Stability of Clustering under the Empirical Risk Minimization (ERM) Scheme with Infinite Large Dataset

This project studies the stability of clustering algorithms under infinite large dataset. Usually, people use the stability of clustering as a metric to tune parameters (e.g. number of clusters) in clustering algorithms. However, Ben-David and Luxburg showed that the stability of clustering is determined by the data structure and unrelated to clustering parameters, and thus using stability to tune clustering parameters seemed questionable. This project summarizes stability theorems from Ben-David and Luxburg's work and demonstrates stability behaviors using the k-means algorithm. This is part of the course project from ECE 543 - Statistical Learning Theory. [project paper] [project slides] - Posted on May 29, 2017

Expectation Maximization for Medical Imaging Reconstruction

An introduction of MLEM (maximum likelihood expectation maximization) algorithm for medical imaging reconstruction (emission tomography such as PET and SPECT). The MLEM algorithm for emmision image reconstruction was originally developed by Shepp and Vardi in 1982. This blog will explain this method under the expectation maximization framework that we introduced in the previous post.- Feb 12, 2017

Modeling Background Radiation with Hidden Markov Model

This project demonstrates the usage of Hidden Markov Model (HMM) in radiation modeling. Real radiation measureemnts are acquired, and a Poisson HMM is used to model the fluctuation of radiation mean values. This is part of the course project from STAT 555 - Applied Stochastic Processes - Posted on Dec 04, 2016

A Primer on Expectation Maximization

An easy introduction of maximum likelihood estimation (MLE) and expectation maximization (EM). In this blog, I will explain the basic structure of EM algorithm and also show how EM algorithm actually maximizes the likelihood through iterations. - Nov 13, 2016