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The main focus of this article is on computing the point that minimizes the sum of the "distances" to *n* points in a *d*-dimensional space, called centroid or center, in the presence of outliers.

This long article has several sections.

**Content**

1. A related physics problem

2. Algorithm to find the centroid

- Source code to generate points and compute centroid, using Monte Carlo
- Generating point clouds with simulation

3. Examples and results

4. Convergence of the algorithm

5. Interesting Contour Maps

A lot of material is presented in this article, and chances are that you will find something interesting for you, for instance about

- Several outlier detection techniques
- How to display contour maps and images corresponding to an intensity function or heatmap, in R (in just a few lines of code, and very easy to understand)
- How to produce data sets that simulate clustering structures or other patterns
- Distribution of arrival times for successive records in a time series
- Convergence of Monte Carlo optimization

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