Abstract
Nowadays, huge size data-sets are commonly publicly available, and it becomes increasingly important to eefficiently process them to discover worthwhile structures (or “patterns”) in those seas of data. Exploratory data analysis is concerned with this challenge of finding such structural information without any prior knowledge: in this case, those techniques that consist in learning from data without prior knowledge are called generically unsupervised machine learning.
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Notes
- 1.
Available online at https://archive.ics.uci.edu/ml/datasets.html.
- 2.
- 3.
Otherwise, we can choose the “smallest” x that yields the minimum value according to some lexicographic order on \({\mathbb {X}}\).
- 4.
- 5.
Freely available online at https://www.r-project.org/.
- 6.
The 3 -SAT problem consists in answering whether a boolean formula with n clauses of 3 literals can be satisfiable or not. 3-SAT is a famous NP-complete problem (Cook’s theorem, 1971), a corner stone of theoretical computer science.
- 7.
The number of distinct partitions of a set of n elements into k non-empty subsets is defined by the second kind of Stirling number: \(\left\{ \begin{matrix} n \\ k \end{matrix}\right\} = \frac{1}{k!}\sum _{j=0}^{k} (-1)^{k-j}\left( {\begin{array}{c}k\\ j\end{array}}\right) j^n\).
- 8.
Vertical partitioning means that each entity has only a block of attributes.
- 9.
It is mathematically always possible to separate data by increasing by lifting the features into higher dimensions using a kernel mapping.
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Nielsen, F. (2016). Partition-Based Clustering with k-Means. In: Introduction to HPC with MPI for Data Science. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-21903-5_7
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