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Geometry Meets Attention: Understanding SVDA from the Ground Up Based on our newly (2025) published IEEE Access paper: Geometry Meets Attention: Interpretable Transformers via SVD Inspiration Self-attention is the engine behind modern Transformers, but standard dot-product attention is a black box. Why does a model attend to certain tokens? Can we understand what dimensions matter […]

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’. […]

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 […]