Developed a community detection algorithm using Heat Kernel and PageRank-based diffusion. Implemented in Python using NetworkX and Scipy.
Built regression models using graph-based SDE learning on UCI Energy Efficiency dataset.
My thesis project acknowledges the complex behavior of time series data, renowned for its inherent chaotic nature and inclination toward sudden, significant high jumps. To address such intricate data, the incorporation of Stochastic Differential Equations (SDEs) with noise can be done to accurately represent the data and its inherent traits. To better comprehend the distribution sustained by the data, the thesis explores the realms of stable distribution, which is majorly relevant for data exhibiting heavier tails. Therefore, this thesis highlights the utility of modeling white noise within the framework of a non-Gaussian distribution governed by L´evy motion. In this context, it proposes the use of alpha-stable L´evy motion due to its remarkable ability to closely mirror the data’s characteristics. Thus harmonizing the noise modeling process with the data’s intricate dynamics. This thesis aims at the techniques proposed in various research papers, discerning the most effective approach to analyze financial time series data. In addition, it also outlines the major improvements and future implementation in this domain.