Topics
 What is a data warehouse?
 A multi-dimensional data model
 Data warehouse architecture
 Data warehouse implementation
 From data warehousing to data mining
2
What is Data Warehouse?
 Defined in many different ways, but not rigorously.
 A decision support database that is maintained separately from
the organization’s operational database
 Support information processing by providing a solid platform of
consolidated, historical data for analysis.
 “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
 Data warehousing:
 The process of constructing and using data warehouses
3
Data Warehouse—Subject-Oriented
 Organized around major subjects, such as customer,
product, sales.
 Focusing on the modeling and analysis of data for decision
makers, not on daily operations or transaction processing.
 Provide a simple and concise view around particular
subject issues by excluding data that are not useful in the
decision support process.
4
Data Warehouse—Integrated
 Constructed by integrating multiple, heterogeneous data
sources
 relational databases, flat files, on-line transaction
records
 Data cleaning and data integration techniques are
applied.
 Ensure consistency in naming conventions, encoding
structures, attribute measures, etc. among different
data sources
 E.g., Hotel price: currency, tax, breakfast covered, etc.
 When data is moved to the warehouse, it is
converted.
5
Data Warehouse—Time Variant
 The time horizon for the data warehouse is significantly
longer than that of operational systems.
 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
 Contains an element of time, explicitly or implicitly
 But the key of operational data may or may not contain
“time element”.
6
Data Warehouse—Non-Volatile
 A physically separate store of data transformed from the
operational environment.
 Operational update of data does not occur in the data
warehouse environment.
 Does not require transaction processing, recovery,
and concurrency control mechanisms
 Requires only two operations in data accessing:
 initial loading of data and access of data.
7
Data Warehouse vs. Heterogeneous DBMS
 Traditional heterogeneous DB integration:
 Build wrappers/mediators on top of heterogeneous databases
 Query driven approach
 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
 Information from heterogeneous sources is integrated in advance
and stored in warehouses for direct query and analysis
8
Data Warehouse vs. Operational DBMS
 OLTP (on-line transaction processing)
 Major task of traditional relational DBMS
 Day-to-day operations: purchasing, inventory, banking,
manufacturing, payroll, registration, accounting, etc.
 OLAP (on-line analytical processing)
 Major task of data warehouse system
 Data analysis and decision making
 Distinct features (OLTP vs. OLAP):
 User and system orientation: customer vs. market
 Data contents: current, detailed vs. historical, consolidated
 Database design: ER + application vs. star + subject
 View: current, local vs. evolutionary, integrated
 Access patterns: update vs. read-only but complex queries
9
OLTP vs. OLAP
OLTP OLAP
users clerk, IT professional knowledge worker
function day to day operations decision support
DB design application-oriented subject-oriented
data current, up-to-date
detailed, flat relational
isolated
historical,
summarized, multidimensional
integrated, consolidated
usage repetitive ad-hoc
access read/write
index/hash on prim. key
lots of scans
unit of work short, simple transaction complex query

records accessed tens millions

users thousands hundreds

DB size 100MB-GB 100GB-TB
metric transaction throughput query throughput, response
10
Why Separate Data Warehouse?
 High performance for both systems
 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:
 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
11
A MULTI-DIMENSIONAL DATA
MODEL
12
From Tables and Spreadsheets to Data Cubes
 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
 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.
13
Cube: A Lattice of Cuboids
14
all
time item location supplier
time,item time,location
time,supplier
item,location
item,supplier
location,supplier
time,item,location
time,item,supplier
time,location,supplier
item,location,supplier
time, item, location, supplier
0-D(apex) cuboid
1-D cuboids
2-D cuboids
3-D cuboids
4-D(base) cuboid
Conceptual Modeling of Data Warehouses
 Modeling data warehouses: dimensions & measures
 Star schema: A fact table in the middle connected to a
set of dimension tables
 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
 Fact constellations: Multiple fact tables share
dimension tables, viewed as a collection of stars,
therefore called galaxy schema or fact constellation
15
Example of Star Schema
16
time_key
day
day_of_the_week
month
quarter
year
time
location_key
street
city
state_or_province
country
location
Sales Fact Table
time_key
item_key
branch_key
location_key
units_sold
dollars_sold
avg_sales
Measures
item_key
item_name
brand
type
supplier_type
item
branch_key
branch_name
branch_type
branch
Example of Snowflake Schema
17
time_key
day
day_of_the_week
month
quarter
year
time
location_key
street
city_key
location
Sales Fact Table
time_key
item_key
branch_key
location_key
units_sold
dollars_sold
avg_sales
Measures
item_key
item_name
brand
type
supplier_key
item
branch_key
branch_name
branch_type
branch
supplier_key
supplier_type
supplier
city_key
city
state_or_province
country
city
Example of Fact Constellation
18
time_key
day
day_of_the_week
month
quarter
year
time
location_key
street
city
province_or_state
country
location
Sales Fact Table
time_key
item_key
branch_key
location_key
units_sold
dollars_sold
avg_sales
Measures
item_key
item_name
brand
type
supplier_type
item
branch_key
branch_name
branch_type
branch
Shipping Fact Table
time_key
item_key
shipper_key
from_location
to_location
dollars_cost
units_shipped
shipper_key
shipper_name
location_key
shipper_type
shipper
A Data Mining Query Language: DMQL
 Cube Definition (Fact Table)
define cube []:

 Dimension Definition ( Dimension Table )
define dimension as
()
 Special Case (Shared Dimension Tables)
 First time as “cube definition”
 define dimension as
in cube

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, 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) 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, 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))
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, 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
22
Measures: Three Categories
 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.
 E.g., count(), sum(), min(), max().
 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.
 E.g., avg(), min_N(), standard_deviation().
 holistic: if there is no constant bound on the storage size
needed to describe a subaggregate.
 E.g., median(), mode(), rank().
23
A Concept Hierarchy: Dimension (location)
24
all
Europe North_America
Germany Spain Canada Mexico
Vancouver
L. Chan M. Wind
…
… …
… …
…
all
region
office
country
city Frankfurt Toronto
View of Warehouses and Hierarchies
Specification of hierarchies
 Schema hierarchy
day < month < quarter;
week < year
 Set_grouping hierarchy
1..10 < inexpensive
25
Multidimensional Data
 Sales volume as a function of product, month,
and region
26
Product
Region
Month
Dimensions: Product, Location, Time
Hierarchical summarization paths
Industry Region Year
Category Country Quarter
Product City Month Week
Office Day
A Sample Data Cube
27
Total annual sales
Date of TV in U.S.A.
Product
Country
sum
sum
TV
VCR
PC
1Qtr 2Qtr 3Qtr 4Qtr
U.S.A
Canada
Mexico
sum
Cuboids Corresponding to the Cube
28
all
product date country
product,date product,country date, country
product, date, country
0-D(apex) cuboid
1-D cuboids
2-D cuboids
3-D(base) cuboid
Browsing a Data Cube
 Visualization
 OLAP capabilities
 Interactive manipulation
29
Typical OLAP Operations
 Roll up (drill-up): summarize data
 by climbing up hierarchy or by dimension reduction
 Drill down (roll down): reverse of roll-up
 from higher level summary to lower level summary or detailed data,
or introducing new dimensions
 Slice and dice:
 project and select
 Pivot (rotate):
 reorient the cube, visualization, 3D to series of 2D planes.
 Other operations
 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)
30
A Star-Net Query Model
31
Shipping Method
AIR-EXPRESS
TRUCK ORDER
Customer Orders
CONTRACTS
Customer
Product
PRODUCT GROUP
PRODUCT LINE
PRODUCT ITEM
SALES PERSON
DISTRICT
DIVISION
Promotion Organization
CITY
COUNTRY
REGION
Location
ANNUALY QTRLY DAILY
Time
Each circle is
called a footprint
DATA WAREHOUSE ARCHITECTURE
32
Design of a Data Warehouse: A Business
Analysis Framework
 Four views regarding the design of a data warehouse
 Top-down view
 allows selection of the relevant information necessary for the
data warehouse
 Data source view
 exposes the information being captured, stored, and
managed by operational systems
 Data warehouse view
 consists of fact tables and dimension tables
 Business query view
 sees the perspectives of data in the warehouse from the view
of end-user
33
Data Warehouse Design Process
 Top-down, bottom-up approaches or a combination of both
 Top-down: Starts with overall design and planning (mature)
 Bottom-up: Starts with experiments and prototypes (rapid)
 From software engineering point of view
 Waterfall: structured and systematic analysis at each step before
proceeding to the next
 Spiral: rapid generation of increasingly functional systems, short
turn around time, quick turn around
 Typical data warehouse design process
 Choose a business process to model, e.g., orders, invoices, etc.
 Choose the grain (atomic level of data) of the business process
 Choose the dimensions that will apply to each fact table record
 Choose the measure that will populate each fact table record
34
35
Multi-Tiered Architecture
Data
Warehouse
Extract
Transform
Load
Refresh
OLAP Engine
Analysis
Query
Reports
Data mining
Monitor
&
Integrator
Metadata
Data Sources Front-End Tools
Serve
Data Marts
Operational
DBs
other
source
s
Data Storage
OLAP Server
Three Data Warehouse Models
 Enterprise warehouse
 collects all of the information about subjects spanning the
entire organization
 Data Mart
 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
 Independent vs. dependent (directly from warehouse) data mart
 Virtual warehouse
 A set of views over operational databases
 Only some of the possible summary views may be
materialized
36
Data Warehouse Development:
A Recommended Approach
37
Define a high-level corporate data model
Data
Mart
Data
Mart
Distributed
Data Marts
Multi-Tier Data
Warehouse
Enterprise
Data
Warehouse
Model refinement Model refinement
OLAP Server Architectures
 Relational OLAP (ROLAP)
 Use relational or extended-relational DBMS to store and manage
warehouse data and OLAP middle ware to support missing pieces
 Include optimization of DBMS backend, implementation of
aggregation navigation logic, and additional tools and services
 greater scalability
 Multidimensional OLAP (MOLAP)
 Array-based multidimensional storage engine (sparse matrix
techniques)
 fast indexing to pre-computed summarized data
 Hybrid OLAP (HOLAP)
 User flexibility, e.g., low level: relational, high-level: array
 Specialized SQL servers
 specialized support for SQL queries over star/snowflake schemas
38
DATA WAREHOUSE IMPLEMENTATION
39
Efficient Data Cube Computation
 Data cube can be viewed as a lattice of cuboids
 The bottom-most cuboid is the base cuboid
 The top-most cuboid (apex) contains only one cell
 How many cuboids in an n-dimensional cube with L
levels?
 Materialization of data cube
 Materialize every (cuboid) (full materialization), none (no
materialization), or some (partial materialization)
 Selection of which cuboids to materialize
 Based on size, sharing, access frequency, etc.
40
1)
1
(  


n
i i T L
Cube Operation
 Cube definition and computation in DMQL
define cube sales[item, city, year]: sum(sales_in_dollars)
compute cube sales
 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
CUBE BY item, city, year
 Need compute the following Group-Bys
(date, product, customer),
(date,product),(date, customer), (product, customer),
(date), (product), (customer)
()
41
(city) (item)
()
(year)
(city, item) (city, year) (item, year)
(city, item, year)
Cube Computation: ROLAP-Based Method
 Efficient cube computation methods
 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)
 ROLAP-based cubing algorithms
 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
42
Cube Computation: ROLAP-Based Method (2)
 This is not in the textbook but in a research paper
 Hash/sort based methods (Agarwal et. al. VLDB’96)
 Smallest-parent: computing a cuboid from the
smallest, previously computed cuboid
 Cache-results: caching results of a cuboid from which
other cuboids are computed to reduce disk I/Os
 Amortize-scans: computing as many as possible
cuboids at the same time to amortize disk reads
 Share-sorts: sharing sorting costs cross multiple
cuboids when sort-based method is used
 Share-partitions: sharing the partitioning cost across
multiple cuboids when hash-based algorithms are used
43
Multi-way Array Aggregation for Cube
Computation
 Partition arrays into chunks (a small subcube which fits in memory).
 Compressed sparse array addressing: (chunk_id, offset)
 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.
44
What is the best
traversing order
to do multi-way
aggregation?
A
B
29 30 31 32
1 2 3 4
5
9
13 14 15 16
61 62 63 64
45 46 47 48
a0 a1
c2 c3
c 0c1
b3
b2
b1
b0
a2 a3
C
B
44
28 56
24 4036 52
20
60
Multi-way Array Aggregation for
Cube Computation
45
A
B
29 30 31 32
1 2 3 4
5
9
13 14 15 16
61 62 63 64
45 46 47 48
a0 a1
c3
c2
c1
c 0
b3
b2
b1
b0
a2 a3
C
44
28 56
40
24 52
36
20
60
B
Multi-way Array Aggregation for
Cube Computation
46
A
B
29 30 31 32
1 2 3 4
5
9
13 14 15 16
61 62 63 64
45 46 47 48
a0 a1
c3
c2
c1
c 0
b3
b2
b1
b0
a2 a3
C
44
28 56
40
24 52
36
20
60
B
Multi-Way Array Aggregation for
Cube Computation (Cont.)
 Method: the planes should be sorted and computed
according to their size in ascending order.
 See the details of Example 2.12 (pp. 75-78)
 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
 If there are a large number of dimensions, “bottomup
computation” and iceberg cube computation
methods can be explored
47
Indexing OLAP Data: Bitmap Index
 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
48
Cust Region Type
C1 Asia Retail
C2 Europe Dealer
C3 Asia Dealer
C4 America Retail
C5 Europe Dealer
RecID Retail Dealer
1 1 0
2 0 1
3 0 1
4 1 0
5 0 1
RecIDAsia Europe America
1 1 0 0
2 0 1 0
3 1 0 0
4 0 0 1
5 0 1 0
Base table Index on Region Index on Type
Indexing OLAP Data: Join Indices
 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
 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.
 E.g. fact table: Sales and two dimensions city
and product
 A join index on city maintains for each
distinct city a list of R-IDs of the tuples
recording the Sales in the city
 Join indices can span multiple dimensions
49
Efficient Processing OLAP Queries
 Determine which operations should be performed on the
available cuboids:
 transform drill, roll, etc. into corresponding SQL and/or
OLAP operations, e.g, dice = selection + projection
 Determine to which materialized cuboid(s) the relevant
operations should be applied.
 Exploring indexing structures and compressed vs. dense
array structures in MOLAP
50
Metadata Repository
 Meta data is the data defining warehouse objects. It has the following
kinds
 Description of the structure of the warehouse
 schema, view, dimensions, hierarchies, derived data defn, data mart
locations and contents
 Operational meta-data
 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
 warehouse schema, view and derived data definitions
 Business data
 business terms and definitions, ownership of data, charging policies
51
Data Warehouse Back-End Tools and Utilities
 Data extraction:
 get data from multiple, heterogeneous, and external
sources
 Data cleaning:
 detect errors in the data and rectify them when possible
 Data transformation:
 convert data from legacy or host format to warehouse
format
 Load:
 sort, summarize, consolidate, compute views, check
integrity, and build indicies and partitions
 Refresh
 propagate the updates from the data sources to the
warehouse
52
FROM DATA WAREHOUSING TO
DATA MINING
53
Data Warehouse Usage
 Three kinds of data warehouse applications
 Information processing
 supports querying, basic statistical analysis, and reporting using
crosstabs, tables, charts and graphs
 Analytical processing
 multidimensional analysis of data warehouse data
 supports basic OLAP operations, slice-dice, drilling, pivoting
 Data mining
 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
54
From On-Line Analytical Processing
to On Line Analytical Mining (OLAM)
 Why online analytical mining?
 High quality of data in data warehouses
 DW contains integrated, consistent, cleaned data
 Available information processing structure surrounding data
warehouses
 ODBC, OLEDB, Web accessing, service facilities, reporting and
OLAP tools
 OLAP-based exploratory data analysis
 mining with drilling, dicing, pivoting, etc.
 On-line selection of data mining functions
 integration and swapping of multiple mining functions,
algorithms, and tasks.
 Architecture of OLAM
55
An OLAM Architecture
56
Data
Warehouse
Meta
Data
MDDB
OLAM
Engine
OLAP
Engine
User GUI API
Data Cube API
Database API
Data cleaning
Data integration
Layer3
OLAP/OLAM
Layer2
MDDB
Layer1
Data
Repository
Layer4
User Interface
Filtering&Integration Filtering
Databases
Mining query Mining result
Discovery-Driven Exploration of Data
Cubes
 Hypothesis-driven
 exploration by user, huge search space
 Discovery-driven (Sarawagi, et al.’98)
 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
57
Kinds of Exceptions and their Computation
 Parameters
 SelfExp: surprise of cell relative to other cells at same
level of aggregation
 InExp: surprise beneath the cell
 PathExp: surprise beneath cell for each drill-down
path
 Computation of exception indicator (modeling fitting and
computing SelfExp, InExp, and PathExp values) can be
overlapped with cube construction
 Exception themselves can be stored, indexed and
retrieved like precomputed aggregates
58
Examples: Discovery-Driven Data Cubes
59
Complex Aggregation at Multiple
Granularities: Multi-Feature Cubes
 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)
 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
60
Cube-Gradient (Cubegrade)
 Analysis of changes of sophisticated measures
in multi-dimensional spaces
 Query: changes of average house price in
Vancouver in ‘00 comparing against ’99
 Answer: Apts in West went down 20%,
houses in Metrotown went up 10%
 Cubegrade problem by Imielinski et al.
 Changes in dimensions  changes in
measures
 Drill-down, roll-up, and mutation
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From Cubegrade to Multi-dimensional
Constrained Gradients in Data Cubes
 Significantly more expressive than association rules
 Capture trends in user-specified measures
 Serious challenges
 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
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MD Constrained Gradient Mining
 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)
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Dimensions Measures
cid Yr City Cst_grp Prd_grp Cnt Avg_price
c1 00 Van Busi PC 300 2100
c2 * Van Busi PC 2800 1800
c3 * Tor Busi PC 7900 2350
c4 * * busi PC 58600 2250
Base cell
Aggregated cell
Siblings
Ancestor
Probe cell: satisfied Cprb (c4, c2) satisfies Cgrad!
A LiveSet-Driven Algorithm
 Compute probe cells using Csig and Cprb
 The set of probe cells P is often very small
 Use probe P and constraints to find gradients
 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
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Summary
 Data warehouse
 A multi-dimensional model of a data warehouse
 Star schema, snowflake schema, fact constellations
 A data cube consists of dimensions & measures
 OLAP operations: drilling, rolling, slicing, dicing and pivoting
 OLAP servers: ROLAP, MOLAP, HOLAP
 Efficient computation of data cubes
 Partial vs. full vs. no materialization
 Multiway array aggregation
 Bitmap index and join index implementations
 Further development of data cube technology
 Discovery-drive and multi-feature cubes
 From OLAP to OLAM (on-line analytical mining)
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Thank you !!!
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Questions
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1. How are users of data warehouse be classified?
2. Draw and explain the different components of data warehouse.
3. Enumerate and explain the reasons why traditional method of analysis
   provided in the data warehouse are not sufficient.
4. Explain the OLAM Architecture(fig.slide77)
5. Enumerate and explain the advantages and disadvantages of top down
   and bottom up approaches for building a data warehouse?
6. What is enterprise data warehouse? List and explain the features of
   enterprise data warehouse.

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