1. Data Warehouses and OLAP
*Slides by Nikos Mamoulis

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

3. 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

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

5. 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 with L levels?
Materialization of data cube
Materialize every (cuboid) (full materialization), none (no materialization), or some (partial materialization)
Selection of which cuboids to materialize
Based on size, sharing, access frequency, etc.

6. Cube Operations Cube definition and computation in DMQL
define cube sales[item, city, year]: sum(sales_in_dollars)
compute cube sales
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
Need compute the following Group-Bys
(date, product, customer),
(date,product),(date, customer), (product, customer),
(date), (product), (customer) () ()
(city)
(item)
(year)
(city, item)
(city, year)
(item, year)
(city, item, year)

7. Cube Computation: ROLAP-Based Method
Efficient cube computation methods
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
Sorting, hashing, and grouping operations are applied to the dimension attributes in order to reorder and cluster related tuples
Grouping is performed on some sub-aggregates as a “partial grouping step”
Aggregates may be computed from previously computed aggregates, rather than from the base fact table

8. Cube Computation: ROLAP-Based Method (2)
Hash/sort based methods (Agarwal et. al. VLDB’96)
Smallest-parent: computing a cuboid from the smallest cubod previously computed cuboid.
Cache-results: caching results of a cuboid from which other cuboids are computed to reduce disk I/Os
Amortize-scans: computing as many as possible cuboids at the same time to amortize disk reads
Share-sorts: sharing sorting costs cross multiple cuboids when sort-based method is used
Share-partitions: sharing the partitioning cost cross multiple cuboids when hash-based algorithms are used

9. Multi-way Array Aggregation for Cube Computation
Partition arrays into chunks (a small subcube which fits in memory).
Compressed sparse array addressing: (chunk_id, offset)
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. A B 29 30 31 32 1 2 3 4 5 9 13 14 15 16 64 63 62 61 48 47 46 45 a1 a0 c3 c2 c1
c 0 b3 b2 b1 b0 a2 a3 C 44 28 56 40 24 52 36 20 60
What is the best traversing order to do multi-way aggregation?

10. Multi-way Array Aggregation for Cube Computation29 30 31 32 1 2 3 4 5 9 13 14 15 16 64 63 62 61 48 47 46 45 a1 a0 c3 c2 c1
c 0 b3 b2 b1 b0 a2 a3 C 44 28 56 40 24 52 36 20 60 B

11. Multi-way Array Aggregation for Cube Computation61 62 63 64 c2 45 46 47 48 c1 29 30 31 32
c 0 B 13 14 15 16 60 b3 44 B 28 b2 9 56 40 24 b1 5 52 36 20 b0 1 2 3 4 a0 a1 a2 a3 A

12. Multi-Way Array Aggregation for Cube Computation (Cont.)
Method: the planes should be sorted and computed according to their size in ascending order.
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
If there are a large number of dimensions, “bottom-up computation” and iceberg cube computation methods can be explored

13. 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
Index on Region
Index on Type

14. 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

15. Efficient Processing 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

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

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

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

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

20. Examples: Discovery-Driven Data Cubes

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

22. Data Warehouse Usage Three kinds of data warehouse applications
Information processing
supports querying, basic statistical analysis, and reporting using crosstabs, tables, charts and graphs
Analytical processing
multidimensional analysis of data warehouse data
supports basic OLAP operations, slice-dice, drilling, pivoting
Data mining
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

23. From On-Line Analytical Processing to On Line Analytical Mining (OLAM)
Why online analytical mining?
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.
Architecture of OLAM

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

25. Summary Data warehouse A multi-dimensional model of a data warehouse
A subject-oriented, integrated, time-variant, and nonvolatile collection of data in support of management’s decision-making process
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
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)

26. References (I)
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 Int. Conf. Very Large Data Bases, , Bombay, India, Sept
D. Agrawal, A. E. Abbadi, A. Singh, and T. Yurek. Efficient view maintenance in data warehouses. In Proc ACM-SIGMOD Int. Conf. Management of Data, , Tucson, Arizona, May 1997.
R. Agrawal, J. Gehrke, D. Gunopulos, and P. Raghavan. Automatic subspace clustering of high dimensional data for data mining applications. In Proc ACM-SIGMOD Int. Conf. Management of Data, , Seattle, Washington, June 1998.
R. Agrawal, A. Gupta, and S. Sarawagi. Modeling multidimensional databases. In Proc Int. Conf. Data Engineering, , Birmingham, England, April 1997.
K. Beyer and R. Ramakrishnan. Bottom-Up Computation of Sparse and Iceberg CUBEs. In Proc ACM-SIGMOD Int. Conf. Management of Data (SIGMOD'99), , Philadelphia, PA, June 1999.
S. Chaudhuri and U. Dayal. An overview of data warehousing and OLAP technology. ACM SIGMOD Record, 26:65-74, 1997.
OLAP council. MDAPI specification version 2.0. In
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.

27. References (II)
V. Harinarayan, A. Rajaraman, and J. D. Ullman. Implementing data cubes efficiently. In Proc ACM-SIGMOD Int. Conf. Management of Data, pages , Montreal, Canada, June 1996.
Microsoft. OLEDB for OLAP programmer's reference version 1.0. In
K. Ross and D. Srivastava. Fast computation of sparse datacubes. In Proc Int. Conf. Very Large Data Bases, , Athens, Greece, Aug
K. A. Ross, D. Srivastava, and D. Chatziantoniou. Complex aggregation at multiple granularities. In Proc. Int. Conf. of Extending Database Technology (EDBT'98), , Valencia, Spain, March 1998.
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 , Valencia, Spain, March 1998.
E. Thomsen. OLAP Solutions: Building Multidimensional Information Systems. John Wiley & Sons, 1997.
Y. Zhao, P. M. Deshpande, and J. F. Naughton. An array-based algorithm for simultaneous multidimensional aggregates. In Proc ACM-SIGMOD Int. Conf. Management of Data, , Tucson, Arizona, May 1997.

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

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

30. Example: requirements and selection
Requirements of the data warehouse
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
central theme(s): sales
measure(s): sum(sales_in_dollars), avg(price_sold_units)
dimensions: time, part, customer

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

32. Exercise time: day, week, month, quarter, year
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

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

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

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

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

37. Example: how to populate the DW? Load, Clean, Integrate
Convert attribute names and types
E.g., part.name = part.title
Convert values to be consistent
Join tables if necessary
Join customer,location,city from “New York” DB
Derive time if not present
Check transaction log for sales table to get the time and convert it to the required format
Complete missing values
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
Tables employee, department are ignored
Attributes zip, tel, id are ignored.

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

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

40. Redundancy in views A non-redundant combination of attributes:
(month, part_type)
A redundant (not useful) combination of attributes:
(part_brand, part_manufacturer)
part_type
month 23 12 11 50 67 58 18 72 25 43 33 13 30 10 20 22 40 90 2 56 6 45 1
manufacturer
part_brand 23 12 43 33 13 25

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

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

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

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

45. How to answer queries from a set of materialized cuboids?
In real-life examples it is not possible to materialize the whole data cube
Typically, a small subset of cuboids is materialized
To answer a query we have to select the cuboid that results in the minimum cost for the query
A query typically consists of
a set of group-by attributes
a set of selection clauses
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:
the size of the cuboid
any indexes on the attributes of the “select” clause of the query

46. Cube: A Lattice of Cuboids
How would you compute the following queries?
Q1: <time,item>
Q2: <supplier>
Q3: <location>
Q4: <time,supplier>
Q5: <item>
= materialized
cuboid
all
time
item
location
supplier
time,item
time,location
item,location
location,supplier
time,supplier
item,supplier
time,location,supplier
time,item,location
time,item,supplier
item,location,supplier
time, item, location, supplier

47. Which cuboids should we materialize?
In real-life examples it is not possible to materialize the whole data cube
We have to select the most beneficial cuboids to materialize
This depends mainly on the size of the cuboids and their usage by queries
Thus to select we need information about (i) the size of cuboids, (ii) the queries and their frequency
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:
time_id to derive the day
part_id to derive part.name
cust_id to derive customer.name

48. Which cuboids should we materialize?
Example
candidate cuboids:
(day,pname,cname) – 100GB (already materialized)
(day,pname) – 60GB
(day,cname) – 20GB
(pname,cname) – 1GB
(day) – 10GB
(pname) – 200MB
(cname) – 30MB
(ALL) – 8 bytes
queries (with equal probability)
Q1: total sales per (pname,cname)
Q2: total sales per (pname)
Q3: total sales per (cname)
Exercise: Which views
should we materialize if
the available space is:
10GB
1GB
100MB

49. Which cuboids should we materialize?
Case 1: Available space = 10GB
We can materialize all three views (pname,cname) , (pname), and (cname)
The cost of Q1 is reading 1GB
The cost of Q2 is reading 200MB
The cost of Q3 is reading 30MB
Average query cost = (1230MB)/3=410 MB/query

50. Which cuboids should we materialize?
Case 2: Available space = 1GB
We have two choices:
materialize (pname,cname) using 1GB
Q1 costs 1GB, Q2 costs 1GB, Q3 costs 1GB
Average query cost = 1GB
materialize (pname) and (cname) using 230MB
Q1 costs 100GB, Q2 costs 200MB, Q3 costs 30MB
Average query cost = (100,230MB)/3 = 34GB
First choice is better than the second!

51. Which cuboids should we materialize?
Case 3: Available space = 100MB
We can only materialize (cname)
Q1 costs 100GB
Q2 costs 100GB
Q3 costs 30MB
Average query cost = (200,030MB)/3 = 67GB

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

53. Bitmap Indexes - Example
100 bytes
date
pcolor
cname
cgender
sales
10/10/00
red
Smith M 21
12/10/00
green
Jones F 13
15/10/00
Kane 14
20/10/00
blue
Nike 23
22/11/00
Ellis 9
26/11/00 92
...
1 billion rows
index for pcolor
index for gender
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:
the table is used
the indexes are used
red
green
blue 1
... M F 1
...

54. Bitmap Indexes - Example
The size of the table is 100GB=100bytes*1billion
The size of the indexes are:
3bits*1billion = 3000Mbits = 375MB
2bits*1billion = 2000Mbits = 250MB
The cost of evaluating the query directly on the table is reading 100GB and for each of the 1 billion tuples perform a comparison with “red” and “F” (expensive)
The cost of evaluating the query using the indexes is:
read bitmap for red, read bitmap for F and join them.
This costs reading 1Gbits+1Gbits = 250MB
for each join result accumulate the sales for the corresponding rid
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.