OLAP and Data Warehousing Advanced Topics in Database Management - - PDF document

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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,

• ften augmented with summary information.

Several gigabytes to terabytes common. Interactive response times expected for complex queries; ad-hoc updates uncommon. EXTERNAL DATA SOURCES EXTRACT TRANSFORM LOAD REFRESH DATA WAREHOUSE

Metadata Repository

SUPPORTS

OLAP

DATA MINING 3 4

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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

• ther 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 3 timeid 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 timeid locid sales locid

Slice locid=1 is 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

• n 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’) 9 10

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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) 11 12

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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 S WHERE 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

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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;

• ther 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

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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

• ver 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 ratings

Aggregate 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 3 timeid 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 timeid locid sales locid

Slice locid=1 is 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.

price category pname pid country state city locid sales locid timeid pid holiday_flag week date timeid 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

176 223 339

Total

Slicing and Dicing: Equality and range selections on one

• r 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 L WHERE S.timeid=T.timeid AND S.timeid=L.timeid GROUP BY T.year, L.state SELECT SUM(S.sales) FROM Sales S, Times T WHERE S.timeid=T.timeid GROUP BY T.year SELECT SUM(S.sales) FROM Sales S, Location L WHERE S.timeid=L.timeid GROUP 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 S GROUP BY grouping-list Lots of work on

• ptimizing 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 L WHERE 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 L WHERE P.pid=S.pid AND S.locid=L.locid) AS R GROUP BY R.category, R.state

View Query Modified Query

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

• n 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

• f 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

• ther,

% 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

• verdetermined

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 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 = 50 RD = 50 Shift = 25 RD = 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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