A Super-Dimension Approach in ROLAP Environments

Often the designer of ROLAP applications follows up with the question “can I create a little joiner table with just the two dimension keys and then connect that table to the fact table?” In a classic dimensional model there are two options - (a) both dimensions are modeled independently or (b) two dimensions are combined into a super-dimension with a single key. The second approach is not widely used in ROLAP environments but it is an important sparsity handling method in MOLAP systems. In ROLAP this design technique can also bring storage and performance benefits, although the model becomes more complicated. The dependency between dimensions is a key factor that the designers have to consider when choosing between the two options. In this paper we present the results of our storage and performance experiments over a real life data cubes in reference to these design approaches. Some conclusions are drawn.

A Taxonomy of Big Data for Optimal Predictive Machine Learning and Data Mining

Big data comes in various ways, types, shapes, forms and sizes. Indeed, almost all areas of science, technology, medicine, public health, economics, business, linguistics and social science are bombarded by ever increasing flows of data begging to be analyzed efficiently and effectively. In this paper, we propose a rough idea of a possible taxonomy of big data, along with some of the most commonly used tools for handling each particular category of bigness. The dimensionality p of the input space and the sample size n are usually the main ingredients in the characterization of data bigness. The specific statistical machine learning technique used to handle a particular big data set will depend on which category it falls in within the bigness taxonomy. Large p small n data sets for instance require a different set of tools from the large n small p variety. Among other tools, we discuss Preprocessing, Standardization, Imputation, Projection, Regularization, Penalization, Compression, Reduction, Selection, Kernelization, Hybridization, Parallelization, Aggregation, Randomization, Replication, Sequentialization. Indeed, it is important to emphasize right away that the so-called no free lunch theorem applies here, in the sense that there is no universally superior method that outperforms all other methods on all categories of bigness. It is also important to stress the fact that simplicity in the sense of Ockham’s razor non-plurality principle of parsimony tends to reign supreme when it comes to massive data. We conclude with a comparison of the predictive performance of some of the most commonly used methods on a few data sets.