Researches about theory
5_R. Explain a possibly unified conceptual framework to obtain all most common measures of central tendency and of dispersion using the concept of distance (or “premetric”, or similarity in general). Discuss why it is useful to discuss these concepts introducing the notion of distance. Finally, point out the difference between the mathematical definition of “distance” and the properties of the “premetrics” useful in statistics, pointing out trhe most important distances, indexes and similarity measures used in statistics, data analysis and machine learning (such as for instance; Mahalanobis distance, Euclidean distance, Minkowski distance, Manhattan distance, Hamming distance, Cosine distance, Chebishev distance, Jaccard index, Haversine distance, Sørensen-Dice index, etc.).
Applications
6_A. (For this exercises use only 1 language chosen between C# or VB.NET, according to your preference)
Prepare separately the following charts: 1) Scatterplot, 2) Histogram/Column chart [in the histogram, within each class interval, draw also a vertical colored line where lies the true mean of the observations falling in that class] and 3) Contingency table, using the graphics object and its methods (Drawstring(), MeasureString(), DrawLine(), etc).
Use them to represent 2 numerical variables that you select from a CSV file. In particular, in the same picture box, you will make at least 2 separate charts: 1 dynamic rectangle will contain the contingency table, and 1 rectangle (chart) will contain the scatterplot, with the histograms/column charts and rug plots drawn respectively near the two axis (and oriented accordingly).
Researches about applications
4_RA. Do a personal research about the real world window to viewport transformation, and note separately the formulas and code which can be useful for your present and future applications.
Optional applications
Translate the last exercises 6_A to web browser applications, in plain javascript (no “third party libraries”, check also
https://www.datatime.eu/public/cybersecurity/JSTutorial/ for some progressive examples)
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