The architecture of a business intelligence system, is depicted in three major components.

⎯ Data sources

In the first stage, it is necessary to gather and integrate the data stored in the various primary and secondary sources, which are heterogeneous in origin and type. 

The sources consist for the most part of data belonging to operational systems but may also include unstructured documents, such as emails and data received from external providers.

⎯ Data warehouses and data marts 

Using extraction and transformation tools known as extract, transform, load (ETL), the data originating from the different sources are stored in databases intended to support business intelligence analyses.

⎯ Businessintelligencemethodologies 

Data are finally extracted and used to feed mathematical models and analysis methodologies intended to support decision-makers.In a business intelligence system, several decision support applications may be implemented, most of which will be described in the following chapters: 

• multidimensional cube analysis; 

• exploratory data analysis; 

• time series analysis; 

• inductive learning models for data mining; 

• optimization models. 

⎯ Data exploration 

At the third level of the pyramid, we find the tools for performing a passive business intelligence analysis, which consists of query and reporting systems, as well as statistical methods. 

These are referred to as passive methodologies because decision-makers are requested to generate prior hypotheses or define data extraction criteria, and then use the analysis tools to find answers and confirm their original insight. 

 For instance, consider the sales manager of a company who notices that revenues in a given geographic area have dropped for a specific group of customers. 

Hence, she might want to bear out her hypothesis by using extraction and visualization tools and then apply a statistical test to verify that her conclusions are adequately supported by data. 

 ⎯ Data mining 

The fourth level includes active business intelligence methodologies, whose purpose is the extraction of information and knowledge from data. These include mathematical models for pattern recognition, machine learning, and data mining techniques. 

Unlike the tools described at the previous level of the pyramid, the models of an active kind do not require decision-makers to formulate any prior hypothesis to be later verified. Their purpose is instead to expand the decision makers’ knowledge. 

⎯ Optimization 

By moving up one level in the pyramid we find optimization models that allow us to determine the best solution out of a set of alternative actions, which is usually fairly extensive and sometimes even infinite. 

⎯ Decisions 

Finally, the top of the pyramid corresponds to the choice and the actual adoption of a specific decision, and in some way represents the natural conclusion of the decision-making process. 

Even when business intelligence methodologies are available and successfully adopted, the choice of a decision pertains to the decision-makers, who may also take advantage of informal and unstructured information available to adapt and modify the recommendations and the conclusions achieved through the use of mathematical models.

As we progress from the bottom to the top of the pyramid, business intelligence systems offer increasingly more advanced support tools of an active type. 

Even roles and competencies change. At the bottom, the required competencies are provided for the most part by the information systems specialists within the organization, usually referred to as database administrators. Analysts and experts in mathematical and statistical models are responsible for the intermediate phases. 

Finally, the activities of decision-makers responsible for the application domain appear dominant at the top. As described above, business intelligence systems address the needs of different types of complex organizations, including agencies of public administration and associations. 

However, if we restrict our attention to enterprises, business intelligence methodologies can be found mainly within three departments of a company, as depicted in logistics and production accounting and control. 

 ⎯ A business intelligence system provides decision-makers with information and knowledge extracted from data, through the application of mathematical models and algorithms. 

In some instances, this activity may reduce to calculations of totals and percentages, graphically represented by simple histograms, whereas more elaborate analyses require the development of advanced optimization and learning models. 

⎯ In general terms, the adoption of a business intelligence system tends to promote a scientific and rational approach to the management of enterprises and complex organizations. Even the use of a spreadsheet to estimate the effects on the budget of fluctuations in interest rates, despite its simplicity, forces decision-makers to generate a mental representation of the process of the financial flow. 

⎯ Classical scientific disciplines, such as physics, have always resorted to mathematical models for the abstract representation of real systems. Other disciplines, such as operations research, have instead exploited the application of scientific methods and mathematical models to the study of artificial systems, for example,  public and private organizations. Part II of this book will describe the main mathematical models used in business intelligence architectures and decision support systems, as well as the corresponding solution methods, while PartIIIwill illustrates several related applications. 

⎯ The rational approach typical of a business intelligence analysis can be summarized schematically in the following main characteristics. 

⎯ First, the objectives of the analysis are identified and the performance indicators that will be used to evaluate alternative options are defined. ⎯ Mathematical models are then developed by exploiting the relationships among system control variables, parameters, and evaluation metrics. ⎯ Finally, what-if analyses are carried out to evaluate the effects on the performance determined by variations in the control variables and changes in the parameters. 

⎯ Although their primary objective is to enhance the effectiveness of the decision-making process, the adoption of mathematical models also affords other advantages, which can be appreciated particularly in the long term. First, the development of an abstract model forces decision-makers to focus on the main features of the analyzed domain, thus inducing a deeper understanding of the phenomenon under investigation. Furthermore, the knowledge about the domain acquired when building a mathematical model can be more easily transferred in the long run to other individuals within the same organization, thus allowing sharper preservation of knowledge in comparison to empirical decision-making processes. Finally, a mathematical model developed for a specific decision-making task is so general and flexible that in most cases it can be applied to other ensuing situations to solve problems of similar type.

 • Several public and private enterprises and organizations have developed in recent years formal and systematic mechanisms to gather, store and share their wealth of knowledge, which is now perceived as an invaluable intangible asset. 

• The activity of providing support to knowledge workers through the integration of decision-making processes and enabling information technologies is usually referred to as knowledge management. Similarity 

• It is apparent that business intelligence and knowledge management share some degree of similarity in their objectives. The main purpose of both disciplines is to develop environments that can support knowledge workers in decision-making processes and complex problem-solving activities. 

• To draw a boundary between the two approaches, we may observe that knowledge management methodologies primarily focus on the treatment of information that is usually unstructured, at times implicit, contained mostly in documents, conversations, and past experience. Dissimilarity 

• Conversely, business intelligence systems are based on structured information, most often of a quantitative nature and usually organized in a database. 

 • However, this distinction is a somewhat fuzzy one: for example, the ability to analyze emails and web pages through text mining methods progressively induces business intelligence systems to deal with unstructured information.

 Data 

⎯ As observed above, a vast amount of data has been accumulated within the information systems of public and private organizations. 

These data originate partly from internal transactions of an administrative, logistical and commercial nature and partly from external sources.

 ⎯ However, even if they have been gathered and stored in a systematic and structured way, these data cannot be used directly for decision-making purposes. 

They need to be processed by means of appropriate extraction tools and analytical methods capable of transforming them into information and knowledge that can be subsequently used by decision-makers.

⎯ The difference between data, information, and knowledge can be better understood through the following remarks.

 ⎯ Data. Generally, data represent a structured codification of single primary entities, as well as of transactions involving two or more primary entities. 

For example, for a retailer data refer to primary entities such as customers, points of sale, and sale items, while sales receipts represent the commercial transactions.

Information 

Knowledge

The main purpose of business intelligence systemsisto provides knowledge workers with tools and methodologies that allow them to make effective and timelydecisions.

Effective decisions

Timely decisions

Effective and timely decisions

Principal component analysis (PCA) is the most widely known technique of attribute reduction by means of projection. 

Generally speaking, the purpose of this method is to obtain a projective transformation that replaces a subset of the original numerical attributes with a lower number of new attributes obtained as their linear combination, without this change causing a loss of information. 

Experience shows that a transformation of the attributes may lead to many instances of better accuracy in the learning models subsequently developed.

Before applying the principal component method, it is expedient to standardize the data, so as to obtain for all the attributes the same range of values, usually represented by the interval [−1, 1]. Moreover, the mean of each attribute aj is made equal to 0 by applying the transformation Let X denote the matrix resulting from applying the transformation (6.6) to the

X be the covariance matrix of the attributes (for original data, and let V = X )

a definition of the covariance and variance matrices, see Section 7.3.1). If the correlation matrix is used to develop the principal component analysis method

instead of the covariance matrix, the transformation (6.6) is not required. Starting from the n attributes in the original dataset, represented by the matrix X, the principal component method derives n orthogonal vectors, namely the principal components, which constitute a new basis of the space Rn. 

Principal components are better suited than the original attributes to explain fluctuations in the data, in the sense that usually a subset consisting of q principal components, with q<n, has an information content that is almost equivalent to that of the original dataset. As a consequence, the original data are projected into a lower-dimensional space of dimension q having the same explanatory capability.

Principal components are generated in sequence by means of an iterative algorithm. The first component is determined by solving an appropriate optimization problem, in order to explain the highest percentage of variation in the data. 

At each iteration, the next principal component is selected, among those vectors that are orthogonal to all components already determined, as the one which explains the maximum percentage of variance not yet explained by the previously generated components. At the end of the procedure, the principal components are ranked in non-increasing order with respect to the amount of variance that they are able to explain.