@sepdek's

Recognising the value of light in life, humans throughout history devised ways of capturing the images created by light, while, at the same time, wondering and exploring the very nature of this magical element, sometimes using science, sometimes using logic and philosophy, and sometimes relying on feeling and superstition. What is certain is that light […]

Definition Typically, three Pythagorean means are defined and constitute the classical means used in various scientific fields; they are the arithmetic mean, the geometric mean, and the harmonic mean. Pythagoreans are reported to have first studied these means, along with later generations of Greek mathematicians, and this is why the means got the name ‘Pythagorean’. […]

A Brief History of Colour Theory tells the story of almost two and a half millennia, written by protagonists of a variety of characters. In the era of philosophy, colour science was founded upon logic, experience and philosophical worldviews. During the middle ages, the theory shifted towards experimental verification, although still strongly influenced by personal […]

In a recent post (Analysis of live COVID-19 data – a MATLAB/Octave approach) I described how it is possible to analyse live COVID-19 data from reliable online data sources and create intuitive graphical representations. Apparently, this task is also simple when using Python programming language. To this end, a Colab Python notebook was created to […]

Analysis of (time-series) data being collected in (near) realtime often provides insight for a process underway. As the current situation with COVID-19 is still critical lots of data are being collected, curated and streamed throughout the world, and researchers strive to get the most out of them to identify patterns and, maybe, make predictions. In […]

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 […]

Of the most basic forms of a machine learning system based on neural networks is the one in which training is accomplished using back error propagation, or simply back-propagation. Back-propagation is a technique, like many others, that targets the minimisation of a cost function during a learning process by following the descending gradient of the […]

Machine learning is a research domain that is becoming the holy grail of data science towards the modelling and solution of science and engineering problems. I have already witnessed researchers proposing solutions to problems out of their area of expertise using machine learning methods, basing their approach on the success of modern machine learning algorithm […]

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 method for finding maximum likelihood solutions in cases where the hypothesis involves a gaussian mixture model and latent variables. Introduction EM is connected with the […]

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 […]

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. […]

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. […]