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This is obviously a very open ended question, but so as to stay on topic, here is one CS theory approach to the idea of "fairness" and how to enforce it. "Fairness Through Awareness" Dwork, Hardt, Pitassi, Reingold, Zemel http://arxiv.org/abs/1104.3913


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The bound is $2^{\min(n, m)}$. It is an upper bound because no two "formal concepts" (i.e., closed itemsets with their respective transaction sets) can have the same subset of items or the same subset of transactions. Considering $D$ as an $n$ by $m$ matrix of $0$ or $1$ such that each cell indicates whether item $i$ is part of the $j$-th transaction of $D$, ...


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A range space is just a pair $(X,\mathcal{R})$ where $X$ is a finite or infinite set and a $\mathcal{R}$ is a finite or infinite collection of subsets of $X$ (the elements of $\mathcal{R}$ are called "ranges"). Note that a range space is not used to "represent" the VC-dimension (whatever meaning of "represent" you are using). Rather, the VC-dimension is a ...


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As told in the previous comments, $min\{2^{|O|}, 2^{|A|}\}$ is a correct upper bound. When the parameter $R$ is also available, we can improve the upper bound to $min\{2^{|O|}, 2^{|A|}, 2^{1+\sqrt{|R|}}\}$


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Visualization of clusters. The same ordered display can be used for illustrating the clustering density in different regions of the data space. The density of the reference vectors of an organized map will reflect the density of the input samples [Kohonen, 1995c, Ritter, 1991]. In clustered areas the reference vectors will be close to each other, and in the ...


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