Data Mining Data Warehousing January 2, 2023 1

Data Mining Data Warehousing January 2, 2023 1

Data Warehousing and OLAP Technology for Data Mining What is a data warehouse? A multi-dimensional data model Data warehouse architecture Data warehouse implementation From data warehousing to data mining January 2, 2023 2

What is Data Warehouse? Defined in many different ways, but not rigorously. A decision support database that is maintained separately from the organization’s operational database Supports information processing by providing a solid platform of consolidated, historical data for analysis. “A data warehouse is a subject-oriented, integrated, time-variant, and nonvolatile collection of data in support of management’s decision-making process.”—W. H. Inmon Data warehousing: The process of constructing and using data warehouses January 2, 2023 3

Data Warehouse—SubjectOriented Organized around major subjects, such as customer, product, sales. Focusing on the modeling and analysis of data for decision makers, not on daily operations or transaction processing. Provide a simple and concise view around particular subject issues by excluding data that are not useful in the decision support process. January 2, 2023 4

Data Warehouse—Integrated Constructed by integrating multiple, heterogeneous data sources relational databases, flat files, on-line transaction records Data cleaning and data integration techniques are applied. Ensure consistency in naming conventions, encoding structures, attribute measures, etc. among different data sources E.g., Hotel price: currency, tax, breakfast covered, etc. When data is moved to the warehouse, it is converted. January 2, 2023 5

Data Warehouse—Time Variant The time horizon for the data warehouse is significantly longer than that of operational systems. Operational database: current value data. Data warehouse data: provide information from a historical perspective (e.g., past 5-10 years) Every key structure in the data warehouse Contains an element of time, explicitly or implicitly But the key of operational data may or may not contain “time element”. January 2, 2023 6

Data Warehouse—Non-Volatile A physically separate store of data transformed from the operational environment. Operational update of data does not occur in the data warehouse environment. Does not require transaction processing, recovery, and concurrency control mechanisms Requires only two operations in data accessing: January 2, 2023 initial loading of data and access of data. 7

Data Warehouse vs. Heterogeneous DBMS Traditional heterogeneous DB integration: Build wrappers/mediators on top of heterogeneous databases Query driven approach When a query is posed to a client site, a meta-dictionary is used to translate the query into queries appropriate for individual heterogeneous sites involved, and the results are integrated into a global answer set Data warehouse: update-driven, high performance Information from heterogeneous sources is integrated in advance and stored in warehouses for direct query and analysis January 2, 2023 8

Data Warehouse vs. Operational DBMS OLTP (on-line transaction processing) Major task of traditional relational DBMS Day-to-day operations: purchasing, inventory, banking, manufacturing, payroll, registration, accounting, etc. OLAP (on-line analytical processing) Major task of data warehouse system Data analysis and decision making Distinct features (OLTP vs. OLAP): User and system orientation: customer vs. market Data contents: current, detailed vs. historical, consolidated Database design: ER application vs. star subject View: current, local vs. evolutionary, integrated Access patterns: update vs. read-only but complex queries January 2, 2023 9

OLTP vs. OLAP OLTP OLAP users clerk, IT professional knowledge worker function day to day operations decision support DB design application-oriented subject-oriented data current, up-to-date detailed, flat relational isolated repetitive historical, summarized, multidimensional integrated, consolidated ad-hoc lots of scans unit of work read/write index/hash on prim. key short, simple transaction # records accessed tens millions #users thousands hundreds DB size 100MB-GB 100GB-TB metric transaction throughput query throughput, response usage access January 2, 2023 complex query 10

Why Separate Data Warehouse? High performance for both systems DBMS— tuned for OLTP: access methods, indexing, concurrency control, recovery Warehouse—tuned for OLAP: complex OLAP queries, multidimensional view, consolidation. Different functions and different data: missing data: Decision support requires historical data which operational DBs do not typically maintain data consolidation: DS requires consolidation (aggregation, summarization) of data from heterogeneous sources data quality: different sources typically use inconsistent data representations, codes and formats which have to be reconciled January 2, 2023 11

Data Warehousing and OLAP Technology for Data Mining What is a data warehouse? A multi-dimensional data model Data warehouse architecture Data warehouse implementation From data warehousing to data mining January 2, 2023 12

Conceptual Modeling of Data Warehouses Modeling data warehouses: dimensions & measures Star schema: A fact table in the middle connected to a set of dimension tables Snowflake schema: A refinement of star schema where some dimensional hierarchy is normalized into a set of smaller dimension tables, forming a shape similar to snowflake Fact constellations: Multiple fact tables share dimension tables, viewed as a collection of stars, therefore called galaxy schema or fact constellation January 2, 2023 13

Example of Star Schema time item time key day day of the week month quarter year Sales Fact Table time key item key branch key branch branch key branch name branch type location key units sold dollars sold avg sales item key item name brand type supplier type location location key street city province or street country Measures January 2, 2023 14

Example of Snowflake Schema time time key day day of the week month quarter year item Sales Fact Table time key item key branch key branch location key branch key branch name branch type units sold dollars sold avg sales Measures January 2, 2023 item key item name brand type supplier key supplier supplier key supplier type location location key street city key city city key city province or street country 15

Example of Fact Constellation time time key day day of the week month quarter year item Sales Fact Table time key item key item key item name brand type supplier type location key branch key branch name branch type units sold dollars sold avg sales Measures January 2, 2023 time key item key shipper key from location branch key branch Shipping Fact Table location to location location key street city province or street country dollars cost units shipped shipper shipper key shipper name location key shipper type 16

Measures: Three Categories distributive: if the result derived by applying the function to n aggregate values is the same as that derived by applying the function on all the data without partitioning. algebraic: if it can be computed by an algebraic function with M arguments (where M is a bounded integer), each of which is obtained by applying a distributive aggregate function. E.g., count(), sum(), min(), max(). E.g., avg(), min N(), standard deviation(). holistic: if there is no constant bound on the storage size needed to describe a subaggregate. January 2, 2023 E.g., median(), mode(), rank(). 17

A Concept Hierarchy: Dimension (location) all all Europe region country city office January 2, 2023 Germany Frankfurt . . . Spain North America Canada Vancouver . L. Chan . Mexico Toronto . M. Wind 18

View of Warehouses and Hierarchies January 2, 2023 19

From Tables and Spreadsheets to Data Cubes A data warehouse is based on a multidimensional data model which views data in the form of a data cube A data cube, such as sales, allows data to be modeled and viewed in multiple dimensions Dimension tables, such as item (item name, brand, type), or time(day, week, month, quarter, year) Fact table contains measures (such as dollars sold) and keys to each of the related dimension tables In data warehousing literature, an n-D base cube is called a base cuboid. The top most 0-D cuboid, which holds the highest-level of summarization, is called the apex cuboid. The lattice of cuboids forms a data cube. January 2, 2023 20

Multidimensional Data Sales volume as a function of product, month, and region Dimensions: Product, Location, Time Hierarchical summarization paths Re gi on Industry Region Year Product Category Country Quarter Product City Office Month Week Day Month January 2, 2023 21

TV PC VCR sum 1Qtr 2Qtr Date 3Qtr 4Qtr sum Total annual sales of TV in U.S.A. U.S.A Canada Mexico Country Pr od uc t A Sample Data Cube sum January 2, 2023 22

Cuboids Corresponding to the Cube all 0-D(apex) cuboid product product,date date country product,country 1-D cuboids date, country 2-D cuboids product, date, country January 2, 2023 3-D(base) cuboid 23

Typical OLAP Operations Roll up (drill-up): summarize data Drill down (roll down): reverse of roll-up project and select Pivot (rotate): from higher level summary to lower level summary or detailed data, or introducing new dimensions Slice and dice: by climbing up hierarchy or by dimension reduction reorient the cube, visualization, 3D to series of 2D planes. Other operations January 2, 2023 drill across: involving (across) more than one fact table drill through: through the bottom level of the cube to its back-end relational tables (using SQL) 24

Data Warehousing and OLAP Technology for Data Mining What is a data warehouse? A multi-dimensional data model Data warehouse architecture Data warehouse implementation From data warehousing to data mining January 2, 2023 25

Multi-Tiered Architecture other Metadata source s Operational DBs Extract Transform Load Refresh Monitor & Integrator Data Warehouse OLAP Server Serve Analysis Query Reports Data mining Data Marts Data Sources January 2, 2023 Data Storage OLAP Engine Front-End Tools 26

Three Data Warehouse Models Enterprise warehouse collects all of the information about subjects spanning the entire organization Data Mart a subset of corporate-wide data that is of value to a specific groups of users. Its scope is confined to specific, selected groups, such as marketing data mart Independent vs. dependent (directly from warehouse) data mart Virtual warehouse A set of views over operational databases Only some of the possible summary views may be materialized January 2, 2023 27

Data Warehouse Development: A Recommended Approach Multi-Tier Data Warehouse Distributed Data Marts Data Mart Data Mart Model refinement Enterprise Data Warehouse Model refinement Define a high-level corporate data model January 2, 2023 28

OLAP Server Architectures Relational OLAP (ROLAP) Use relational or extended-relational DBMS to store and manage warehouse data and OLAP middle ware to support missing pieces Include optimization of DBMS backend, implementation of aggregation navigation logic, and additional tools and services Greater scalability Multidimensional OLAP (MOLAP) Array-based multidimensional storage engine (sparse matrix techniques) Fast indexing to pre-computed summarized data Hybrid OLAP (HOLAP) User flexibility, e.g., low level: relational, high-level: array Specialized SQL servers Specialized support for SQL queries over star/snowflake schemas January 2, 2023 29

Data Warehousing and OLAP Technology for Data Mining What is a data warehouse? A multi-dimensional data model Data warehouse architecture Data warehouse implementation From data warehousing to data mining January 2, 2023 30

Efficient Data Cube Computation Data cube can be viewed as a lattice of cuboids The bottom-most cuboid is the base cuboid The top-most cuboid (apex) contains only one cell How many cuboids in an n-dimensional cube? 2 January 2, 2023 n 31

Problem: How to Implement Data Cube Efficiently? Physically materialize the whole data cube Materialize nothing Space consuming in storage and time consuming in construction Indexing overhead No extra space needed but unacceptable response time Materialize only part of the data cube Intuition: precompute frequently-asked queries? However: each cell of data cube is an aggregation, the value of many cells are dependent on the values of other cells in the data cube A better approach: materialize queries which can help answer many other queries quickly January 2, 2023 32

Motivating example Assume the data cube: Stored in a relational DB (MDDB is not very scalable) Different cuboids are assigned to different tables The cost of answering a query is proportional to the number of rows examined Use TPC-D decision-support benchmark Attributes: part, supplier, and customer Measure: total sales 3-D data cube: cell (p, s ,c) January 2, 2023 33

Motivating example (cont.) Hypercube lattice: the eight views (cuboids) constructed by grouping on some of part, supplier, and customer Finding total sales grouped by part Processing 6 million rows if cuboid pc is materialized Processing 0.2 million rows if cuboid p is materialized Processing 0.8 million rows if cuboid ps is materialized January 2, 2023 34

Motivating example (cont.) How to find a good set of queries? How many views must be materialized to get reasonable performance? Given space S, what views should be materialized to get the minimal average query cost? If we are willing to tolerate an X% degradation in average query cost from a fully materialized data cube, how much space can we save over the fully materialized data cube? January 2, 2023 35

Dependence relation The dependence relation on queries: Q1 Q2 iff Q1 can be answered using only the results of query Q2 (Q1 is dependent on Q2). In which is a partial order, and There is a top element, a view upon which is dependent (base cuboid) Example: (part) (part, customer) (part) (part) (customer) and (customer) January 2, 2023 36

Lattice notation A lattice with set of elements L and dependance relation is denoted by L, a b means that a b, and a b ancestor(a) {b a b } descendant(a) {b b a } next(a) {b a b, c, a c , c b} Lattice diagrams: a lattice can be represented as a graph, where the lattice elements (views) are nodes and there is January 2, 2023 an edge from a below b iff b is in next(a). 37

Hierarchies Dimensions of a data cube consist of more than one attribute, organized as hierarchies Operations on hierarchies: roll up and drill down Hierarchies are not all total orders but partial orders on the dimension: Consider the time dimension with the hierarchy day, week, month, and year : (month) (week) and (week) (month) Since month (year) can’t be divided by weeks January 2, 2023 38

Hierachies (cont.) January 2, 2023 39

The lattice framework: Composite lattices Query dependencies can be: caused by the interaction of the different dimen sions (hypercube) within a dimension caused by attribute hierarchi es across attribute hierarchies of different dimensions Views can be represented as an n-tuple (a1, a2, ,an), where ai is a point in the hierachy for the i-th dimension (a1, a2, ,an) (b1, b2, ,bn) iff ai bi for all January 2, 2023 40

The lattice framework: Composite lattices (cont.) Combining two hierarchical dimensions (n, s) (c, s) Dimension hierarchies Lattice frameworkof (Direct-product lattices) January 2, 2023 41

The advantages of lattice framework Provide a clean framework to reason with dimensional hierarchies We can model the common queries asked by users better Tells us in what order to materialize the views January 2, 2023 42

The linear cost model For L, , Q QA, C(Q) is the number of rows in the table for that query QA used to compute Q This linear relationship can be expressed as: T m*S c (m: time/size ratio; c: query overhead; S: size of the view) Validation of the model using TPC-D data: January 2, 2023 43

The benefit of a materialized view Denote the benefit of a materialized view v, relative to some set of views S, as B(v, S) For each w v, define BW by: Let C(v) be the cost of view v Let u be the view of least cost in S such that w u (such u must exist) BW C(u) – C(v) if C(v) C(u) 0 if C(v) C(u) BW is the benefit that it can obtain from v Define B(v, S) Σ w v Bw which means how v can improve the cost of evaluating views, including itself January 2, 2023 44

The greedy algorithm Objective Assume materializing a fixed number of views, regardless of the space they use How to minimize the average time taken to evaluate a view? The greedy algorithm for materializing a set of k views Performance: Greedy/Optimal 1 – (1 – 1/k) k (e - 1) / e January 2, 2023 45

Greedy algorithm: example 1 Suppose we want to choose three views (k 3) The selection is optimal (reduce cost from 800 to 420) January 2, 2023 46

Greedy algorithm: example 2 Suppose k 2 Greedy algorithm picks c and b: benefit 101*41 100*21 6241 Optimal selection is b and d: benefit 100*41 100*41 8200 However, greedy/optimal 6241/8200 3/4 January 2, 2023 47

An experiment: how many views should be materialized? Time and space for the greedy selection for the TPC-D-based example (full materialization is not efficient) January 2, 2023 Number of materialized views 48

Indexing OLAP Data: Bitmap Index Index on a particular column Each value in the column has a bit vector: bit-op is fast The length of the bit vector: # of records in the base table The i-th bit is set if the i-th row of the base table has the value for the indexed column not suitable for high cardinality domains Base table Cust C1 C2 C3 C4 C5 Region Asia Europe Asia America Europe January 2, 2023 Index on Region Index on Type Type RecIDAsia Europe America RecID Retail Dealer Retail 1 1 0 0 1 1 0 Dealer 2 0 1 0 2 0 1 Dealer 3 1 0 0 3 0 1 Retail 4 0 0 1 4 1 0 0 1 0 5 0 1 Dealer 5 49

Indexing OLAP Data: Join Indices Join index: JI(R-id, S-id) where R (R-id, ) S (S-id, ) Traditional indices map the values to a list of record ids It materializes relational join in JI file and speeds up relational join — a rather costly operation In data warehouses, join index relates the values of the dimensions of a start schema to rows in the fact table. E.g. fact table: Sales and two dimensions city and product A join index on city maintains for each distinct city a list of R-IDs of the tuples recording the Sales in the city Join indices can span multiple dimensions January 2, 2023 50

Efficient Processing of OLAP Queries Determine which operations should be performed on the available cuboids: transform drill, roll, etc. into corresponding SQL and/or OLAP operations, e.g, dice selection projection Determine to which materialized cuboid(s) the relevant operations should be applied. Exploring indexing structures and compressed vs. dense array structures in MOLAP January 2, 2023 51

Metadata Repository Meta data is the data defining warehouse objects. It has the following kinds Description of the structure of the warehouse Operational meta-data data lineage (history of migrated data and transformation path), currency of data (active, archived, or purged), monitoring information (warehouse usage statistics, error reports, audit trails) The algorithms used for summarization The mapping from operational environment to the data warehouse Data related to system performance schema, view, dimensions, hierarchies, derived data defn, data mart locations and contents warehouse schema, view and derived data definitions Business data January 2, 2023 business terms and definitions, ownership of data, charging policies 52

Data Warehouse Back-End Tools and Utilities Data extraction: Data cleaning: convert data from legacy or host format to warehouse format Load: detect errors in the data and rectify them when possible Data transformation: get data from multiple, heterogeneous, and external sources sort, summarize, consolidate, compute views, check integrity, and build indicies and partitions Refresh propagate the updates from the data sources to the warehouse January 2, 2023 53

Data Warehousing and OLAP Technology for Data Mining What is a data warehouse? A multi-dimensional data model Data warehouse architecture Data warehouse implementation From data warehousing to data mining January 2, 2023 54

Data Warehouse Usage Three kinds of data warehouse applications Information processing Analytical processing multidimensional analysis of data warehouse data supports basic OLAP operations, slice-dice, drilling, pivoting Data mining supports querying, basic statistical analysis, and reporting using crosstabs, tables, charts and graphs knowledge discovery from hidden patterns supports associations, constructing analytical models, performing classification and prediction, and presenting the mining results using visualization tools. Differences among the three tasks January 2, 2023 55

From On-Line Analytical Processing to On Line Analytical Mining (OLAM) Why online analytical mining? January 2, 2023 High quality of data in data warehouses DW contains integrated, consistent, cleaned data Available information processing structure surrounding data warehouses ODBC, OLEDB, Web accessing, service facilities, reporting and OLAP tools OLAP-based exploratory data analysis mining with drilling, dicing, pivoting, etc. On-line selection of data mining functions integration and swapping of multiple mining functions, algorithms, and tasks. 56

An OLAM Architecture Mining query Mining result Layer4 User Interface User GUI API OLAM Engine OLAP Engine Layer3 OLAP/OLAM Data Cube API Layer2 MDDB Filtering&Integration Database API MDDB Meta Data Filtering Layer1 Databases January 2, 2023 Data cleaning Data Data integration Warehouse Data Repository 57

Summary Data warehouse A multi-dimensional model of a data warehouse Star schema, snowflake schema, fact constellations A data cube consists of dimensions & measures OLAP operations: drilling, rolling, slicing, dicing and pivoting OLAP servers: ROLAP, MOLAP, HOLAP Efficient computation of data cubes A subject-oriented, integrated, time-variant, and nonvolatile collection of data in support of management’s decision-making process Partial vs. full vs. no materialization Multiway array aggregation Bitmap index and join index implementations Further development of data cube technology Discovery-drive and multi-feature cubes From OLAP to OLAM (on-line analytical mining) January 2, 2023 58