A glimpse into the Self-Organizing Maps (SOM)

Self-Organizing Maps (SOM) are neural structures proposed for the first time by the computer scientist T. Kohonen in the late 1980s (that’s why they are also known as Kohonen Networks). Their peculiarities are the ability to auto-cluster data according to the topological features of the samples and the approach to…

ML Algorithms addendum: Passive Aggressive Algorithms

Passive Aggressive Algorithms are a family of online learning algorithms (for both classification and regression) proposed by Crammer at al. The idea is very simple and their performance has been proofed to be superior to many other alternative methods like Online Perceptron and MIRA (see the original paper in the…

A Brief (and Comprehensive) Guide to Stochastic Gradient Descent Algorithms

Stochastic Gradient Descent (SGD) is a very powerful technique, currently employed to optimize all deep learning models. However, the vanilla algorithm has many limitations, in particular when the system is ill-conditioned and could never find the global minimum. In this post, we’re going to analyze how it works and the…

Linearly Separable? No? For me it is! A Brief introduction to Kernel Methods

This is a crash-introduction to kernel methods and the best thing to do is starting with a very simple question? Is this bidimensional set linearly separable? Of course, the answer is yes, it is. Why? A dataset defined in a subspace Ω ⊆ ℜn is linearly separable if there exists a (n-1)-dimensional hypersurface…

Hopfield Networks addendum: Brain-State-in-a-Box model

The Brain-State-in-a-Box is neural model proposed by Anderson, Silverstein, Ritz and Jones in 1977, that presents very strong analogies with Hopfield networks (read the previous post about them). The structure of the network is similar: recurrent, fully-connected with symmetric weights and non-null auto-recurrent connections. All neurons are bipolar (-1 and…

ML Algorithms Addendum: Hopfield Networks

Hopfield networks (named after the scientist John Hopfield) are a family of recurrent neural networks with bipolar thresholded neurons. Even if they are have replaced by more efficient models, they represent an excellent example of associative memory, based on the shaping of an energy surface. In the following picture, there’s…

Quickprop: an almost forgotten neural training algorithm

Standard Back-propagation is probably the best neural training algorithm for shallow and deep networks, however, it is based on the chain rule of derivatives and an update in the first layers requires a knowledge back-propagated from the last layer. This non-locality, especially in deep neural networks, reduces the biological plausibility…