Systems Engineering Neural Networks

8Cost Function, Back-Propagation and Other Iterative Methods

Dimensional models implemented in relational database management systems are referred to as star schemas because of their resemblance to a star-like structure. Dimensional models implemented in multidimensional database environments are referred to as online analytical processing (OLAP)[…]. Both stars and cubes have a common logical design with recognizable dimensions; however, the physical implementation differs. When data is loaded into an OLAP cube, it is stored and indexed using formats and techniques that are designed for dimensional data. Performance aggregations or precalculated summary tables are often created and managed by the OLAP cube engine. Consequently, cubes deliver superior query performance because of the precalculations, indexing strategies, and other optimizations […]. The downside is that you pay a load performance price for these capabilities, especially with large data sets.

Ralph Kimball, The Data Warehouse Toolkit: The Definitive Guide to Dimensional Modelling

In this chapter, we will introduce loss or cost functions allowing us to measure the error of the network while it is evaluating, classifying or predicting a specific event starting from a set of data.

Using a mathematical approach, we will find the minimum value that these functions can reach and define the network's ability to get as close to reality as possible - the smaller the error, the better the ability of the network to describe ...