Data Warehouses and OLAP Slides by Nikos Mamoulis

Data Warehouses and OLAP *Slides by Nikos Mamoulis

Multi-Tiered Architecture other Metadata sources Operational DBs Extract Transform Load Refresh Monitor & Integrator Data Warehouse OLAP Server Serve Analysis Query Reports Data mining Data Marts Data Sources Data Storage OLAP Engine Front-End Tools

OLAP Server Architectures p Relational OLAP (ROLAP) n n n p Multidimensional OLAP (MOLAP) n n p Array-based multidimensional storage engine (sparse matrix techniques) fast indexing to pre-computed summarized data Hybrid OLAP (HOLAP) n p 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 User flexibility, e. g. , low level: relational, high-level: array Specialized SQL servers n specialized support for SQL queries over star/snowflake schemas

Data Warehousing and OLAP Technology for Data Mining p What is a data warehouse? p A multi-dimensional data model p Data warehouse architecture p Data warehouse implementation p Further development of data cube technology p From data warehousing to data mining

Efficient Data Cube Computation p p Data cube can be viewed as a lattice of cuboids n The bottom-most cuboid is the base cuboid n The top-most cuboid (apex) contains only one cell n How many cuboids in an n-dimensional cube with L levels? Materialization of data cube n Materialize every (cuboid) (full materialization), none (no materialization), or some (partial materialization) n Selection of which cuboids to materialize p Based on size, sharing, access frequency, etc.

Cube Operations p Cube definition and computation in DMQL define cube sales[item, city, year]: sum(sales_in_dollars) compute cube sales p Transform it into a SQL-like language (with a new operator cube by, introduced by Gray et al. ’ 96) SELECT item, city, year, SUM (amount) () FROM SALES CUBE BY item, city, year p (city) (item) (year) Need compute the following Group-Bys (date, product, customer), (date, product), (date, customer), (product, customer), (city, item) (city, year) (item, year) (date), (product), (customer) () (city, item, year)

Cube Computation: ROLAP-Based Method p Efficient cube computation methods n n n p ROLAP-based cubing algorithms (Agarwal et al’ 96) Array-based cubing algorithm (Zhao et al’ 97) Bottom-up computation method (Bayer & Ramarkrishnan’ 99) ROLAP-based cubing algorithms n Sorting, hashing, and grouping operations are applied to the dimension attributes in order to reorder and cluster related tuples n Grouping is performed on some sub-aggregates as a “partial grouping step” n Aggregates may be computed from previously computed aggregates, rather than from the base fact table

Multi-way Array Aggregation for Cube Computation p Partition arrays into chunks (a small subcube which fits in memory). p Compressed sparse array addressing: (chunk_id, offset) p Compute aggregates in “multiway” by visiting cube cells in the order which minimizes the # of times to visit each cell, and reduces memory access and storage cost. c 3 61 62 63 64 C c 2 45 46 47 48 c 1 29 30 31 32 c 0 B b 3 B 13 b 2 9 b 1 5 b 0 14 15 16 1 2 3 4 a 0 a 1 a 2 a 3 A 60 44 28 56 40 24 52 36 20 What is the best traversing order to do multi-way aggregation?

Multi-way Array Aggregation for Cube Computation C c 3 61 62 63 64 c 2 45 46 47 48 c 1 29 30 31 32 c 0 b 3 B b 2 B 13 14 15 16 28 9 24 b 1 5 b 0 1 2 3 4 a 0 a 1 a 2 a 3 A 20 44 40 36 60 56 52

Aggregation for Cube Computation C c 3 61 62 63 64 c 2 45 46 47 48 c 1 29 30 31 32 c 0 b 3 B b 2 B 13 14 15 16 28 9 24 b 1 5 b 0 1 2 3 4 a 0 a 1 a 2 a 3 A 20 44 40 36 60 56 52

Multi-Way Array Aggregation for Cube Computation (Cont. ) p Method: the planes should be sorted and computed according to their size in ascending order. n n p See the details of Example 4. 4 Idea: keep the smallest plane in the main memory, fetch and compute only one chunk at a time for the largest plane Limitation of the method: works well only for a small number of dimensions n If there a large number of dimensions, “bottom-up computation” and iceberg cube computation methods can be explored

Indexing OLAP Data: Bitmap Index p p p 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 Index on Region Index on Type

Indexing OLAP Data: Join Indices p p 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 n p 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. n n E. g. fact table: Sales and two dimensions city and product p 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

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

Metadata Repository p Meta data is the data defining warehouse objects. It has the following kinds n Description of the structure of the warehouse p n Operational meta-data p n n n 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 p n schema, view, dimensions, hierarchies, derived data defn, data mart locations and contents warehouse schema, view and derived data definitions Business data p business terms and definitions, ownership of data, charging policies

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

Data Warehousing and OLAP Technology for Data Mining p What is a data warehouse? p A multi-dimensional data model p Data warehouse architecture p Data warehouse implementation p Further development of data cube technology p From data warehousing to data mining

Discovery-Driven Exploration of Data Cubes p Hypothesis-driven: exploration by user, huge search space p Discovery-driven (Sarawagi et al. ’ 98) n pre-compute measures indicating exceptions, guide user in the data analysis, at all levels of aggregation n Exception: significantly different from the value anticipated, based on a statistical model n Visual cues such as background color are used to reflect the degree of exception of each cell n Computation of exception indicator (modeling fitting and computing Self. Exp, In. Exp, and Path. Exp values) can be overlapped with cube construction

Examples: Discovery-Driven Data Cubes

Data Warehousing and OLAP Technology for Data Mining p What is a data warehouse? p A multi-dimensional data model p Data warehouse architecture p Data warehouse implementation p Further development of data cube technology p From data warehousing to data mining

Data Warehouse Usage p Three kinds of data warehouse applications n Information processing p n Analytical processing p p n multidimensional analysis of data warehouse data supports basic OLAP operations, slice-dice, drilling, pivoting Data mining p p p 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

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

An OLAM Architecture Mining query Mining result Layer 4 User Interface User GUI API OLAM Engine OLAP Engine Layer 3 OLAP/OLAM Data Cube API Layer 2 MDDB Meta Data Filtering&Integration Database API Filtering Layer 1 Databases Data cleaning Data integration Warehouse Data Repository

Summary p Data warehouse n p p A multi-dimensional model of a data warehouse n Star schema, snowflake schema, fact constellations n 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 n n n p 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 n n Discovery-drive and multi-feature cubes From OLAP to OLAM (on-line analytical mining)

References (I) p S. Agarwal, R. Agrawal, P. M. Deshpande, A. Gupta, J. F. Naughton, R. Ramakrishnan, and S. Sarawagi. On the computation of multidimensional aggregates. In Proc. 1996 Int. Conf. Very Large Data Bases, 506 -521, Bombay, India, Sept. 1996. p D. Agrawal, A. E. Abbadi, A. Singh, and T. Yurek. Efficient view maintenance in data warehouses. In Proc. 1997 ACM-SIGMOD Int. Conf. Management of Data, 417 -427, Tucson, Arizona, May 1997. p R. Agrawal, J. Gehrke, D. Gunopulos, and P. Raghavan. Automatic subspace clustering of high dimensional data for data mining applications. In Proc. 1998 ACM-SIGMOD Int. Conf. Management of Data, 94 -105, Seattle, Washington, June 1998. p R. Agrawal, A. Gupta, and S. Sarawagi. Modeling multidimensional databases. In Proc. 1997 Int. Conf. Data Engineering, 232 -243, Birmingham, England, April 1997. p K. Beyer and R. Ramakrishnan. Bottom-Up Computation of Sparse and Iceberg CUBEs. In Proc. 1999 ACM-SIGMOD Int. Conf. Management of Data (SIGMOD'99), 359 -370, Philadelphia, PA, June 1999. p S. Chaudhuri and U. Dayal. An overview of data warehousing and OLAP technology. ACM SIGMOD Record, 26: 65 -74, 1997. p OLAP council. MDAPI specification version 2. 0. In http: //www. olapcouncil. org/research/apily. htm, 1998. p J. Gray, S. Chaudhuri, A. Bosworth, A. Layman, D. Reichart, M. Venkatrao, F. Pellow, and H. Pirahesh. Data cube: A relational aggregation operator generalizing group-by, cross-tab and sub-totals. Data Mining and Knowledge Discovery, 1: 29 -54, 1997.

References (II) p V. Harinarayan, A. Rajaraman, and J. D. Ullman. Implementing data cubes efficiently. In Proc. 1996 ACM-SIGMOD Int. Conf. Management of Data, pages 205 -216, Montreal, Canada, June 1996. p Microsoft. OLEDB for OLAP programmer's reference version 1. 0. In http: //www. microsoft. com/data/oledb/olap, 1998. p K. Ross and D. Srivastava. Fast computation of sparse datacubes. In Proc. 1997 Int. Conf. Very Large Data Bases, 116 -125, Athens, Greece, Aug. 1997. p K. A. Ross, D. Srivastava, and D. Chatziantoniou. Complex aggregation at multiple granularities. In Proc. Int. Conf. of Extending Database Technology (EDBT'98), 263277, Valencia, Spain, March 1998. p S. Sarawagi, R. Agrawal, and N. Megiddo. Discovery-driven exploration of OLAP data cubes. In Proc. Int. Conf. of Extending Database Technology (EDBT'98), pages 168182, Valencia, Spain, March 1998. p E. Thomsen. OLAP Solutions: Building Multidimensional Information Systems. John Wiley & Sons, 1997. p Y. Zhao, P. M. Deshpande, and J. F. Naughton. An array-based algorithm for simultaneous multidimensional aggregates. In Proc. 1997 ACM-SIGMOD Int. Conf. Management of Data, 159 -170, Tucson, Arizona, May 1997.

Selection of tables, attributes, domains in the DW design process p If you are asked to design a data warehouse for a set of operational databases how would you do it? n Use specifications of requirements to design the data warehouse schema and select: p p n The central theme(s) of the analysis (e. g. , sales) The measures on the central themes (e. g. , sum(dollars)) p The dimensions used by analytical processing p The attributes and hierarchies of the dimensions Clean, transform, and integrate information

Example p A large company which sells engine parts n n Database 1 (Los Angeles) p employee(id, name, dept, lot, salary, age) p department(id, name, type, manager_id) p part(id, name, type, brand, manufacturer, color) p customer(id, name, type, age, city, state, zip, tel) p sales(id, part_id, customer_id, quantity, price) Database 2 (New York) p employee(id, ename, dept_id, salary, age) p department(id, name, type, manager) p part(id, title, type, brand, manufacturer, color) p customer(id, name, type, zip, tel) p location(zip, city_id) p city(city_id, state, country) p sales(id, part_id, customer_id, quantity, price)

Example: requirements and selection p Requirements of the data warehouse n p we want to analyze the total sales in dollars and the average price of sold units with respect to time, part, customer. Selection of the basic features of the warehouse n central theme(s): sales n measure(s): sum(sales_in_dollars), avg(price_sold_units) n dimensions: time, part, customer

Example: selection of hierarchies p To determine the dimension hierarchies we have to select which dimensional attributes are required to include for analysis p We go back to the requirements and ask the analyst: n time: day, week, month, quarter, year n part: name, type, color, brand, manufacturer n customer: name, type, city, state, country

Exercise p Find the hierarchies for time, part, customer • time: day, week, month, quarter, year • part: name, type, color, brand, manufacturer • customer: name, type, city, state, country

Example: selection of hierarchies p Definition of the hierarchies: year manufacturer state quarter month country week type color brand type city day name time part customer

Example: is the information that we need to analyze available? p We have to check if the required information for analysis exists in the databases to be integrated n All requested attributes exist, except from the time. This can be determined by accessing the transaction logs of the databases.

Example: Design the DW schema p We use the star schema in this example Time time_id day week month quarter year Part part_id name type color brand manufacturer Fact table time_id part_id cust_id quantity price Customer cust_id name type city state country We need just quantity and (unit) price to derive sum(sales_in_dollars) = quantity*price avg(price_sold_units) = Σ(quantity*price)/ Σ(quantity)

Integration tasks p A large company which sells engine parts n n Database 1 (Los Angeles) p employee(id, name, dept, lot, salary, age) p department(id, name, type, manager_id) p part(id, name, type, brand, manufacturer, color) p customer(id, name, type, age, city, state, zip, tel) p sales(id, part_id, customer_id, quantity, price) Database 2 (New York) p employee(id, ename, dept_id, salary, age) p department(id, name, type, manager) p part(id, title, type, brand, manufacturer, color) p customer(id, name, type, zip, tel) p location(zip, city_id) p city(city_id, state, country) p sales(id, part_id, customer_id, quantity, price) convert: • attribute names • attribute types join tables derive data not stored explicitly in the databases fill in missing values ignore irrelevant data: • tables • attributes

Example: how to populate the DW? Load, Clean, Integrate p Convert attribute names and types n E. g. , part. name = part. title p Convert values to be consistent p Join tables if necessary n p Derive time if not present n p Check transaction log for sales table to get the time and convert it to the required format Complete missing values n p Join customer, location, city from “New York” DB The “Los Angeles” database does not record customer country information because all its customers are from US. In the integrated data from LA country value is set to “USA” Ignore irrelevant tables and attributes n Tables employee, department are ignored n Attributes zip, tel, id are ignored.

How many cuboids ? p How do we compute the total number of cuboids of a data cube? p Compute the product of the number of levels for each dimension n Number of cuboids = (levels for time)* (levels for part)* (levels for customer) = 5*4*5 = 100

What is the data cube? p The data cube is NOT a cube n Multiple dimensions, variable range and interpretations of the cells, does not look always like a “cube” p The data cube is the set of all non-redundand, multidimensional views from which we can analyze the measures on the central theme(s) p Remember: the terms multidimensional view and cuboid have the same meaning p A multidimensional view is non-redundant, if there are no hierarchical relationships between its dimensional attributes

Redundancy in views A non-redundant combination of attributes: p (month, part_type) A redundant (not useful) combination of attributes: n (part_brand, part_manufacturer) part_type n month manufacturer p 23 12 23 11 5067 10 20 43 33 13 22 58 18 72 25 30 25 23 12 0 40 9012 23 45 43 33 13 1 2 0 56 23 6 25 part_brand 23 12 0 0 0 43 33 13 0 0 0 25

Exercise p Find the non-redundant combinations of the attributes of part. manufacturer type color brand name part

Visualization of non-redundant attribute combinations for part ALL manufacturer type color (type, color) (color, brand) brand (type, manufacturer) (color, manufacturer) (type, brand) (type, color, manufacturer) (type, color, brand) name part

How many (non-redundant) cuboids ? p How do we compute the total number of cuboids of a data cube? p Compute the product of the number of combinations for each dimension n Number of cuboids = (combinations for time)* (combinations for part)* (combinations for customer) = 6*13*9 = 702 p Note: sometimes we use the term cuboid to also denote multidimensional views with selections: n p total sales for each (part. type, customer. city) for year = “ 2001” We do not count such cuboids in the computation above

Cube: A Lattice of Cuboids E. g. , (location) is dependent on (time, item, location) all time, item time, location item, location time, supplier time, item, location supplier location, supplier item, supplier time, location, supplier time, item, supplier item, location, supplier time, item, location, supplier

How to answer queries from a set of materialized cuboids? p In real-life examples it is not possible to materialize the whole data cube p Typically, a small subset of cuboids is materialized p To answer a query we have to select the cuboid that results in the minimum cost for the query p A query typically consists of p n a set of group-by attributes n a set of selection clauses n E. g. , compute the total sales per part. type, cust. city for year=2002. The factors for selecting the best cuboid for a particular query are: n the size of the cuboid n any indexes on the attributes of the “select” clause of the query

Cube: A Lattice of Cuboids = materialized cuboid time, item all item time, location item, location time, supplier time, item, location supplier How would you compute the following queries? Q 1: <time, item> Q 2: <supplier> Q 3: <location> Q 4: <time, supplier> Q 5: <item> location, supplier item, supplier time, location, supplier time, item, supplier item, location, supplier time, item, location, supplier

Which cuboids should we materialize? p In real-life examples it is not possible to materialize the whole data cube p We have to select the most beneficial cuboids to materialize p This depends mainly on the size of the cuboids and their usage by queries p Thus to select we need information about (i) the size of cuboids, (ii) the queries and their frequency p The base cuboid almost always corresponds to the fact table, which is already materialized. For example, if the products have unique name, and customers unique name, we can use: n time_id to derive the day n part_id to derive part. name n cust_id to derive customer. name

Which cuboids should we materialize? p Example n n candidate cuboids: p (day, pname, cname) – 100 GB (already materialized) p (day, pname) – 60 GB p (day, cname) – 20 GB p (pname, cname) – 1 GB p (day) – 10 GB p (pname) – 200 MB p (cname) – 30 MB p (ALL) – 8 bytes queries (with equal probability) p Q 1: total sales per (pname, cname) p Q 2: total sales per (pname) p Q 3: total sales per (cname) Exercise: Which views should we materialize if the available space is: 1. 10 GB 2. 1 GB 3. 100 MB

Which cuboids should we materialize? p Case 1: Available space = 10 GB n We can materialize all three views (pname, cname) , (pname), and (cname) n The cost of Q 1 is reading 1 GB n The cost of Q 2 is reading 200 MB n The cost of Q 3 is reading 30 MB n Average query cost = (1230 MB)/3=410 MB/query

Which cuboids should we materialize? p Case 2: Available space = 1 GB p We have two choices: n n p materialize (pname, cname) using 1 GB p Q 1 costs 1 GB, Q 2 costs 1 GB, Q 3 costs 1 GB p Average query cost = 1 GB materialize (pname) and (cname) using 230 MB p Q 1 costs 100 GB, Q 2 costs 200 MB, Q 3 costs 30 MB p Average query cost = (100, 230 MB)/3 = 34 GB First choice is better than the second!

Which cuboids should we materialize? p Case 3: Available space = 100 MB p We can only materialize (cname) n Q 1 costs 100 GB n Q 2 costs 100 GB n Q 3 costs 30 MB n Average query cost = (200, 030 MB)/3 = 67 GB

Bitmap Indexes p The bitmap index is used to index attributes with small domains p For each attribute value, a bitmap is defined to indicate the rows of the table that contain this value p Bitmaps are useful especially when we want to join some attribute values p Example: find the total sales of red parts to female customers

Bitmap Indexes - Example 100 bytes date 10/10/00 12/10/00 15/10/00 20/10/00 22/11/00 26/11/00. . . pcolor red green blue red. . . cname Smith Jones Kane Nike Ellis Jones. . . index for pcolor red 1 0 0 0 1 1. . . green 0 1 1 0 0 0. . . blue 0 0 0 1 0 0. . . cgender M F M M F F. . . sales 21 13 14 23 9 92. . . index for gender M 1 0 1 1 0 0. . . F 0 1 0 0 1 1. . . 1 billion rows Exercise: 1. what are the sizes of the table and indexes 2. what is the cost of the query: “find the total sales of red parts to female customers” if: a) the table is used b) the indexes are used

Bitmap Indexes - Example p The size of the table is 100 GB=100 bytes*1 billion p The size of the indexes are: n 3 bits*1 billion = 3000 Mbits = 375 MB n 2 bits*1 billion = 2000 Mbits = 250 MB p The cost of evaluating the query directly on the table is reading 100 GB and for each of the 1 billion tuples perform a comparison with “red” and “F” (expensive) p The cost of evaluating the query using the indexes is: n read bitmap for red, read bitmap for F and join them. p n This costs reading 1 Gbits+1 Gbits = 250 MB for each join result accumulate the sales for the corresponding rid p p this retrieves (1/3)*(1/2) = 1/6 tuples (estimated) and accumulates them we will probably read the whole table (since we want to avoid random accesses), but we will avoid any comparisons.