Data Analysis

1. Data Analysis

2. Overview • Traditional database systems are tuned to many, small, simple queries. • Some applications use fewer, more time-consuming, analytic queries.

3. 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.

4. 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.

5. 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.

6. Star Schemas • A star schema is a common organization for data at a warehouse. It consists of: • Fact table : a very large accumulation of facts such as sales. • Dimension tables : smaller, generally static information about the entities involved in the facts.

7. 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)

8. 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.

9. Visualization – Star Schema Dimension Table (Autos) Dimension Table (Dealer) Dimension Attrs. Dependent Attrs., e.g. price Fact Table - Sales Dimension Table (Day) Dimension Table (etc.)

10. 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.

11. Visualization -- Data Cubes car price dealer date

12. Slicing and Dicing • Slice • focus on particular partitions along (one or more) dimension i.e., focus on a particular slice of the cube WHERE clause in SQL • Dice • partition the cube into smaller subcubes and aggregated the points in each GROUP BY clause in SQL

13. Slicing and Dicing in SQL SELECT 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 */

14. 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;

15. 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;

16. 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;

17. 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;

18. 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.

19. car SUM over all Days price dealer date Marginals --- Data Cube w/Aggregation

20. 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

21. Example Sales(serialNo, date, dealer, price) Sales(model, color, date, dealer, val, cnt) 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. 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.

22. 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.

23. 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.

24. CUBE Helps Answering Queries SELECT 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.

25. CUBE in SQL SELECT model, color, date, dealer, SUM(val) AS v, SUM(cnt) AS n FROM Sales GROUP BY model, color, date, dealer WITH CUBE; Suppose we materialize this into SalesCube. Then the previous query is rewritten into: SELECT color, SUM(v)/SUM(n) FROM SalesCube WHERE model = 'Gobi' AND date IS NULL AND dealer IS NULL;

26. Data Mining Data mining is a popular term for summarization of big data sets in useful ways. Examples: • Clustering Web pages by topic. • Finding characteristics of fraudulent credit-card use. • Finding products that are usually bought together.

27. 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.

28. Example: Market Baskets • If people often buy hamburger and ketchup together, the store can: • Put hamburger and ketchup near each other and put potato chips between. • Run a sale on hamburger and raise the price of ketchup.

29. 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 thresholds is the minimum number of baskets in which a pair appears before we are interested.

30. Look for two Basket tuples with the same basket and different items. First item must precede second, so we don’t count the same pair twice. Create a group for each pair of items that appears in at least one basket. Throw away pairs of items that do not appear at least s times. 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;

31. 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.

32. Items that appear in at least s baskets. 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 );

33. A-Priori Algorithm • Materialize the view Baskets1. • Run the obvious query, but on Baskets1 instead of Baskets. Notes • ComputingBaskets1 is cheap, since it doesn’t involve a join. • Baskets1probably has many fewer tuples than Baskets. • Running time shrinks with the square of the number of tuples involved in the join.

34. Course Plug Fall 2009: CSC 485E / CSC 571: Advanced Databases Spring 2010: SENG 474: Data Mining