Data Analysis

Overview

• Traditional database systems are tuned to many, small, simple queries.

• Some applications use fewer, more time-consuming, analytic queries.

OLTP

• Most database operations involve On-Line Transaction Processing (OTLP).– Short, simple, frequent queries and/or modifications,

each involving a small number of tuples.

• Examples: – Answering queries from a Web interface,

– sales at cash registers,

– selling airline tickets.

OLAP

• On-Line Analytical Processing (OLAP, or “analytic”) queries are, typically:– Few, but complex queries --- may run for hours.

– Queries don't depend on having an absolutely up-to-date database.

• Example– Partition car sales by years, and look at only the last two

years (2007 and 2008). Aggregate price.

Common Architecture

• Databases at store branches handle OLTP.• Local store databases copied to a central data warehouse

overnight.• Analysts use the data warehouse for OLAP.

Star Schemas

• A star schema is a common organization for data at a warehouse. It consists of:

1. Fact table : a very large accumulation of facts such as sales.

2. Dimension tables : smaller, generally static information about the entities involved in the facts.

Example: Star Schema

• Suppose we want to record in a warehouse information about every car sale, e.g.: – serial number,

– dealer who sold the car,

– date of the sale, and

– price charged.

• The fact table is thus:

Sales(serialNo, dealer, day, price)

Example -- Continued

• The dimension tables include information about the autos, dealers, and days “dimensions”:

Autos(serialNo, model, color)

Dealers(name, city, province)

Days(day, week, month, year)

Days dimension table probably not stored.

Visualization – Star Schema

Dimension Table (Day) Dimension Table (etc.)

Dimension Table (Dealer)Dimension Table (Autos)

Fact Table - Sales

Dimension Attrs. Dependent Attrs., e.g. price

Data Cubes

• Keys of dimension tables are the dimensions of a hypercube.

• Example: for the Sales data, the three dimensions are serialNo, date, and dealer.

• Dependent attributes (e.g., price) appear at the points of the cube.

Visualization -- Data Cubes

price

dealer

car

date

Slicing and Dicing

• Slice– focus on particular partitions along (one or more) dimension

i.e., focus on a particular slice of the cubeWHERE clause in SQL

• Dice– partition the cube into smaller subcubes and aggregated the

points in eachGROUP BY clause in SQL

Slicing and Dicing in SQLSELECT grouping-attributes and aggregations

FROM fact table joined with (zero or more) dimension tables

WHERE certain attributes are compared with constants /* slicing */

GROUP BY grouping-attributes /* dicing */

Slicing and Dicing Example

• Suppose a particular car model, say ‘Gobi’, isn't selling as well as anticipated. How to analyze?

• Maybe it’s the color…

• Slice for ‘Gobi.’ Dice for color.

SELECT color, SUM(price)

FROM Sales NATURAL JOIN Autos

WHERE model = 'Gobi'

GROUP BY color;

Slicing and Dicing Example

• Suppose the previous query doesn't tell us much; each color produces about the same revenue.

• Since the query does not dice for time, we only see the total over all time for each color. – We may thus issue a revised query that also partitions time by

month.

SELECT color, month, SUM(price)

FROM (Sales NATURAL JOIN Autos) NATURAL JOIN Days

WHERE model = 'Gobi'

GROUP BY color, month;

Slicing and Dicing Example

• We might discover that red Gobis haven’t sold well recently. • Does this problem exists at all dealers, or only some dealers

have had low sales of red Gobis? • Let’s dice on dealer dimension.

SELECT dealer, month, SUM(price)

FROM (Sales NATURAL JOIN Autos) NATURAL JOIN Days

WHERE model = 'Gobi' AND color = 'red‘

GROUP BY month, dealer;

Slicing and Dicing Example

• At this point, we find that the sales per month for red Gobis are so small that we cannot observe any trends easily.

• We decide it was a mistake to dice by month. A better partition by years, and look at only the last two years (2007 and 2008).

SELECT dealer, year, SUM(price)

FROM (Sales NATURAL JOIN Autos) NATURAL JOIN Days

WHERE model = 'Gobi' AND color = 'red' AND

(year = 2007 OR year = 2008)

GROUP BY year, dealer;

Drill-Down and Roll-Up

• Previous examples illustrate two common patterns in sequences of queries that slice-and-dice the data cube.

• Drill-down is the process of partitioning more finely and/or focusing on specific values in certain dimensions. – Each of the example steps except the last is an instance of

drill-down.

• Roll-up is the process of partitioning more coarsely. – The last step, where we grouped by years instead of months

to eliminate the effect of randomness in the data, is an example of roll-up.

Marginals --- Data Cube w/Aggregation

price

dealer

car

dateSU

M o

ver

all D

ays

Cube operator• CUBE(F) is an augmented table for fact table F

– tuples (or points) added in CUBE(F)• have a value, denoted * to each dimension

– * represents aggregation along that dimension

Example

Sales(serialNo, date, dealer, price)

Sales(model, color, date, dealer, val, cnt)

We replace the serialNo by model and color to which the serial number connects.

Also, we will have as independent attributes, val for sum of prices and cnt for number of cars sold.

serialNo dimension not well suited for the cube as summing the price over all dates, or over all dealers, but keeping the serial number fixed has no effect.

Example: CUBE(Sale)

• ('Gobi', 'red', '2001-05-21', 'Friendly Fred', 45000, 2)– On May 21, 2001, dealer Friendly Fred sold two red Gobis

for a total of $45,000.

– This tuple is in both Sales and CUBE(Sales).

• ('Gobi', *, '2001-05-21', 'Friendly Fred', 152000, 7) – On May 21, 2001, Friendly Fred sold seven Gobis of all

colors, for a total price of $152,000.

– Note that this tuple is in CUBE(Sales) but not in Sales.

Example: CUBE(Sale)

• ('Gobi', *, '2001-05-21', *, 2348000, 100)– On May 21, 2001, there were 100 Gobis sold by all the

dealers, and the total price of those Gobis was $2,348,000.

• ('Gobi', *, *, *, 1339800000, 58000)– Over all time, dealers, and colors, 58,000 Gobis have been

sold for a total price of $1,339,800,000.

• (*, *, *, *, 3521727000, 198000)– Total sales of all models in all colors, over all time at all

dealers is 198,000 cars for a total price of $3,521,727,000.

CUBE Helps Answering QueriesSELECT color, AVG(price)

FROM Sales

WHERE model = 'Gobi'

GROUP BY color;

is answered by looking for all tuples of CUBE(Sales) with the form

('Gobi', c, *, *, v, n)

where c is any specific color. v and n will be the sum and number of sales of Gobis in that color. The average price, is v/n. The answer to query is the set of (c; v/n) pairs obtained from all ('Gobi', c, *, *, v, n) tuples.

CUBE in SQL

SELECT model, color, date, dealer, SUM(val) AS v, SUM(cnt) AS nFROM Sales GROUP BY model, color, date, dealerWITH CUBE;

Suppose we materialize this into SalesCube.Then the previous query is rewritten into:

SELECT color, SUM(v)/SUM(n)FROM SalesCubeWHERE model = 'Gobi' AND

date IS NULL AND dealer IS NULL;

Data Mining

Data mining is a popular term for summarization of big data sets in useful ways.

Examples:1. Clustering Web pages by topic.

2. Finding characteristics of fraudulent credit-card use.

3. Finding products that are usually bought together.

Market-Basket Data

• An important form of mining from relational data involves market baskets = sets of “items” that are purchased together as a customer leaves a store.

• Summary of basket data is frequent itemsets = sets of items that often appear together in baskets.

Example: Market Baskets

• If people often buy hamburger and ketchup together, the store can:

1. Put hamburger and ketchup near each other and put potato chips between.

2. Run a sale on hamburger and raise the price of ketchup.

Finding Frequent Pairs

• The simplest case is when we only want to find “frequent pairs” of items.

• Assume data is in a relation Baskets(basket, item).

• The support threshold s is the minimum number of baskets in which a pair appears before we are interested.

Frequent Pairs in SQL

SELECT b1.item, b2.item

FROM Baskets b1, Baskets b2

WHERE b1.basket = b2.basket

AND b1.item < b2.item

GROUP BY b1.item, b2.item

HAVING COUNT(*) >= s;

Look for twoBasket tupleswith the samebasket anddifferent items.First item mustprecede second,so we don’tcount the samepair twice.

Create a group foreach pair of itemsthat appears in atleast one basket.

Throw away pairs of itemsthat do not appear at leasts times.

A-Priori Trick – (1)

• Straightforward implementation involves a join of a huge Baskets table with itself.

• The A-Priori algorithm speeds the query by recognizing that a pair of items {i, j } cannot have support s unless both {i } and {j } do.

A-Priori Trick – (2)• Use a materialized view to hold only

information about frequent items.

INSERT INTO Baskets1(basket, item)

SELECT * FROM Baskets

WHERE item IN (

SELECT item FROM Baskets

GROUP BY item

HAVING COUNT(*) >= s

);

Items thatappear in atleast s baskets.

A-Priori Algorithm

1. Materialize the view Baskets1.

2. Run the obvious query, but on Baskets1 instead of Baskets.

Notes• Computing Baskets1 is cheap, since it doesn’t involve a

join.• Baskets1 probably has many fewer tuples than Baskets.

– Running time shrinks with the square of the number of tuples involved in the join.

Course Plug

Fall 2009: CSC 485E / CSC 571: Advanced Databases

Spring 2010: SENG 474: Data Mining