Chapter 3. The Multidimensional Model: Basic Concepts. Introduction. The multidimensional model. The multidimensional model

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1 Chapter 3 The Multidimensional Model: Basic Concepts Introduction Multidimensional Model Multidimensional concepts Star Schema Representation Conceptual modeling using ER, UML Conceptual modeling using DFM Logical Relational modeling Physical modeling (Oracle) 56 Introduction Why a new Data Model? Do conventional data models (E/R, UML Class diagram, relational model) are not effective for DWing? These data models have inconvenient: Centered on operational data (daily activities: Transactions) Ignore Decision-makers requirements (Statistical analysis) Complex, technical Not easy for use by D-Makers directly Need new model (and approach) for DW: Support the DSS Takes into consideration Decision-maker: ad-hoc Analytical requirements Encourages D-makers to use then in a stand-alone mode, without being assisted by IT technicians 57 The multidimensional model The multidimensional model The Multidimensional Model (MM) is specific for Data Warehouses MM models data for Decisional Analyses and Data Mining purposes Examples: Decisional Analyses Total of sold quantities of products by month Average amount of sold products by month and by region Sum of daily sales ( & quantity) of products by employee Total of quantities of sold products per client and per city These examples analyze the according to many criteria Month, Region, Employee, client, City How this data should be modelled? 58 The multidimensional model considers a subject (i.e., an activity to be analyzed) as a point in a multidimensional space where data is organized in order to highlight the subject and its n (n 2) axes of analysis: Star schema. D1: What? D2: Where? D4: Who?... Fact D3: When? 1 Subject: is the activity to be analyzed, called Fact n Dimensions: The axes for recording and analyzing the Subject; they answer questions like: What Where When Who Etc. 59 1

2 The multidimensional model The multidimensional model considers a subject (i.e., an activity to be analyzed) as a point in a multidimensional space where data is organized in order to highlight the subject and its n (n 2) axes of analysis: Star schema. D1: What? D2: Where? D4: Who?... Fact D3: When? 1 Subject: is the activity to be analyzed, called Fact : n Dimensions: The axes for recording and analyzing the Subject; they answer questions like: What : PRODUCT Where: PLACE of Sale When: Who Etc. The multidimensional model The DFM (The Multidimensional Fact Model) is just a graphical conceptual model based on the MM. It is created specifically to function as data mart support. The goals of the DFM are to Bring effective support to conceptual design Create an environment in which user queries may be formulated intuitively Facilitate communication between designers & end users with the goal of formalizing requirement specifications Enable early testing & verification of user requirements Build a stable platform for logical design Provide clear & expressive design documentation. These characteristics make the DFM a good candidate for use in real DW applications. In the remaining of this course we use the DFM for the graphical representation of the Multidimensional concepts Basic The multidimensional Concepts model The Multidimensional Model has two main concepts Fact & Dimension They are useful for designing Multidimensional schemas as Star schema, Constellation schema,... Fact A fact is a concept relevant to Decision-Making processes, and it typically models a set of events (i.e., Activity) taking place within a company. A fact must evolve over time. Examples of facts In the Commercial domain: Sales, Shipments, Purchases, Complaints In the Academic domain: RESULTS of students; The multidimensional Concepts Basic Concepts Measure A Measure is a fact attribute. It is an indicator of the business activity, often numeric to be summarizable (aggregated using Sum, Avg, Min, Max ). Examples Measures of the fact : sold, of sale, Measures of the fact RESULTS of students: Grade, Appreciation

3 The multidimensional Concepts DFM Graphical representation FACT_NAME Measure 1 Measure 2 Dimension A Dimension is an Axis for analyzing the fact s measures. It is composed of n (n>0) attributes. Examples RESULTS of students, Grade is a measure, RESULTS Grade of products,, Measures are Measure Granularity: Within a fact, Measures are recorded (and later aggregated) according to a set of criteria organized as axes called Dimensions. Measure Measure n Measures (or indicators) 64 DFM Graphical representation Example In the Commerce: PRODUCT, CLIENT, In the Academic : STUDENT, COURSE, SEMESTER DIM_NAME Attribute 1 Attribute 2 Attribute n 65 Star Schema: First draft Advantages Simple diagram Subject highlighted Axes of analyses highlighted Easy for use by D-Makers Dimension: DFM Notation We distinguish the attributes of a dimension into two types: parameters and Weak attributes: A Parameter represents a hierarchical level according to which measures can be aggregated. Drawbacks Dimensions do not explicit the analyses levels Necessity to improve the model CLIENTS ID-C Fname Lname City Country Example: Product-ID,, A Weak attribute, is a textual Descriptor associated with a parameter; useful to label the results of analysis. Example: Product_

4 A Hierarchy is a tree whose nodes are dimensional attributes and whose arcs model many-to-many associations between dimensional attribute pairs. Hierarchies: DFM Notation Hierarchy for the Dimension Hierarchy Parameters (levels) Hierarchy for the Dimension Example 1: Hierarchy of the PRODUCT dimension Product-ID ory a Hierarchy semantically organizes a subset of parameters of dimension d from the finest (e.g. Product-ID) to the highest granularity.(e.g., ) Example 2: Organize the dimension attributes (Month,, Semester, Quarter) into a hierarchy.. 68 Weak Attribute The length of a hierarchy is the number of its parameters Weak Attributes 69 Hierarchy Instance H_CATEGORY hierarchy Star Schema: A complete example (DFM Notation) This H_CATEGORY hierarchy instance has:.. Products... ories.. Categories F L CLIENTS ID-C City Country

5 Star Schema Data Cube= Schema + Content Libanon France Italy CLIENTS.Country C3 C2 C1. P CLIENTS ID-C F City L Country 72 Star Schema specification S = ( S, F, <D 1,, D x >) where: S is the name of the star schema F = ( F, {m 1, m 2,, m u }) is its fact D = ( D, {p 1, p 2,, p v }, <H 1, H 2,, H w >) dimension among the x dimensions of S H = ( H, <p 1 :{wa: }, p 2 :{wa: }, p n :{wa: }> with 1 n v {wa: } is a possibly emty set of weak attributes separated with colon (:) 73 a Example S = ( SAnalyse', F, < D 1, D 2, D 3 >) F = ( ', {, }) D 1 = ('', {, :, }, <H 1 >) D 2 = ('', {: P:,, }, <H 2 >) D 3 = ('CLIENTS', {ID-C: Fname: L, City, Country}, <H 3 >) H 1 = ('H_YEAR', <, :, >) H 2 = ('H_PROD', <: :,, >) H 3 = ('H_CLI', <ID-C: Fname: L, City, Country>) Note that in a star schema: All dimensions are directly related to the Fact. The relationships from Dimension to Fact is One-To-Many. The Fact contains "measures" (usually numeric) to be aggregated through Dimensions. A Dimension contains criteria level-organized for aggregating the fact measures. Practical tips: The identifier issued from an operational system should not be used i as a key; instead use an artificial identifier commonly known as Surrogate key or DW-key

6 Practical tips (continued): The identifier issued from an operational system should not be used as a key; instead use an artificial identifier commonly known as Surrogate key or DW-key. The granularity of Dimensions and the Fact must be the same: Imagine that the Fact contains information for hours and the Time dimension manages minutes, it will not be possible to link the Time dimension with facts (multi determination). Each row in the fact table must have a relationship with each dimension table: otherwise, there would be a loss of information or an incorrect analysis. We never have relationships between dimensions. It would be too complicated to manage. The schema must be easy to understand by non-it (i.e., decision-makers ) in order to exploit. Star Schema: Design Steps Define the Schema Structure Identify the Fact Identify Dimensions Define completely the Fact: Identify Measures (, Description, Extraction formula ) Define completely each Dimension: Identify Parameters (name, type ) Specify Hierarchies A precise knowledge of the domain is required (i.e., geography ) Analysis of values from the source (Product, Sub- Categories) Associate Weak attributes with Parameters of hierarchies Snowflake Schema It is an extension of the Star schema, where each dimension is normalized and therefore splits into multiple tables each representing a level in the dimensional hierarchy. Benefits: 1. Highlights the analyses levels 2. No redundancy. Disadvantages: 1. Many Joins. Snowflake Schema: Example CATEGORY ID-Ca SUB_CATEGORY ID-SCa ID-Ca# ID-SCa# # # ID-C# YEAR ID- MONTH ID-# # CLIENT ID-C Fname Lname Id-CT# CITY ID-CT City COUNTRY ID-CT# ID-CT Country

7 Constellation Schema The constellation schema is a group of star schemas having n (n 2) shared dimensions. Benefits: 1. Brings together two related facts thus facilitating the analysis and interpretation of one of them referring to the other. 2. Shared dimensions are stored once: less ETL efforts. Give example of shared dimension : 80 7