The problem of efficiently visualizing multidimensional data sets produced by scientific and statistical tasks/ processes is becoming increasingly challenging, and is attracting the attention of a wide multidisciplinary community of researchers and practitioners. Basically, this problem consists in visualizing multidimensional data sets by capturing the dimensionality of data, which is the most difficult aspect to be considered. Human analysts interacting with high-dimensional data often experience disorientation and cognitive overload. Analysis of high- dimensional data is a challenge encountered in a wide set of real-life applications such as (i) biological databases storing massive gene and protein data sets, (ii) real-time monitoring systems accumulating data sets produced by multiple, multi-rate streaming sources, (iii) advanced Business Intelligence (BI) systems collecting business data for decision making purposes etc. Traditional DBMS front-end tools, which are usually tuple-bag-oriented, are completely inadequate to fulfill the requirements posed by an interactive exploration of high-dimensional data sets due to two major reasons: (i) DBMS implement the OLTP paradigm, which is optimized for transaction processing and deliberately neglects the dimensionality of data; (ii) DBMS operators are very poor and offer nothing beyond the capability of conventional SQL statements, what makes such tools very inefficient with respect to the goal of visualizing and, above all, interacting with multidimensional data sets embedding a large number of dimensions. Despite the above-highlighted practical relevance of the problem of visualizing multidimensional data sets, the literature in this field is rather scarce, due to the fact that, for many years, this problem has been of relevance for life science research communities only, and interaction of the latter with the computer science research community has been insufficient. Following the enormous growth of scientific disciplines like Bio-Informatics, this problem has then become a fundamental field in the computer science academic as well as industrial research. At the same time, a number of proposals dealing with the multidimensional data visualization problem appeared in literature, with the amenity of stimulating novel and exciting application fields such as the visualization of Data Mining results generated by challenging techniques like clustering and association rule discovery. The above-mentioned issues are meant to facilitate understanding of the high relevance and attractiveness of the problem of visualizing multidimensional data sets at present and in the future, with challenging research findings accompanied by significant spin-offs in the Information Technology (IT) industrial field. A possible solution to tackle this problem is represented by well-known OLAP techniques (Codd et al., 1993; Chaudhuri & Dayal, 1997; Gray et al., 1997), focused on obtaining very efficient representations of multidimensional data sets, called data cubes, thus leading to the research field which is known in literature under the terms OLAP Visualization and Visual OLAP, which, in the remaining part of the article, are used interchangeably.
Equation Chapter 1 Section 1 Differentially Private High-Dimensional Binary Data Publication via Adaptive Bayesian Network
