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Machine Learning: concepts & procedures
Machine Learning: fundamental algorithms
Machine Learning: model assessment
Artificial neural networks
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The computer science appendix
Some geometry

# Voronoi tasselation

The Voronoi tasselation consists in partitioning the plane into regions based on the distance to points in a specific subset of the plane.
For each point, there is a region of all points closer to it than any other one (Voronoi cells).

# Simplex

A simplex is the generalisation of a triangle/tetrahedron to an arbitrary number of dimensions. The k simplex is a k-dimensional polytope, the convex hull of its k+1 vertices.
Given points
$u_0, \ldots, u_k \in \mathbb{R}^k$
, with
$u_1 - u_0, \ldots, u_k - u_0$
linearly independent, the simplex determined by them is the set of points
$C : {\theta_0 u_0 + \cdots + \theta_k u_k | \theta_i \geq 0, 0 \leq i \leq k, \sum_{i=0}^k \theta_i = 1}$
the 2-simplex is a triangle;
the 3-simplex is a tetrahedron;
the 4-simplex is a 5-cell