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Probability, statistics and data analysis

Machine Learning: concepts & procedures

Machine Learning: fundamental algorithms

Machine Learning: model assessment

Artificial neural networks

Natural language processing

The computer science appendix

The mathematics 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

References

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