Science

sepdek February 16, 2018

Clustering is an important category of machine learning methods and a main form of unsupervised learning. Clustering is essentially distinctive and substantially different from the other dominant form of machine learning, classification, in that it does not rely on training (supervised learning). In principle, clustering represents any method that tries to identify and distinguish groups […]

sepdek January 23, 2018

This post serves as a practical approach towards a vectorized implementation of the Expectation Maximization (EM) algorithm mainly for MATLAB or OCTAVE applications. EM is a really powerful and elegant methods for finding maximum likelihood solutions in cases where the hypothesis involves a gaussian mixture model and latent variables. Introduction EM is connected with the […]

sepdek October 13, 2016

This post serves as a cheat sheet for differentiation. It just includes the most basic of the rules to be remembered when computing derivatives. First a little reminder on the notation being used in differentiation. Leibniz’s notation for the first derivative of a function f(x) is Newton’s notation for the first derivative of a function […]

sepdek October 12, 2016

There is a really large number of applications in engineering, in which the identification of critical points of a function is crucial for the analysis and modeling of a process or a system. Generally, one may identify three kinds of critical points, that is (a) maxima, (b) minima and (c) saddle or stationary inflection points. […]

sepdek October 9, 2016

A function is a rule that maps each of the elements in a domain to one and only one element in a range. The set of all possible elements in the input is the domain D of a function; the set of all possible elements in the output is the range R of a function. […]

sepdek October 8, 2016

Formally stated, the derivative of a function of the form with k a constant and with respect to an independent variable x, is simply, I find this to be extremely handy in all cases. Consider the simple case in which, In the same way, In a more complex example, In an even more complex example, […]

sepdek October 8, 2016

The thing starts with invariance, conservation and symmetry… Invariant is something that is unchanged by a coordinate transformation. Conserved is something that is unchanged by a process within a given coordinate system. Symmetry could be considered a broader property of some ‘universe’ in which some entity of interest remains the same under a specific operation. […]

sepdek October 8, 2016

In order to be a measure (distance) d must:   In order to be a metric (distance) d has to be a measure and:   …and here is the cheat sheet:  

sepdek July 17, 2015

DIGITAL TECHNOLOGIES IN CULTURAL HERITAGE & TOURISM 11 Days equivalent workload to 130 hours (incl. 20 hours essay), 5 ECTS 30 July – 10 August 2015 Delphi, Greece Complete summer school programme. COURSE: Introduction, current state-of-the-art, innovation, trends UNIT: Innovative applications of technology in cultural heritage and trends for future research and development PDF edition […]

sepdek May 15, 2014

It has been many years working on digitization, reconstruction and virtual world applications; tested and used various techniques covering almost all aspects in the digital recording workflow. In the recent past years our team has been successfully engaged in a very productive workflow regarding digitization and reconstruction in 3D. Specifically, this workflow involved the application […]