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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.
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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
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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:
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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
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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’)
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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)
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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
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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
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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):
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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
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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
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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.
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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
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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!
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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).
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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.
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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.
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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)
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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
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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 =
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Drill down (reconstruction) accuracy
RD = 100, shift = 50
Drill down (reconstruction) accuracy
RD = 20, shift = 10
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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
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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
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