Data Mining Concepts and Techniques Slides for Textbook

Data Mining: Concepts and Techniques — Slides for Textbook — — Chapter 2 — ©Jiawei Han and Micheline Kamber Department of Computer Science University of Illinois at Urbana-Champaign www. cs. uiuc. edu/~hanj 11/28/2020 Data Mining: Concepts and Techniques 1

Chapter 2: Data Warehousing and OLAP Technology for Data Mining n What is a data warehouse? n A multi-dimensional data model n Data warehouse architecture n Data warehouse implementation n Further development of data cube technology n From data warehousing to data mining 11/28/2020 Data Mining: Concepts and Techniques 2

What is Data Warehouse? n Defined in many different ways, but not rigorously. n A decision support database that is maintained separately from the organization’s operational database n Support information processing by providing a solid platform of consolidated, historical data for analysis. n “A data warehouse is a subject-oriented, integrated, time-variant, and nonvolatile collection of data in support of management’s decision-making process. ”—W. H. Inmon n Data warehousing: n 11/28/2020 The process of constructing and using data warehouses Data Mining: Concepts and Techniques 3

Data Warehouse—Subject-Oriented n Organized around major subjects, such as customer, product, sales. n Focusing on the modeling and analysis of data for decision makers, not on daily operations or transaction processing. n Provide a simple and concise view around particular subject issues by excluding data that are not useful in the decision support process. 11/28/2020 Data Mining: Concepts and Techniques 4

Data Warehouse—Integrated n n Constructed by integrating multiple, heterogeneous data sources n relational databases, flat files, on-line transaction records Data cleaning and data integration techniques are applied. n Ensure consistency in naming conventions, encoding structures, attribute measures, etc. among different data sources n n 11/28/2020 E. g. , Hotel price: currency, tax, breakfast covered, etc. When data is moved to the warehouse, it is converted. Data Mining: Concepts and Techniques 5

Data Warehouse—Time Variant n The time horizon for the data warehouse is significantly longer than that of operational systems. n n n Operational database: current value data. Data warehouse data: provide information from a historical perspective (e. g. , past 5 -10 years) Every key structure in the data warehouse n n 11/28/2020 Contains an element of time, explicitly or implicitly But the key of operational data may or may not contain “time element”. Data Mining: Concepts and Techniques 6

Data Warehouse—Non-Volatile n A physically separate store of data transformed from the operational environment. n Operational update of data does not occur in the data warehouse environment. n Does not require transaction processing, recovery, and concurrency control mechanisms n Requires only two operations in data accessing: n 11/28/2020 initial loading of data and access of data. Data Mining: Concepts and Techniques 7

Data Warehouse vs. Heterogeneous DBMS n Traditional heterogeneous DB integration: n Build wrappers/mediators on top of heterogeneous databases n Query driven approach n n n When a query is posed to a client site, a meta-dictionary is used to translate the query into queries appropriate for individual heterogeneous sites involved, and the results are integrated into a global answer set Complex information filtering, compete for resources Data warehouse: update-driven, high performance n 11/28/2020 Information from heterogeneous sources is integrated in advance and stored in warehouses for direct query and analysis Data Mining: Concepts and Techniques 8

Data Warehouse vs. Operational DBMS n OLTP (on-line transaction processing) n n Major task of traditional relational DBMS Day-to-day operations: purchasing, inventory, banking, manufacturing, payroll, registration, accounting, etc. OLAP (on-line analytical processing) n Major task of data warehouse system n Data analysis and decision making Distinct features (OLTP vs. OLAP): n User and system orientation: customer vs. market n Data contents: current, detailed vs. historical, consolidated n Database design: ER + application vs. star + subject n View: current, local vs. evolutionary, integrated n Access patterns: update vs. read-only but complex queries 11/28/2020 Data Mining: Concepts and Techniques 9

OLTP vs. OLAP 11/28/2020 Data Mining: Concepts and Techniques 10

Why Separate Data Warehouse? n High performance for both systems n n n DBMS— tuned for OLTP: access methods, indexing, concurrency control, recovery Warehouse—tuned for OLAP: complex OLAP queries, multidimensional view, consolidation. Different functions and different data: n n n 11/28/2020 missing data: Decision support requires historical data which operational DBs do not typically maintain data consolidation: DS requires consolidation (aggregation, summarization) of data from heterogeneous sources data quality: different sources typically use inconsistent data representations, codes and formats which have to be reconciled Data Mining: Concepts and Techniques 11

Chapter 2: Data Warehousing and OLAP Technology for Data Mining n What is a data warehouse? n A multi-dimensional data model n Data warehouse architecture n Data warehouse implementation n Further development of data cube technology n From data warehousing to data mining 11/28/2020 Data Mining: Concepts and Techniques 12

From Tables and Spreadsheets to Data Cubes n n A data warehouse is based on a multidimensional data model which views data in the form of a data cube A data cube, such as sales, allows data to be modeled and viewed in multiple dimensions n n n Dimension tables, such as item (item_name, brand, type), or time(day, week, month, quarter, year) Fact table contains measures (such as dollars_sold) and keys to each of the related dimension tables In data warehousing literature, an n-D base cube is called a base cuboid. The top most 0 -D cuboid, which holds the highest-level of summarization, is called the apex cuboid. The lattice of cuboids forms a data cube. 11/28/2020 Data Mining: Concepts and Techniques 13

Cube: A Lattice of Cuboids all time, item 0 -D(apex) cuboid item time, location item, location time, supplier time, item, location supplier location, supplier item, supplier time, location, supplier time, item, supplier 1 -D cuboids 2 -D cuboids 3 -D cuboids item, location, supplier 4 -D(base) cuboid time, item, location, supplier 11/28/2020 Data Mining: Concepts and Techniques 14

Conceptual Modeling of Data Warehouses n Modeling data warehouses: dimensions & measures n Star schema: A fact table in the middle connected to a set of dimension tables n Snowflake schema: A refinement of star schema where some dimensional hierarchy is normalized into a set of smaller dimension tables, forming a shape similar to snowflake n Fact constellations: Multiple fact tables share dimension tables, viewed as a collection of stars, therefore called galaxy schema or fact constellation 11/28/2020 Data Mining: Concepts and Techniques 15

Example of Star Schema time item time_key day_of_the_week month quarter year Sales Fact Table time_key item_key branch_key branch_name branch_type location_key units_sold dollars_sold avg_sales item_key item_name brand type supplier_type location_key street city state_or_province country Measures 11/28/2020 Data Mining: Concepts and Techniques 16

Example of Snowflake Schema time_key day_of_the_week month quarter year item Sales Fact Table time_key item_key branch location_key branch_name branch_type units_sold dollars_sold avg_sales Measures 11/28/2020 Data Mining: Concepts and Techniques item_key item_name brand type supplier_key supplier_type location_key street city_key city state_or_province country 17

Example of Fact Constellation time_key day_of_the_week month quarter year item Sales Fact Table time_key item_key item_name brand type supplier_type location_key branch_name branch_type units_sold dollars_sold avg_sales item_key shipper_key location to_location_key street city province_or_state country dollars_cost Measures 11/28/2020 time_key from_location branch_key branch Shipping Fact Table Data Mining: Concepts and Techniques units_shipped shipper_key shipper_name location_key shipper_type 18

A Data Mining Query Language: DMQL n n n 11/28/2020 Cube Definition (Fact Table) define cube <cube_name> [<dimension_list>]: <measure_list> Dimension Definition ( Dimension Table ) define dimension <dimension_name> as (<attribute_or_subdimension_list>) Special Case (Shared Dimension Tables) n First time as “cube definition” n define dimension <dimension_name> as <dimension_name_first_time> in cube <cube_name_first_time> Data Mining: Concepts and Techniques 19

Defining a Star Schema in DMQL define cube sales_star [time, item, branch, location]: dollars_sold = sum(sales_in_dollars), avg_sales = avg(sales_in_dollars), units_sold = count(*) define dimension time as (time_key, day_of_week, month, quarter, year) define dimension item as (item_key, item_name, brand, type, supplier_type) define dimension branch as (branch_key, branch_name, branch_type) define dimension location as (location_key, street, city, province_or_state, country) 11/28/2020 Data Mining: Concepts and Techniques 20

Defining a Snowflake Schema in DMQL define cube sales_snowflake [time, item, branch, location]: dollars_sold = sum(sales_in_dollars), avg_sales = avg(sales_in_dollars), units_sold = count(*) define dimension time as (time_key, day_of_week, month, quarter, year) define dimension item as (item_key, item_name, brand, type, supplier(supplier_key, supplier_type)) define dimension branch as (branch_key, branch_name, branch_type) define dimension location as (location_key, street, city(city_key, province_or_state, country)) 11/28/2020 Data Mining: Concepts and Techniques 21

Defining a Fact Constellation in DMQL define cube sales [time, item, branch, location]: dollars_sold = sum(sales_in_dollars), avg_sales = avg(sales_in_dollars), units_sold = count(*) define dimension time as (time_key, day_of_week, month, quarter, year) define dimension item as (item_key, item_name, brand, type, supplier_type) define dimension branch as (branch_key, branch_name, branch_type) define dimension location as (location_key, street, city, province_or_state, country) define cube shipping [time, item, shipper, from_location, to_location]: dollar_cost = sum(cost_in_dollars), unit_shipped = count(*) define dimension time as time in cube sales define dimension item as item in cube sales define dimension shipper as (shipper_key, shipper_name, location as location in cube sales, shipper_type) define dimension from_location as location in cube sales define dimension to_location as location in cube sales 11/28/2020 Data Mining: Concepts and Techniques 22

Measures: Three Categories n distributive: if the result derived by applying the function to n aggregate values is the same as that derived by applying the function on all the data without partitioning. n n algebraic: if it can be computed by an algebraic function with M arguments (where M is a bounded integer), each of which is obtained by applying a distributive aggregate function. n n E. g. , count(), sum(), min(), max(). E. g. , avg(), min_N(), standard_deviation(). holistic: if there is no constant bound on the storage size needed to describe a subaggregate. n 11/28/2020 E. g. , median(), mode(), rank(). Data Mining: Concepts and Techniques 23

A Concept Hierarchy: Dimension (location) all Europe region country city office 11/28/2020 Germany Frankfurt . . Spain North_America Canada Vancouver. . . L. Chan . . . Data Mining: Concepts and Techniques . . . Mexico Toronto M. Wind 24

View of Warehouses and Hierarchies Specification of hierarchies n Schema hierarchy day < {month < quarter; week} < year n Set_grouping hierarchy {1. . 10} < inexpensive 11/28/2020 Data Mining: Concepts and Techniques 25

Multidimensional Data Sales volume as a function of product, month, and region Dimensions: Product, Location, Time Hierarchical summarization paths gi on n Re Industry Region Year Product Category Country Quarter Product City Office Month Week Day Month 11/28/2020 Data Mining: Concepts and Techniques 26

2 Qtr 3 Qtr 4 Qtr Total annual sales sum of TV in U. S. A. od TV PC VCR sum 1 Qtr Date Pr U. S. A Canada Mexico Country uc t A Sample Data Cube sum 11/28/2020 Data Mining: Concepts and Techniques 27

Cuboids Corresponding to the Cube all 0 -D(apex) cuboid product, date country product, country 1 -D cuboids date, country 2 -D cuboids product, date, country 11/28/2020 Data Mining: Concepts and Techniques 3 -D(base) cuboid 28

Browsing a Data Cube n n n 11/28/2020 Visualization OLAP capabilities Interactive manipulation Data Mining: Concepts and Techniques 29

Typical OLAP Operations n Roll up (drill-up): summarize data n n Drill down (roll down): reverse of roll-up n n project and select Pivot (rotate): n n from higher level summary to lower level summary or detailed data, or introducing new dimensions Slice and dice: n n by climbing up hierarchy or by dimension reduction reorient the cube, visualization, 3 D to series of 2 D planes. Other operations n n 11/28/2020 drill across: involving (across) more than one fact table drill through: through the bottom level of the cube to its back-end relational tables (using SQL) Data Mining: Concepts and Techniques 30

A Star-Net Query Model Customer Orders Shipping Method Customer CONTRACTS AIR-EXPRESS ORDER TRUCK Time PRODUCT LINE ANNUALY QTRLY DAILY CITY Product PRODUCT ITEM PRODUCT GROUP SALES PERSON COUNTRY DISTRICT REGION Location 11/28/2020 Each circle is called a footprint DIVISION Promotion Data Mining: Concepts and Techniques Organization 31

Chapter 2: Data Warehousing and OLAP Technology for Data Mining n What is a data warehouse? n A multi-dimensional data model n Data warehouse architecture n Data warehouse implementation n Further development of data cube technology n From data warehousing to data mining 11/28/2020 Data Mining: Concepts and Techniques 32

Design of a Data Warehouse: A Business Analysis Framework n Four views regarding the design of a data warehouse n Top-down view n n Data source view n n consists of fact tables and dimension tables Business query view n 11/28/2020 exposes the information being captured, stored, and managed by operational systems Data warehouse view n n allows selection of the relevant information necessary for the data warehouse sees the perspectives of data in the warehouse from the view of end-user Data Mining: Concepts and Techniques 33

Data Warehouse Design Process n n n Top-down, bottom-up approaches or a combination of both n Top-down: Starts with overall design and planning (mature) n Bottom-up: Starts with experiments and prototypes (rapid) From software engineering point of view n Waterfall: structured and systematic analysis at each step before proceeding to the next n Spiral: rapid generation of increasingly functional systems, short turn around time, quick turn around Typical data warehouse design process n Choose a business process to model, e. g. , orders, invoices, etc. n Choose the grain (atomic level of data) of the business process n Choose the dimensions that will apply to each fact table record n Choose the measure that will populate each fact table record 11/28/2020 Data Mining: Concepts and Techniques 34

Multi-Tiered Architecture other Metadata sources Operational DBs Extract Transform Load Refresh Monitor & Integrator Data Warehouse OLAP Server Serve Analysis Query Reports Data mining Data Marts Data Sources 11/28/2020 Data Storage OLAP Engine Front-End Tools Data Mining: Concepts and Techniques 35

Three Data Warehouse Models n n Enterprise warehouse n collects all of the information about subjects spanning the entire organization Data Mart n a subset of corporate-wide data that is of value to a specific groups of users. Its scope is confined to specific, selected groups, such as marketing data mart n n Independent vs. dependent (directly from warehouse) data mart Virtual warehouse n A set of views over operational databases n Only some of the possible summary views may be materialized 11/28/2020 Data Mining: Concepts and Techniques 36

Data Warehouse Development: A Recommended Approach Multi-Tier Data Warehouse Distributed Data Marts Data Mart Model refinement Enterprise Data Warehouse Model refinement Define a high-level corporate data model 11/28/2020 Data Mining: Concepts and Techniques 37

OLAP Server Architectures n n Relational OLAP (ROLAP) n Use relational or extended-relational DBMS to store and manage warehouse data and OLAP middle ware to support missing pieces n Include optimization of DBMS backend, implementation of aggregation navigation logic, and additional tools and services n greater scalability Multidimensional OLAP (MOLAP) n Array-based multidimensional storage engine (sparse matrix techniques) n fast indexing to pre-computed summarized data Hybrid OLAP (HOLAP) n User flexibility, e. g. , low level: relational, high-level: array Specialized SQL servers n specialized support for SQL queries over star/snowflake schemas 11/28/2020 Data Mining: Concepts and Techniques 38

Chapter 2: Data Warehousing and OLAP Technology for Data Mining n What is a data warehouse? n A multi-dimensional data model n Data warehouse architecture n Data warehouse implementation n Further development of data cube technology n From data warehousing to data mining 11/28/2020 Data Mining: Concepts and Techniques 39

Efficient Data Cube Computation n Data cube can be viewed as a lattice of cuboids n The bottom-most cuboid is the base cuboid n The top-most cuboid (apex) contains only one cell n n How many cuboids in an n-dimensional cube with L levels? Materialization of data cube n n Materialize every (cuboid) (full materialization), none (no materialization), or some (partial materialization) Selection of which cuboids to materialize n 11/28/2020 Based on size, sharing, access frequency, etc. Data Mining: Concepts and Techniques 40

Cube Operation n Cube definition and computation in DMQL define cube sales[item, city, year]: sum(sales_in_dollars) compute cube sales n Transform it into a SQL-like language (with a new operator cube by, introduced by Gray et al. ’ 96) () SELECT item, city, year, SUM (amount) FROM SALES n (city) (item) (year) CUBE BY item, city, year Need compute the following Group-Bys (city, item) (city, year) (item, year) (date, product, customer), (date, product), (date, customer), (product, customer), (date), (product), (customer) (city, item, year) () 11/28/2020 Data Mining: Concepts and Techniques 41

Cube Computation: ROLAP-Based Method n Efficient cube computation methods n n n ROLAP-based cubing algorithms n n n 11/28/2020 ROLAP-based cubing algorithms (Agarwal et al’ 96) Array-based cubing algorithm (Zhao et al’ 97) Bottom-up computation method (Beyer & Ramarkrishnan’ 99) H-cubing technique (Han, Pei, Dong & Wang: SIGMOD’ 01) Sorting, hashing, and grouping operations are applied to the dimension attributes in order to reorder and cluster related tuples Grouping is performed on some sub-aggregates as a “partial grouping step” Aggregates may be computed from previously computed aggregates, rather than from the base fact table Data Mining: Concepts and Techniques 42

Cube Computation: ROLAP-Based Method (2) n n This is not in the textbook but in a research paper Hash/sort based methods (Agarwal et. al. VLDB’ 96) n Smallest-parent: computing a cuboid from the smallest, previously computed cuboid n Cache-results: caching results of a cuboid from which other cuboids are computed to reduce disk I/Os n Amortize-scans: computing as many as possible cuboids at the same time to amortize disk reads n Share-sorts: sharing sorting costs cross multiple cuboids when sort-based method is used n Share-partitions: sharing the partitioning cost across multiple cuboids when hash-based algorithms are used 11/28/2020 Data Mining: Concepts and Techniques 43

Multi-way Array Aggregation for Cube Computation n Partition arrays into chunks (a small subcube which fits in memory). n Compressed sparse array addressing: (chunk_id, offset) n Compute aggregates in “multiway” by visiting cube cells in the order which minimizes the # of times to visit each cell, and reduces memory access and storage cost. C c 3 61 62 63 64 c 2 45 46 47 48 c 1 29 30 31 32 c 0 B b 3 B 13 b 2 9 b 1 5 b 0 11/28/2020 14 15 16 1 2 3 4 a 0 a 1 a 2 a 3 A 60 44 28 56 40 24 52 36 20 Data Mining: Concepts and Techniques What is the best traversing order to do multi-way aggregation? 44

Multi-way Array Aggregation for Cube Computation C c 3 61 62 63 64 c 2 45 46 47 48 c 1 29 30 31 32 c 0 b 3 B b 2 B 13 14 15 16 28 9 24 b 1 5 b 0 1 2 3 4 a 0 a 1 a 2 a 3 20 44 40 36 60 56 52 A 11/28/2020 Data Mining: Concepts and Techniques 45

Multi-way Array Aggregation for Cube Computation C c 3 61 62 63 64 c 2 45 46 47 48 c 1 29 30 31 32 c 0 b 3 B b 2 B 13 14 15 16 28 9 24 b 1 5 b 0 1 2 3 4 a 0 a 1 a 2 a 3 20 44 40 36 60 56 52 A 11/28/2020 Data Mining: Concepts and Techniques 46

Multi-Way Array Aggregation for Cube Computation (Cont. ) n n 11/28/2020 Method: the planes should be sorted and computed according to their size in ascending order. n See the details of Example 2. 12 (pp. 75 -78) n Idea: keep the smallest plane in the main memory, fetch and compute only one chunk at a time for the largest plane Limitation of the method: computing well only for a small number of dimensions n If there a large number of dimensions, “bottomup computation” and iceberg cube computation methods can be explored Data Mining: Concepts and Techniques 47

Indexing OLAP Data: Bitmap Index n n n Index on a particular column Each value in the column has a bit vector: bit-op is fast The length of the bit vector: # of records in the base table The i-th bit is set if the i-th row of the base table has the value for the indexed column not suitable for high cardinality domains Base table 11/28/2020 Index on Region Data Mining: Concepts and Techniques Index on Type 48

Indexing OLAP Data: Join Indices n n n Join index: JI(R-id, S-id) where R (R-id, …) S (S-id, …) Traditional indices map the values to a list of record ids n It materializes relational join in JI file and speeds up relational join — a rather costly operation In data warehouses, join index relates the values of the dimensions of a start schema to rows in the fact table. n E. g. fact table: Sales and two dimensions city and product n A join index on city maintains for each distinct city a list of R-IDs of the tuples recording the Sales in the city n Join indices can span multiple dimensions 11/28/2020 Data Mining: Concepts and Techniques 49

Efficient Processing OLAP Queries n Determine which operations should be performed on the available cuboids: n transform drill, roll, etc. into corresponding SQL and/or OLAP operations, e. g, dice = selection + projection n Determine to which materialized cuboid(s) the relevant operations should be applied. n Exploring indexing structures and compressed vs. dense array structures in MOLAP 11/28/2020 Data Mining: Concepts and Techniques 50

Metadata Repository n Meta data is the data defining warehouse objects. It has the following kinds n Description of the structure of the warehouse n n Operational meta-data n n warehouse schema, view and derived data definitions Business data n 11/28/2020 data lineage (history of migrated data and transformation path), currency of data (active, archived, or purged), monitoring information (warehouse usage statistics, error reports, audit trails) The algorithms used for summarization The mapping from operational environment to the data warehouse Data related to system performance n n schema, view, dimensions, hierarchies, derived data defn, data mart locations and contents business terms and definitions, ownership of data, charging policies Data Mining: Concepts and Techniques 51

Data Warehouse Back-End Tools and Utilities n Data extraction: n n Data cleaning: n n convert data from legacy or host format to warehouse format Load: n n detect errors in the data and rectify them when possible Data transformation: n n get data from multiple, heterogeneous, and external sources sort, summarize, consolidate, compute views, check integrity, and build indicies and partitions Refresh n 11/28/2020 propagate the updates from the data sources to the warehouse Data Mining: Concepts and Techniques 52

Chapter 2: Data Warehousing and OLAP Technology for Data Mining n What is a data warehouse? n A multi-dimensional data model n Data warehouse architecture n Data warehouse implementation n Further development of data cube technology n From data warehousing to data mining 11/28/2020 Data Mining: Concepts and Techniques 53

Iceberg Cube n Computing only the cuboid cells whose count or other aggregates satisfying the condition: HAVING COUNT(*) >= minsup n Motivation n 11/28/2020 Only a small portion of cube cells may be “above the water’’ in a sparse cube Only calculate “interesting” data—data above certain threshold Suppose 100 dimensions, only 1 base cell. How many aggregate (non-base) cells if count >= 1? What about count >= 2? Data Mining: Concepts and Techniques 54

Bottom-Up Computation (BUC) n n BUC (Beyer & Ramakrishnan, SIGMOD’ 99) Bottom-up vs. top-down? — depending on how you view it! Apriori property: n Aggregate the data, then move to the next level n If minsup is not met, stop! If minsup = 1 Þ compute full CUBE! 11/28/2020 Data Mining: Concepts and Techniques 55

Partitioning n n 11/28/2020 Usually, entire data set can’t fit in main memory Sort distinct values, partition into blocks that fit Continue processing Optimizations n Partitioning n External Sorting, Hashing, Counting Sort n Ordering dimensions to encourage pruning n Cardinality, Skew, Correlation n Collapsing duplicates n Can’t do holistic aggregates anymore! Data Mining: Concepts and Techniques 56

Drawbacks of BUC n Requires a significant amount of memory n n On par with most other CUBE algorithms though Does not obtain good performance with dense CUBEs Overly skewed data or a bad choice of dimension ordering reduces performance Cannot compute iceberg cubes with complex measures CREATE CUBE Sales_Iceberg AS SELECT month, city, cust_grp, AVG(price), COUNT(*) FROM Sales_Infor CUBEBY month, city, cust_grp HAVING AVG(price) >= 800 AND COUNT(*) >= 50 11/28/2020 Data Mining: Concepts and Techniques 57

Non-Anti-Monotonic Measures n The cubing query with avg is non-anti-monotonic! n (Mar, *, *, 600, 1800) fails the HAVING clause n (Mar, *, Bus, 1300, 360) passes the clause Month City Cust_grp Prod Cost Price Jan Tor Edu Printer 500 485 Jan Tor Hld TV 800 1200 Jan Tor Edu Camera 1160 1280 Feb Mon Bus Laptop 1500 2500 Mar Van Edu HD 540 520 … … … 11/28/2020 CREATE CUBE Sales_Iceberg AS SELECT month, city, cust_grp, AVG(price), COUNT(*) FROM Sales_Infor CUBEBY month, city, cust_grp HAVING AVG(price) >= 800 AND COUNT(*) >= 50 Data Mining: Concepts and Techniques 58

Top-k Average n Let (*, Van, *) cover 1, 000 records n n n Avg(price) is the average price of those 1000 sales Avg 50(price) is the average price of the top-50 sales (top-50 according to the sales price Top-k average is anti-monotonic n 11/28/2020 The top 50 sales in Van. is with avg(price) <= 800 the top 50 deals in Van. during Feb. must be with avg(price) <= 800 Month City Cust_grp Prod Cost Price … … … Data Mining: Concepts and Techniques 59

Binning for Top-k Average n n Computing top-k avg is costly with large k Binning idea 50 n Avg (c) >= 800 n Large value collapsing: use a sum and a count to summarize records with measure >= 800 n n Small value binning: a group of bins n n 11/28/2020 If count>=800, no need to check “small” records One bin covers a range, e. g. , 600~800, 400~600, etc. Register a sum and a count for each bin Data Mining: Concepts and Techniques 60

Approximate top-k average Suppose for (*, Van, *), we have Range Sum Count Over 800 28000 20 600~800 10600 15 400~600 15200 30 … … … 11/28/2020 Approximate avg 50()= (28000+10600+600*15)/50=952 Top 50 The cell may pass the HAVING clause Month City Cust_grp Prod Cost Price … … … Data Mining: Concepts and Techniques 61

Quant-info for Top-k Average Binning n Accumulate quant-info for cells to compute average iceberg cubes efficiently n Three pieces: sum, count, top-k bins n Use top-k bins to estimate/prune descendants n Use sum and count to consolidate current cell weakest strongest Approximate avg 50() real avg 50() avg() Anti-monotonic, can be computed efficiently Anti-monotonic, but computationally costly Not antimonotonic 11/28/2020 Data Mining: Concepts and Techniques 62

An Efficient Iceberg Cubing Method: Top-k H-Cubing n One can revise Apriori or BUC to compute a top-k avg iceberg cube. This leads to top-k-Apriori and top-k BUC. n Can we compute iceberg cube more efficiently? n Top-k H-cubing: an efficient method to compute iceberg cubes with average measure n H-tree: a hyper-tree structure n H-cubing: computing iceberg cubes using H-tree 11/28/2020 Data Mining: Concepts and Techniques 63

H-tree: A Prefix Hyper-tree Attr. Val. Edu Hhd Bus … Jan Feb … Tor Van Mon … Header table Quant-Info Sum: 2285 … … … Side-link root Jan Mar Jan Feb Tor Van Tor Mon Quant-Info Q. I. Month City Cust_grp Prod Cost Price Jan Tor Edu Printer 500 485 Jan Tor Hhd TV 800 1200 Jan Tor Edu Camera 1160 1280 Feb Mon Bus Laptop 1500 2500 Sum: 1765 Cnt: 2 Mar Van Edu HD 540 520 bins … … … 11/28/2020 bus hhd edu Data Mining: Concepts and Techniques 64

Properties of H-tree n Construction cost: a single database scan n Completeness: It contains the complete information needed for computing the iceberg cube n 11/28/2020 Compactness: # of nodes n*m+1 n n: # of tuples in the table n m: # of attributes Data Mining: Concepts and Techniques 65

Computing Cells Involving Dimension City Header Table HTor Attr. Val. Edu Hhd Bus … Jan Feb … Tor Van Mon … 11/28/2020 Attr. Val. Edu Hhd Bus … Jan Feb … Quant-Info Sum: 2285 … … … Q. I. … … … … Side-link From (*, *, Tor) to (*, Jan, Tor) root Hhd. Edu. Jan. Side-link Tor. Quant-Info Mar. Jan. Bus. Feb. Van. Tor. Mon. Q. I. Sum: 1765 Cnt: 2 bins Data Mining: Concepts and Techniques 66

Computing Cells Involving Month But No City 1. Roll up quant-info 2. Compute cells involving month but no city Attr. Val. Edu. Hhd. Bus. … Jan. Feb. Mar. … Tor. Van. Mont. … 11/28/2020 Quant-Info Sum: 2285 … … … Side-link root Hhd. Edu. Jan. Q. I. Tor. Mar. Jan. Q. I. Van. Tor. Bus. Feb. Q. I. Mont. Top-k OK mark: if Q. I. in a child passes top-k avg threshold, so does its parents. No binning is needed! Data Mining: Concepts and Techniques 67

Computing Cells Involving Only Cust_grp root Check header table directly Attr. Val. Edu Hhd Bus … Jan Feb Mar … Tor Van Mon … 11/28/2020 Quant-Info Sum: 2285 … … … hhd edu Side-link bus Jan Mar Jan Feb Q. I. Van Tor Data Mining: Concepts and Techniques Mon 68

Properties of H-Cubing n n 11/28/2020 Space cost n an H-tree n a stack of up to (m-1) header tables One database scan Main memory-based tree traversal & side-links updates Top-k_OK marking Data Mining: Concepts and Techniques 69

Scalability w. r. t. Count Threshold (No min_avg Setting) 11/28/2020 Data Mining: Concepts and Techniques 70

Computing Iceberg Cubes with Other Complex Measures n Computing other complex measures n Key point: find a function which is weaker but ensures certain anti-monotonicity n Examples n Avg() v: avgk(c) v (bottom-k avg) n Avg() v only (no count): max(price) v n Sum(profit) (profit can be negative): n n 11/28/2020 p_sum(c) v if p_count(c) k; or otherwise, sumk(c) v Others: conjunctions of multiple conditions Data Mining: Concepts and Techniques 71

Discussion: Other Issues n Computing iceberg cubes with more complex measures? n n n A research theme even for complex algebraic functions, e. g. , standard_dev, variance Dynamic vs. static computation of iceberg cubes n n n No general answer for holistic measures, e. g. , median, mode, rank v and k are only available at query time Setting reasonably low parameters for most nontrivial cases Memory-hog? what if the cubing is too big to fit in memory? —projection and then cubing 11/28/2020 Data Mining: Concepts and Techniques 72

Condensed Cube n n W. Wang, H. Lu, J. Feng, J. X. Yu, Condensed Cube: An Effective Approach to Reducing Data Cube Size. ICDE’ 02. Icerberg cube cannot solve all the problems n n Suppose 100 dimensions, only 1 base cell with count = 10. How many aggregate (non-base) cells if count >= 10? Condensed cube n n Only need to store one cell (a 1, a 2, …, a 100, 10), which represents all the corresponding aggregate cells Adv. n n 11/28/2020 Fully precomputed cube without compression Efficient computation of the minimal condensed cube Data Mining: Concepts and Techniques 73

Chapter 2: Data Warehousing and OLAP Technology for Data Mining n What is a data warehouse? n A multi-dimensional data model n Data warehouse architecture n Data warehouse implementation n Further development of data cube technology n From data warehousing to data mining 11/28/2020 Data Mining: Concepts and Techniques 74

Data Warehouse Usage n Three kinds of data warehouse applications n Information processing n n n Analytical processing n multidimensional analysis of data warehouse data n supports basic OLAP operations, slice-dice, drilling, pivoting Data mining n n n supports querying, basic statistical analysis, and reporting using crosstabs, tables, charts and graphs knowledge discovery from hidden patterns supports associations, constructing analytical models, performing classification and prediction, and presenting the mining results using visualization tools. Differences among the three tasks 11/28/2020 Data Mining: Concepts and Techniques 75

From On-Line Analytical Processing to On Line Analytical Mining (OLAM) n Why online analytical mining? n n n High quality of data in data warehouses n DW contains integrated, consistent, cleaned data Available information processing structure surrounding data warehouses n ODBC, OLEDB, Web accessing, service facilities, reporting and OLAP tools OLAP-based exploratory data analysis n mining with drilling, dicing, pivoting, etc. On-line selection of data mining functions n integration and swapping of multiple mining functions, algorithms, and tasks. Architecture of OLAM 11/28/2020 Data Mining: Concepts and Techniques 76

An OLAM Architecture Mining query Mining result Layer 4 User Interface User GUI API OLAM Engine OLAP Engine Layer 3 OLAP/OLAM Data Cube API Layer 2 MDDB Meta Data Filtering&Integration Database API Filtering Layer 1 Databases 11/28/2020 Data cleaning Data integration Warehouse Data Mining: Concepts and Techniques Data Repository 77

Discovery-Driven Exploration of Data Cubes n Hypothesis-driven n n exploration by user, huge search space Discovery-driven (Sarawagi, et al. ’ 98) n n 11/28/2020 Effective navigation of large OLAP data cubes pre-compute measures indicating exceptions, guide user in the data analysis, at all levels of aggregation Exception: significantly different from the value anticipated, based on a statistical model Visual cues such as background color are used to reflect the degree of exception of each cell Data Mining: Concepts and Techniques 78

Kinds of Exceptions and their Computation n Parameters n n n Self. Exp: surprise of cell relative to other cells at same level of aggregation n In. Exp: surprise beneath the cell n Path. Exp: surprise beneath cell for each drill-down path Computation of exception indicator (modeling fitting and computing Self. Exp, In. Exp, and Path. Exp values) can be overlapped with cube construction Exception themselves can be stored, indexed and retrieved like precomputed aggregates 11/28/2020 Data Mining: Concepts and Techniques 79

Examples: Discovery-Driven Data Cubes 11/28/2020 Data Mining: Concepts and Techniques 80

Complex Aggregation at Multiple Granularities: Multi-Feature Cubes n n Multi-feature cubes (Ross, et al. 1998): Compute complex queries involving multiple dependent aggregates at multiple granularities Ex. Grouping by all subsets of {item, region, month}, find the maximum price in 1997 for each group, and the total sales among all maximum price tuples select item, region, month, max(price), sum(R. sales) from purchases where year = 1997 cube by item, region, month: R such that R. price = max(price) n Continuing the last example, among the max price tuples, find the min and max shelf live, and find the fraction of the total sales due to tuple that have min shelf life within the set of all max price tuples 11/28/2020 Data Mining: Concepts and Techniques 81

Cube-Gradient (Cubegrade) n n 11/28/2020 Analysis of changes of sophisticated measures in multi-dimensional spaces n Query: changes of average house price in Vancouver in ‘ 00 comparing against ’ 99 n Answer: Apts in West went down 20%, houses in Metrotown went up 10% Cubegrade problem by Imielinski et al. n Changes in dimensions changes in measures n Drill-down, roll-up, and mutation Data Mining: Concepts and Techniques 82

From Cubegrade to Multi-dimensional Constrained Gradients in Data Cubes n Significantly more expressive than association rules n n Capture trends in user-specified measures Serious challenges n n n 11/28/2020 Many trivial cells in a cube “significance constraint” to prune trivial cells Numerate pairs of cells “probe constraint” to select a subset of cells to examine Only interesting changes wanted “gradient constraint” to capture significant changes Data Mining: Concepts and Techniques 83

MD Constrained Gradient Mining n n n Significance constraint Csig: (cnt 100) Probe constraint Cprb: (city=“Van”, cust_grp=“busi”, prod_grp=“*”) Gradient constraint Cgrad(cg, cp): (avg_price(cg)/avg_price(cp) 1. 3) Probe cell: satisfied Cprb Base cell Aggregated cell Siblings Ancestor 11/28/2020 (c 4, c 2) satisfies Cgrad! Dimensions Measures cid Yr City Cst_grp Prd_grp Cnt Avg_price c 1 00 Van Busi PC 300 2100 c 2 * Van Busi PC 2800 1800 c 3 * Tor Busi PC 7900 2350 c 4 * * busi PC 58600 2250 Data Mining: Concepts and Techniques 84

A Live. Set-Driven Algorithm n Compute probe cells using Csig and Cprb n n The set of probe cells P is often very small Use probe P and constraints to find gradients n n n 11/28/2020 Pushing selection deeply Set-oriented processing for probe cells Iceberg growing from low to high dimensionalities Dynamic pruning probe cells during growth Incorporating efficient iceberg cubing method Data Mining: Concepts and Techniques 85

Summary n n Data warehouse A multi-dimensional model of a data warehouse n n n OLAP operations: drilling, rolling, slicing, dicing and pivoting OLAP servers: ROLAP, MOLAP, HOLAP Efficient computation of data cubes n n Star schema, snowflake schema, fact constellations A data cube consists of dimensions & measures Partial vs. full vs. no materialization Multiway array aggregation Bitmap index and join index implementations Further development of data cube technology n n 11/28/2020 Discovery-drive and multi-feature cubes From OLAP to OLAM (on-line analytical mining) Data Mining: Concepts and Techniques 86

References (I) n n n n S. Agarwal, R. Agrawal, P. M. Deshpande, A. Gupta, J. F. Naughton, R. Ramakrishnan, and S. Sarawagi. On the computation of multidimensional aggregates. VLDB’ 96 D. Agrawal, A. E. Abbadi, A. Singh, and T. Yurek. Efficient view maintenance in data warehouses. SIGMOD’ 97. R. Agrawal, A. Gupta, and S. Sarawagi. Modeling multidimensional databases. ICDE’ 97 K. Beyer and R. Ramakrishnan. Bottom-Up Computation of Sparse and Iceberg CUBEs. . SIGMOD’ 99. S. Chaudhuri and U. Dayal. An overview of data warehousing and OLAP technology. ACM SIGMOD Record, 26: 65 -74, 1997. OLAP council. MDAPI specification version 2. 0. In http: //www. olapcouncil. org/research/apily. htm, 1998. G. Dong, J. Han, J. Lam, J. Pei, K. Wang. Mining Multi-dimensional Constrained Gradients in Data Cubes. VLDB’ 2001 J. Gray, S. Chaudhuri, A. Bosworth, A. Layman, D. Reichart, M. Venkatrao, F. Pellow, and H. Pirahesh. Data cube: A relational aggregation operator generalizing group-by, cross-tab and sub-totals. Data Mining and Knowledge Discovery, 1: 29 -54, 1997. 11/28/2020 Data Mining: Concepts and Techniques 87

References (II) n n n n n J. Han, J. Pei, G. Dong, K. Wang. Efficient Computation of Iceberg Cubes With Complex Measures. SIGMOD’ 01 V. Harinarayan, A. Rajaraman, and J. D. Ullman. Implementing data cubes efficiently. SIGMOD’ 96 Microsoft. OLEDB for OLAP programmer's reference version 1. 0. In http: //www. microsoft. com/data/oledb/olap, 1998. K. Ross and D. Srivastava. Fast computation of sparse datacubes. VLDB’ 97. K. A. Ross, D. Srivastava, and D. Chatziantoniou. Complex aggregation at multiple granularities. EDBT'98. S. Sarawagi, R. Agrawal, and N. Megiddo. Discovery-driven exploration of OLAP data cubes. EDBT'98. E. Thomsen. OLAP Solutions: Building Multidimensional Information Systems. John Wiley & Sons, 1997. W. Wang, H. Lu, J. Feng, J. X. Yu, Condensed Cube: An Effective Approach to Reducing Data Cube Size. ICDE’ 02. Y. Zhao, P. M. Deshpande, and J. F. Naughton. An array-based algorithm for simultaneous multidimensional aggregates. SIGMOD’ 97. 11/28/2020 Data Mining: Concepts and Techniques 88

www. cs. uiuc. edu/~hanj Thank you !!! 11/28/2020 Data Mining: Concepts and Techniques 89

Work to be done n n 11/28/2020 Add MS OLAP snapshots! A tutorial on MS/OLAP Reorganize cube computation materials Into cube computation and cube exploration Data Mining: Concepts and Techniques 90