Category Archives: Mathematic

Revival of Neural Networks

My actual master studies topic was AI (more then 20 years ago).   Artificial Neural Networks (ANNs) were already known and popular branch of AI and we had some introduction to basics of artificial neural networks (like perceptron, back propagation, etc.). Though it was  quite interesting topic, I had not seen many practical applications in those days.  Recently  I’ve chatted with old friend of mine,  who stayed in university and is involved in computer vision research, about recent advancements in AI and computer vision and he told me that most notable change in last years was that neural networks are being now used in large scale. Mainly due to increase in computing power neural networks now can are applied to many real world problems. Another hint about popularity of neural networks came from my former boss, who shared with me this interesting article –  about privacy issues related to machine learning. I’ve been looking around for a while and it looks like neural networks are becoming quite popular recently – especially architectures with many layers used in so called deep learning. In this article I’d like to share my initial experiences with TensorFlow, open source library (created by Google), which can be used to build modern, multi-layered neural networks. Continue reading Revival of Neural Networks

Voronoi Diagrams

Some time ago I was looking for an algorithms that can generate a ‘map like’ like pictures –  e.g. tessellation of a plane into set of more or less random polygons.    I found Voronoi diagrams –   which give very nice pictures and have many useful properties.
Most common case of Voronoi diagram is known in  an Euclidean plane,   where we have a set of points (call seeds) then Voronoi  diagram splits the plane into areas – called Voronoi cells – around each seed,   where inside each area any point is closer to that seed then to any other.   Areas are then convex polygons (for Euclidean metric). This definition is best illustrated on the picture below – the Voronoi diagram for 100 random points in range 0-100 – Voronoi cells are marked by red lines, blue points are seeds:

voro-100

Continue reading Voronoi Diagrams