Data Mining Concepts and Techniques

Data Mining:
Concepts and Techniques
— Slides for Textbook —
— Chapter 2 —
October 8, 2014 Data Mining: Concepts and Techniques 1

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

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

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.

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.

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”.

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.

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

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

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

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

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.

Cube: A Lattice of Cuboids
all
time item location supplier
time,item time,location
item,location
time,supplier
item,supplier
1-D cuboids
location,supplier
time,item,location
time,location,supplier
time,item,supplier
item,location,supplier
time, item, location, supplier
0-D(apex) cuboid
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

Example of Star Schema
time
time_key
day
day_of_the_week
month
quarter
year
item
item_key
item_name
brand
type
supplier_type
location
location_key
street
city
state_or_province
country
Sales Fact Table
time_key
item_key
branch_key
location_key
units_sold
dollars_sold
avg_sales
branch
branch_key
branch_name
branch_type
Measures

Example of Snowflake Schema
time
time_key
day
day_of_the_week
month
quarter
year
item
item_key
item_name
brand
type
supplier_key
location
location_key
street
city_key
Sales Fact Table
time_key
item_key
branch_key
location_key
units_sold
dollars_sold
avg_sales
branch
branch_key
branch_name
branch_type
Measures
supplier
supplier_key
supplier_type
city
city_key
city
state_or_province
country

Example of Fact Constellation
time
time_key
day
day_of_the_week
month
quarter
year
item
item_key
item_name
brand
type
supplier_type
location
location_key
street
city
province_or_state
country
Sales Fact Table
time_key
item_key
branch_key
location_key
units_sold
dollars_sold
avg_sales
branch
branch_key
branch_name
branch_type
Measures
Shipping Fact Table
time_key
item_key
shipper_key
from_location
to_location
dollars_cost
units_shipped
shipper
shipper_key
shipper_name
location_key
shipper_type

A Data Mining Query Language: DMQL
 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)
 First time as “cube definition”
 define dimension <dimension_name> as
<dimension_name_first_time> in cube
<cube_name_first_time>

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)

Defining a Snowflake Schema in DMQL
define cube sales_snowflake [time, item, branch, location]:
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))

Defining a Fact Constellation in DMQL
define cube sales [time, item, branch, location]:
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

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().

A Concept Hierarchy: Dimension (location)
all
Europe ...
North_America
Germany ... Spain Canada ...
Mexico
... Vancouver
...
city Frankfurt Toronto
L. Chan ...
M. Wind
all
region
country
office

View of Warehouses and Hierarchies
Specification of hierarchies
 Schema hierarchy
day < {month < quarter;
week} < year
 Set_grouping hierarchy
{1..10} < inexpensive

Multidimensional Data
 Sales volume as a function of product, month,
and region
Region
Product
Month
Dimensions: Product, Location, Time
Hierarchical summarization paths
Industry Region Year
Category Country Quarter
Product City Month Week
Office Day

A Sample Data Cube
Total annual sales
Date of TV in U.S.A.
Product
Country
PC
VCR
sum
sum
TV
1Qtr 2Qtr 3Qtr 4Qtr
U.S.A
Canada
Mexico
sum

Cuboids Corresponding to the Cube
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

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)

A Star-Net Query Model
Shipping Method
AIR-EXPRESS
Customer Orders
TRUCK
CONTRACTS
ORDER
Customer
Product
PRODUCT LINE
PRODUCT GROUP
PRODUCT ITEM
SALES PERSON
DISTRICT
DIVISION
ANNUALY QTRLY DAILY
Promotion Organization
CITY
COUNTRY
Time
REGION
Location
Each circle is
called a footprint

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

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

MMuullttii--TTiieerreedd AArrcchhiitteeccttuurree
Monitor
&
Integrator
Data
Warehouse
Metadata
Extract
Transform
Load
Refresh
OLAP Server
Serve
Data Marts
other
source
s
Operational
DBs
Data Sources OLAP Engine
Front-End Tools
Analysis
Query
Reports
Data mining
Data Storage

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

Data Warehouse Development:
A Recommended Approach
Data
Mart
Distributed
Data Marts
Data
Mart
Multi-Tier Data
Warehouse
Enterprise
Data
Warehouse
Model refinement Model refinement
Define a high-level corporate data model

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

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?
n
i i T L
( + Õ=
1)
1
=
 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.

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
()
(city) (item)
(date, product, customer),
(date,product),(date, customer), (product, customer),
(date), (product), (customer)
()
(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

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

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.
What is the best
traversing order
to do multi-way
aggregation?
c3
c2
61 62 63 64
45 46 47 48
29 30 31 32
C
c 0c1
b3
b2
b1
b0
13 14 15 16
9
5
1 2 3 4
a0 a1
A
B
a2 a3
B
60
44
28 56
24 4036 52
20

Multi-way Array Aggregation for
Cube Computation
c3
61 62 63 64
45 46 47 48
C
c2
c1
c 0
b3
b2
b1
b0
29 30 31 32
13 14 15 16
9
5
1 2 3 4
A
B
a0 a1
a2 a3
44
60
28 56
40
24 52
36
20
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, “bottom-up
computation” and iceberg cube computation
methods can be explored

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
Base table Index on Region Index on Type
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

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

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

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

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

Iceberg Cube
 Computing only the cuboid cells whose count
or other aggregates satisfying the condition:
HAVING COUNT(*) >= minsup
 Motivation
 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?

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

Partitioning
 Usually, entire data set can’t
fit in main memory
 Sort distinct values, partition into blocks that fit
 Continue processing
 Optimizations
 Partitioning
 External Sorting, Hashing, Counting Sort
 Ordering dimensions to encourage pruning
 Cardinality, Skew, Correlation
 Collapsing duplicates
 Can’t do holistic aggregates anymore!

Drawbacks of BUC
 Requires a significant amount of memory
 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

Non-Anti-Monotonic Measures
 The cubing query with avg is non-anti-monotonic!
 (Mar, *, *, 600, 1800) fails the HAVING clause
 (Mar, *, Bus, 1300, 360) passes the clause
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
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
… … … … … …

Top-k Average
 Let (*, Van, *) cover 1,000 records
 Avg(price) is the average price of those 1000 sales
 Avg50(price) is the average price of the top-50 sales
(top-50 according to the sales price
 Top-k average is anti-monotonic
 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
… … … … … …

Binning for Top-k Average
 Computing top-k avg is costly with large k
 Binning idea
 Avg50(c) >= 800
 Large value collapsing: use a sum and a count
to summarize records with measure >= 800
 If count>=800, no need to check “small” records
 Small value binning: a group of bins
 One bin covers a range, e.g., 600~800, 400~600,
etc.
 Register a sum and a count for each bin

Approximate top-k average
Suppose for (*, Van, *), we have
Range Sum Count
Over 800 28000 20
600~800 10600 15
400~600 15200 30
… … …
Approximate avg50()=
(28000+10600+600*15)/50=95
2
Top 50
The cell may pass the HAVING clause
… … … … … …

Quant-info for Top-k Average
Binning
 Accumulate quant-info for cells to compute
average iceberg cubes efficiently
 Three pieces: sum, count, top-k bins
 Use top-k bins to estimate/prune descendants
 Use sum and count to consolidate current cell
weakest strongest
Approximate avg50()
Anti-monotonic, can
be computed
efficiently
real avg50()
Anti-monotonic, but
computationally
costly
avg()
Not anti-monotonic

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

H-tree: A Prefix Hyper-tree
Attr. Val. Quant-Info Side-link
Edu Sum:2285 …
Hhd …
Bus …
… …
Jan …
Feb …
… …
Tor …
Van …
Mon …
… …
Header
table
Jan Tor Edu Printer 500 485
Jan Tor Hhd TV 800 1200
Jan Tor Edu Camera 1160 1280
Feb Mon Bus Laptop 1500 2500
Mar Van Edu HD 540 520
… … … … … …
root
edu hhd bus
Jan Mar Jan Feb
Tor Van Tor Mon
Quant-Info Q.I. Q.I. Q.I.
Sum: 1765
Cnt: 2
bins

Properties of H-tree
 Construction cost: a single database scan
 Completeness: It contains the complete
information needed for computing the iceberg
cube
 Compactness: # of nodes  n*m+1
 n: # of tuples in the table
 m: # of attributes

Computing Cells Involving
Dimension City
From (*, *, Tor) to (*, Jan, Tor)
root
Edu. Hhd. Bus.
Jan. Mar. Jan. Feb.
Tor. Van. Tor. Mon.
Quant-Info Q.I. Q.I. Q.I.
Sum: 1765
Cnt: 2
bins
Attr.
Val.
Q.I. Side-link
Edu …
Hhd …
Bus …
… …
Jan …
Feb …
… …
Header
Table
HTor
Edu Sum:2285 …
Hhd …
Bus …
… …
Jan …
Feb …
… …
TToorr ……
Van …
Mon …
… …

Computing Cells Involving Month
But No City
root
Edu. Hhd. Bus.
Jan. Mar. Jan. Feb.
Q.I. Q.I. Q.I.
1. Roll up quant-info
2. Compute cells involving
month but no city
Q.I.
Tor. Van. Tor. Mont.
Edu. Sum:2285 …
Hhd. …
Bus. …
… …
Jan. …
Feb. …
Mar. …
… …
Tor. …
Van. …
Mont. …
… …
Top-k OK mark: if Q.I. in a child passes
top-k avg threshold, so does its parents.
No binning is needed!

Computing Cells Involving Only
Cust_grp
root
edu hhd bus
Jan Mar Jan Feb
Q.I. Q.I. Q.I.
Check header table directly
Q.I.
Tor Van Tor Mon
Edu Sum:2285
…
Hhd …
Bus …
… …
Jan …
Feb …
Mar …
… …
Tor …
Van …
Mon …
… …

Properties of H-Cubing
 Space cost
 an H-tree
 a stack of up to (m-1) header tables
 One database scan
 Main memory-based tree traversal & side-links
updates
 Top-k_OK marking

Scalability w.r.t. Count Threshold
(No min_avg Setting)
300
250
200
150
100
50
0
top-k H-Cubing
top-k BUC
0.00% 0.05% 0.10%
Count threshold
Runtime (second)

Computing Iceberg Cubes with Other
Complex Measures
 Computing other complex measures
 Key point: find a function which is weaker but ensures
certain anti-monotonicity
 Examples
 Avg() £ v: avgk(c) £ v (bottom-k avg)
 Avg() ³ v only (no count): max(price) ³ v
 Sum(profit) (profit can be negative):
 p_sum(c) ³ v if p_count(c) ³ k; or otherwise, sumk(c) ³ v
 Others: conjunctions of multiple conditions

Discussion: Other Issues
 Computing iceberg cubes with more complex measures?
 No general answer for holistic measures, e.g., median,
mode, rank
 A research theme even for complex algebraic functions,
e.g., standard_dev, variance
 Dynamic vs . static computation of iceberg cubes
 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

Condensed Cube
 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
 Suppose 100 dimensions, only 1 base cell with count = 10.
How many aggregate (non-base) cells if count >= 10?
 Condensed cube
 Only need to store one cell (a1, a2, …, a100, 10), which represents
all the corresponding aggregate cells
 Adv.
 Fully precomputed cube without compression
 Efficient computation of the minimal condensed cube

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

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

An OLAM Architecture
Mining query Mining result
OLAP
Engine
Meta
Data
Filtering&Integration Filtering
Data
Warehouse
User GUI API
Data Cube API
MDDB
OLAM
Engine
Database API
Data cleaning
Data integration
Layer4
User Interface
Layer3
OLAP/OLAM
Layer2
MDDB
Layer1
Data
Repository
Databases

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

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

Examples: Discovery-Driven Data
Cubes

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

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

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

MD Constrained Gradient Mining
 Significance constraint Csig: (cnt³100)
 Probe constraint Cprb: (city=“Van”, cust_grp=“busi”,
prod_grp=“*”)
 Gradient constraint Cgrad(cg, cp):
(avg_price(cg)/avg_price(cp)³1.3)
Probe cell: satisfied Cprb (c4, c2) satisfies Cgrad!
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

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

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
 Discovery-drive and multi-feature cubes
 From OLAP to OLAM (on-line analytical mining)

Data Mining Concepts and Techniques

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