1

OLAP and Data Warehousing

Advanced Topics in Database Management (INFSCI 2711)

Some materials are from Database Management Systems,

R. Ramakrishnan and J. Gehrke

and from

https://www.kimballgroup.com/

Vladimir Zadorozhny, DINS, University of Pittsburgh

Introduction

Increasingly, organizations are analyzing current and historical data to

identify useful patterns and support business strategies.

Emphasis is on complex, interactive, exploratory analysis of very large

datasets created by integrating data from across all parts of an

enterprise; data is fairly static.

Contrast such On-Line Analytic Processing (OLAP) with

traditional On-line Transaction Processing (OLTP): mostly long

queries, instead of short update Xacts.

1

2

2

Three Complementary Trends

Data Warehousing: Consolidate data from many sources in one large repository.

Loading, periodic synchronization of replicas.

Semantic integration.

OLAP:

Complex SQL queries and views.

Queries based on spreadsheet-style operations and “multidimensional”view of data.

Interactive and “online” queries.

Data Mining: Exploratory search for interesting trends and anomalies (not considered in this class)

Data Warehousing

Integrated data spanning long time periods,

often augmented with summary information.

Several gigabytes to terabytes common.

Interactive response times expected for

complex queries; ad-hoc updates

uncommon.

EXTERNAL DATA SOURCES

EXTRACTTRANSFORM

LOADREFRESH

DATAWAREHOUSE

MetadataRepository

SUPPORTS

OLAPDATAMINING

3

4

3

Warehousing Issues

Semantic Integration: When getting data from multiple sources, must

eliminate mismatches, e.g., different currencies, schemas.

Heterogeneous Sources: Must access data from a variety of source

formats and repositories.

Replication capabilities can be exploited here.

Load, Refresh, Purge: Must load data, periodically refresh it, and purge

too-old data.

Metadata Management: Must keep track of source, loading time, and

other information for all data in the warehouse.

Multidimensional Data

Model

Collection of numeric measures, which depend on a set of

dimensions.

E.g., measure Sales, dimensions Product (key: pid),

Location (locid), and Time (timeid).

8 10 10

30 20 50

25 8 15

1 2 3timeid

pid

11 12 13

11 1 1 25

11 2 1 8

11 3 1 15

12 1 1 30

12 2 1 20

12 3 1 50

13 1 1 8

13 2 1 10

13 3 1 10

11 1 2 35

pid

tim

eid

loci

d

sale

s

locid

Slice locid=1is shown:

5

6

4

MOLAP vs ROLAP

Multidimensional data can be stored physically in a (disk-resident,

persistent) array; called MOLAP systems. Alternatively, can store as a

relation; called ROLAP systems.

The main relation, which relates dimensions to a measure, is called the

fact table. Each dimension can have additional attributes and an

associated dimension table.

E.g., Products(pid, pname, category, price)

Fact tables are much larger than dimensional tables.

We will focus on ROLAP, will need some refreshment

on advanced SQL features …

Sailors Database

7

8

5

Nested Queries

A very powerful feature of SQL: a WHERE clause can itself contain an SQL

query! (Actually, so can FROM and HAVING clauses.)

To find sailors who’ve not reserved #103, use NOT IN.

To understand semantics of nested queries, think of a nested loops evaluation: For each Sailors tuple, check the qualification by computing the subquery.

SELECT S.sname

FROM Sailors S

WHERE S.sid IN (SELECT R.sid

FROM Reserves R

WHERE R.bid=103)

Find names of sailors who’ve reserved boat #103:

More on Set-Comparison Operators

We’ve already seen IN, EXISTS and UNIQUE. Can also use NOT IN, NOT EXISTS and NOT UNIQUE.

Also available: op ANY, op ALL, op IN

Find sailors whose rating is greater than that of some sailor called Horatio:

= , , , , ,

SELECT *

FROM Sailors S

WHERE S.rating > ANY (SELECT S2.rating

FROM Sailors S2

WHERE S2.sname=‘Horatio’)

9

10

6

Aggregate Operators

Significant extension of relational algebra.

COUNT (*)

COUNT ( [DISTINCT] A)

SUM ( [DISTINCT] A)

AVG ( [DISTINCT] A)

MAX (A)

MIN (A)

SELECT AVG (S.age)

FROM Sailors S

WHERE S.rating=10

SELECT COUNT (*)

FROM Sailors S

SELECT AVG ( DISTINCT S.age)

FROM Sailors S

WHERE S.rating=10

SELECT S.sname

FROM Sailors S

WHERE S.rating= (SELECT MAX(S2.rating)

FROM Sailors S2)

single column

SELECT COUNT (DISTINCT S.rating)

FROM Sailors S

WHERE S.sname=‘Bob’

Find name and age of the oldest sailor(s)

The first query is illegal! (We’ll look into the reason, when we discuss

GROUP BY.)

SELECT S.sname, MAX (S.age)

FROM Sailors S

SELECT S.sname, S.age

FROM Sailors S

WHERE S.age =

(SELECT MAX (S2.age)

FROM Sailors S2)

11

12

7

GROUP BY and HAVING

So far, we’ve applied aggregate operators to all (qualifying) tuples. Sometimes, we want to apply them to each of several groups of tuples.

Consider: Find the age of the youngest sailor for each rating level.

In general, we don’t know how many rating levels exist, and what the rating values for these levels are!

Suppose we know that rating values go from 1 to 10; we can write 10 queries that look like this (!):

SELECT MIN (S.age)FROM Sailors SWHERE S.rating = i

For i = 1, 2, ... , 10:

Queries With GROUP BY and HAVING

The target-list contains (i) attribute names (ii) terms with aggregate operations (e.g.,

MIN (S.age)).

The attribute list (i) must be a subset of grouping-list. Intuitively, each answer tuple corresponds to a group, and these attributes must have a single value per group. (A group is a set of tuples that have the same value for all attributes in grouping-list.)

SELECT [DISTINCT] target-list

FROM relation-list

WHERE qualification

GROUP BY grouping-list

HAVING group-qualification

13

14

8

Find the age of the youngest sailor with age 18, for each rating with at least 2 such sailors

Only S.rating and S.age are mentioned in the SELECT,

GROUP BY or HAVING clauses; other attributes `unnecessary’.

2nd column of result is unnamed. (Use AS to name it.)

SELECT S.rating, MIN (S.age)

FROM Sailors S

WHERE S.age >= 18

GROUP BY S.rating

HAVING COUNT (*) > 1

sid sname rating age

22 dustin 7 45.0

31 lubber 8 55.5

71 zorba 10 16.0

64 horatio 7 35.0

29 brutus 1 33.0

58 rusty 10 35.0

rating age

1 33.0

7 45.0

7 35.0

8 55.5

10 35.0

rating

7 35.0

Answer relation

For each red boat, find the number of reservations for this boat

Grouping over a join of three relations.

What do we get if we remove B.color=‘red’ from the WHERE clause

and add a HAVING clause with this condition?

What if we drop Sailors and the condition involving S.sid?

SELECT B.bid, COUNT (*) AS scount

FROM Sailors S, Boats B, Reserves R

WHERE S.sid=R.sid AND R.bid=B.bid AND B.color=‘red’

GROUP BY B.bid

15

16

9

Find the age of the youngest sailor with age > 18, for each rating with at least 2 sailors

(of any age)

Shows HAVING clause can also contain a subquery.

Compare this with the query where we considered only ratings with 2 sailors over 18!

What if HAVING clause is replaced by:

HAVING COUNT(*) >1

SELECT S.rating, MIN (S.age)

FROM Sailors S

WHERE S.age > 18

GROUP BY S.rating

HAVING 1 < (SELECT COUNT (*)

FROM Sailors S2

WHERE S.rating=S2.rating)

Find those ratings for which the average age is the minimum over all

ratingsAggregate operations cannot be nested! WRONG:

SELECT S.rating

FROM Sailors S

WHERE S.age = (SELECT MIN (AVG (S2.age)) FROM Sailors S2)

SELECT Temp.rating, Temp.avgage

FROM (SELECT S.rating, AVG (S.age) AS avgage

FROM Sailors S

GROUP BY S.rating) AS Temp

WHERE Temp.avgage = (SELECT MIN (Temp.avgage)

FROM Temp)

Correct solution (in SQL/92):

17

18

10

Multidimensional Data

Model

Collection of numeric measures, which depend on a set of

dimensions.

E.g., measure Sales, dimensions Product (key: pid),

Location (locid), and Time (timeid).

8 10 10

30 20 50

25 8 15

1 2 3timeid

pid

11 12 13

11 1 1 25

11 2 1 8

11 3 1 15

12 1 1 30

12 2 1 20

12 3 1 50

13 1 1 8

13 2 1 10

13 3 1 10

11 1 2 35

pid

tim

eid

loci

d

sale

s

locid

Slice locid=1is shown:

Dimension Hierarchies

For each dimension, the set of values can be organized in a hierarchy:

PRODUCT TIME LOCATION

category week month state

pname date city

year

quarter country

19

20

11

Star Schema Design

Fact table is large, updates are frequent; dimension tables are small,

updates are rare.

This kind of schema is very common in OLAP applications, and is called a

star schema; computing the join of all these relations is called a star join.

pricecategorypnamepid countrystatecitylocid

saleslocidtimeidpid

holiday_flagweekdatetimeid month quarter year

(Fact table)SALES

TIMES

PRODUCTS LOCATIONS

OLAP Queries

Influenced by SQL and by spreadsheets.

A common operation is to aggregate a measure over one or more

dimensions.

Find total sales.

Find total sales for each city, or for each state.

Find top five products ranked by total sales.

Roll-up: Aggregating at different levels of a dimension hierarchy.

E.g., Given total sales by city, we can roll-up to get sales by state.

Drill-down: The inverse of roll-up.

E.g., Given total sales by state, can drill-down to get total sales by

city.

E.g., Can also drill-down on different dimension to get total sales by

product for each state.

21

22

12

OLAP Queries

Pivoting: Aggregation on selected dimensions.

E.g., Pivoting on Location and Time yields this cross-tabulation:

63 81 144

38 107 145

75 35 110

WI CA Total

1995

1996

1997

176 223 339Total

Slicing and Dicing: Equalityand range selections on oneor more dimensions.

Using SQL for Pivoting

The cross-tabulation obtained by pivoting can also be computed using a

collection of SQLqueries:

SELECT SUM(S.sales)FROM Sales S, Times T, Locations LWHERE S.timeid=T.timeid AND S.timeid=L.timeidGROUP BY T.year, L.state

SELECT SUM(S.sales)FROM Sales S, Times TWHERE S.timeid=T.timeidGROUP BY T.year

SELECT SUM(S.sales)FROM Sales S, Location LWHERE S.timeid=L.timeidGROUP BY L.state

23

24

13

The CUBE Operator

Generalizing the previous example, if there are k dimensions, we have

2^k possible SQL GROUP BY queries that can be generated through

pivoting on a subset of dimensions.

CUBE pid, locid, timeid BY SUM Sales

Equivalent to rolling up Sales on all eight subsets of the set {pid,

locid, timeid}; each roll-up corresponds to an SQL query of the

form:

SELECT SUM(S.sales)FROM Sales SGROUP BY grouping-list

Lots of work onoptimizing the CUBE operator!

Views and Decision Support

OLAP queries are typically aggregate queries.

Precomputation is essential for interactive response times.

The CUBE is in fact a collection of aggregate queries, and

precomputation is especially important: lots of work on what is best to

precompute given a limited amount of space to store precomputed

results.

Warehouses can be thought of as a collection of asynchronously

replicated tables and periodically maintained views.

Has renewed interest in view maintenance!

25

26

14

View Modification (Evaluate On Demand)

CREATE VIEW RegionalSales(category,sales,state)AS SELECT P.category, S.sales, L.state

FROM Products P, Sales S, Locations LWHERE P.pid=S.pid AND S.locid=L.locid

SELECT R.category, R.state, SUM(R.sales)FROM RegionalSales AS R GROUP BY R.category, R.state

SELECT R.category, R.state, SUM(R.sales)FROM (SELECT P.category, S.sales, L.state

FROM Products P, Sales S, Locations LWHERE P.pid=S.pid AND S.locid=L.locid) AS R

GROUP BY R.category, R.state

View

Query

ModifiedQuery

View Materialization (Precomputation)

Suppose we precompute RegionalSales and store it.

Then, previous query can be answered more efficiently (modified query will

not be generated).

27

28

15

Issues in View Materialization

What views should we materialize, and what indexes should we build

on the precomputed results?

Given a query and a set of materialized views, can we use the

materialized views to answer the query?

How frequently should we refresh materialized views to make them

consistent with the underlying tables? (And how can we do this

incrementally?)

More on Drilling Down

Drilling down means adding a row header (a grouping column) to an

existing SELECT statement.

E.g., if you’re analyzing the sales of products at a manufacturer level, the select

list of the query reads SELECT MANUFACTURER, SUM(SALES).

If you wish to drill down on the list of manufacturers to show the brands sold,

you add the BRAND row header: SELECT MANUFACTURER, BRAND,

SUM(SALES).

the GROUP BY clause in the second query reads GROUP BY

MANUFACTURER, BRAND. Row headers and grouping columns are the same

thing.

Now each manufacturer row expands into multiple rows listing all the brands

sold.

This example is particularly simple because in a star schema, both the

manufacturer attribute and the brand attribute exist in the same product

dimension table.

29

30

16

Drill Down Paths

Drilling down has nothing to do with descending a predetermined

hierarchy: you can drill down using any attribute drawn from any

dimension (e.g., the weekday from the time dimension).

A good data warehouse designer should always be thinking of

additional drill-down paths to add to an existing environment.

Example: adding an audit dimension to a fact table. The audit

dimension contains indicators of data quality in the fact table, such as

“data element out of bounds.”

You can devise a standard report to drill down to issues of data

quality, including the proportion of questionable data.

By drilling down on data quality, each row of the original report would

appear as multiple rows, each with a different data quality indicator.

Aggregate Navigator

The data warehouse must support drilling down at the user interface level with

the most atomic data possible because the most atomic data is the most

dimensional.

The atomic data must be in the same schema format as any aggregated form

of the data.

An aggregated fact table (materialized view) is a derived table of summary

records.

Aggregated fact tables (materialized views) offer notable performance

advantages compared to using the large, atomic fact tables. But you get this

performance boost only when the user asks for an aggregated result.

A modern data warehouse environment uses a query-rewrite facility called an

aggregate navigator to choose a prebuilt aggregate table whenever possible.

Each time the end user asks for a new drill-down path, the aggregate navigator

decides in real time which aggregate fact table will support the query most

efficiently.

Whenever the user asks for a sufficiently precise and unexpected drill down,

the aggregate navigator gracefully defaults to the atomic data layer.

31

32

17

Drilling down with no drill down path

%Total sales in PA = 100; total sales in NYC = 260

%Drill down to sales by cities: Pitt (x1), Phil (x2) in PA,

%NYC (x3) and Buff (x4) in NYC;

%"Ground truth": x1 = 30, x2 = 70, x3 = 110, x4 = 150

% Linear system: x1+x2 = 100; x3+x4=260;

% Matrix representation:

A = [1 1 0 0; 0 0 1 1];

y = [100;260];

x = pinv(A)*y;

% x=[50;50;130;130]

x_gt = [30 70 110 150]';

rmse = sqrt(mean((x-x_gt).^2));

% rmse = 20

norm_x = norm(x);

% norm_x = 196.977

norm_x_gt = norm(x_gt);

% noxm_x_gt = 200.9975

% Application constraint: sales in Phil are twice as much as in Pitt

A = [1 1 0 0; 0 0 1 1;2 -1 0 0];

y = [100;260;0];

x = pinv(A)*y;

%x = [33.3333; 66.6667; 30.0000; 130.0000];

rmse = sqrt(mean((x-x_gt).^2));

% rmse = 14.3372; 20 > 14.3372

norm_x = norm(x);

% norm_x = 198.3823

Drilling down with no drill down path (cont)

33

34

18

Drilling down with no drill down path (cont)

% Another application constraint: sales in NYC are twice as much as in Buf.

% Apparently this is further from truth than the first constraint,

% so we should expect larger RMSE:

A = [1 1 0 0; 0 0 1 1;2 -1 0 0;0 0 1 -2];

y = [100;260;0;0];

x = pinv(A)*y;

% x = [33.3333; 66.6667; 173.3333; 86.6667]

rmse = sqrt(mean((x-x_gt).^2));

% rmse = 44.8454; 44.8454 > 20 > 14.3372

norm_x = norm(x);

%norm_x = 207.6322;

Drilling down with no drill down path (cont)

% Another domain constraint: values should be close to each other

other,

% no spikes

A = [1 1 0 0; 0 0 1 1; 1 -1 0 0; 0 1 -1 0; 0 0 1 -1];

y = [100;260;0;0;0];

x = pinv(A)*y;

%x = [50.0000; 70.0000; 110.0000; 130.0000]

% this is an approximate solution, since now our system is

overdetermined

rmse = sqrt(mean((x-x_gt).^2));

%rmse = 14.1421

norm_x = norm(x);

%norm_x = 190.7878

35

36

19

Drilling down with no drill down path (cont)

% Now we consider a different application: Historical Data Integration

(see example in notes).

A = [1 1 1 1 0 0; 0 0 1 1 1 1]; % overlap

y = [100;160];

x = pinv(A)*y;

% x = [6.6667; 6.6667; 43.3333; 43.3333; 36.6667; 36.6667];

% Now we add explicit constraints about x1, x2, x5 and x4:

A = [1 1 1 1 0 0; 0 0 1 1 1 1; 1 0 0 0 0 0; 0 1 0 0 0 0; 0 0 0 0 1 0; 0 0 0

0 0 1;];

y = [100;160;10;20;50;60];

x = pinv(A)*y;

%x = [13.3333; 23.3333; 30.0000; 30.0000; 46.6667; 56.6667}

Drilling down with no drill down path (cont)

%Next, add smoothness constraint:

A = [1 1 1 1 0 0; 0 0 1 1 1 1]; % overlap

y = [100;160];

[Asm, ysm] = sm_constraints(A, y); % this function is provided in class

materials

x = pinv(Asm)*ysm;

%x = [17.5000; 21.2500; 28.7500; 36.2500; 43.7500; 47.5000]

Asm =

1 1 1 1 0 0

0 0 1 1 1 1

1 -1 0 0 0 0

0 1 -1 0 0 0

0 0 1 -1 0 0

0 0 0 1 -1 0

0 0 0 0 1 -1

100

160

0

0

0

0

0

ysm =

37

38

20

Drill down (reconstruction) accuracy

RD = 100, shift = 50

Drill down (reconstruction) accuracy

RD = 20, shift = 10

39

40

21

All RDs and shifts

RMSE vs Event Detection Accuracy

RD = 100

Shift = 50RD = 50

Shift = 25RD = 20

Shift = 10

Perfect Reconstruction is not required for

Notable Event Assessment

41

42

22

Summary

Decision support is an emerging, rapidly growing subarea of

databases.

Involves the creation of large, consolidated data repositories called

data warehouses.

Warehouses exploited using sophisticated analysis techniques:

complex SQL queries and OLAP “multidimensional” queries

(influenced by both SQL and spreadsheets).

New techniques for database design, indexing, view maintenance, and

interactive querying need to be supported.

Commonly requires integrating DISTRIBUTED HETEROGENEOUS

DATA

43