Convex Hulls of Special Euclidean Groups

Don't get bogged down by the heavy sounding title. Let's dissect the title first. "Special Euclidean Group" refers to the Euclidean transform aka the rotation and translation matrix together. Recall that the rotation matrix is a 3x3 matrix (9 numbers in all) but have special structure where the determinant of matrix need to be 1.0 … Continue reading Convex Hulls of Special Euclidean Groups

Alternating Minimization

Alternating minimization, is a simple and easy to implement method to compute minima of a function of 2 more variables. Although this looks like a heuristic, the convergence can be proved if the function you are trying to optimize follows the 5-point-property. In this post I am using the alternating minimization approach to finding numerical … Continue reading Alternating Minimization

Toy Gaussian Mixture Estimation with EM Algorithm

This terms quite often in computer vision related research papers. I am going to toyify it (a core simple explanation). All the code snippets are to be found along with the post. This is roughly a summarization of an excellent youtube-mini-series by Victor Lavrenko. The code snippets are my works. Preliminaries To understand this, you … Continue reading Toy Gaussian Mixture Estimation with EM Algorithm

List of Significant Probability Puzzles

I am collecting a list of probability/statistics/random processes puzzle problems. Click on the links for the description and solutions of the problem. It is well worth the effort to study, understand and derive the solutions to these. Helps sharpen the mind and increase your analysis skill. Please feel free to add your suggestion if I … Continue reading List of Significant Probability Puzzles

Part-3 : Controlling a Mechanical System

This is the third post in my series on control systems. In part-1 we explored what the differential equations can do for you and how to make use of a differential equation, particular the Euler-Lagrange equations to describe a mechanical system. In part-2, we derived these differential equations for our 'pendulum on a cart' system. … Continue reading Part-3 : Controlling a Mechanical System