 2019
Nowadays, the analysis of dynamic or time-varying data is of great interest in science and technology, as it is very useful in several applications, such as: time-series forecasting, video analysis, automatic movement segmentation, among others. In particular, pattern recognition techniques, especially those based on spectral analysis and matrix algebra, have proven to be a suitable alternative. Notwithstanding, there is still a wide range of open issues related to the accuracy and interpretation of the movement segments. This master's thesis presents a study on the use -in time-varying data analysis- of an unsupervised pattern recognition technique, so-called kernel spectral clustering. Specifically, it is of interest the possibility of creating a tracking vector able to automatically segmenting movements in a sequence of video frames, which shows its usefulness in the identification of starting and ending points of movements in rotating objects and moving-contour-lines. Also, this work proves the benefit of the properties, the optimization and the algebra of functions with matrices for the analysis of dynamic data.
Kernel-Spectral-Clustering-Driven Motion Segmentation: Rotating-Objects First Trials (2019)
Automatic Motion Segmentation via a Cumulative Kernel Representation and Spectral Clustering (2017)