Other Types of Association Rules
28.2.6 Other Types of Association Rules
Association Rules among Hierarchies. There are certain types of associations that are particularly interesting for a special reason. These associations occur among
3 See Savasere et al. (1995) for details of the algorithm, the data structures used to implement it, and its performance comparisons.
1048 Chapter 28 Data Mining Concepts
hierarchies of items. Typically, it is possible to divide items among disjoint hierar- chies based on the nature of the domain. For example, foods in a supermarket, items in a department store, or articles in a sports shop can be categorized into classes and subclasses that give rise to hierarchies. Consider Figure 28.3, which shows the taxon- omy of items in a supermarket. The figure shows two hierarchies—beverages and desserts, respectively. The entire groups may not produce associations of the form beverages => desserts, or desserts => beverages. However, associations of the type Healthy-brand frozen yogurt => bottled water, or Rich cream-brand ice cream => wine cooler may produce enough confidence and support to be valid association rules of interest.
Therefore, if the application area has a natural classification of the itemsets into hierarchies, discovering associations within the hierarchies is of no particular inter- est. The ones of specific interest are associations across hierarchies. They may occur among item groupings at different levels.
Multidimensional Associations. Discovering association rules involves search- ing for patterns in a file. In Figure 28.1, we have an example of a file of customer transactions with three dimensions: Transaction_id, Time, and Items_bought. However, our data mining tasks and algorithms introduced up to this point only involve one dimension: Items_bought. The following rule is an example of includ- ing the label of the single dimension: Items_bought(milk) => Items_bought(juice). It may be of interest to find association rules that involve multiple dimensions, for
Figure 28.3
Beverages
Taxonomy of items in a supermarket.
Carbonated Noncarbonated
Bottled Wine
water coolers
Plain Clear
Desserts
Ice cream
Baked
Frozen yogurt
28.2 Association Rules 1049
example, Time(6:30...8:00) => Items_bought(milk). Rules like these are called multidimensional association rules. The dimensions represent attributes of records of a file or, in terms of relations, columns of rows of a relation, and can be categori- cal or quantitative. Categorical attributes have a finite set of values that display no ordering relationship. Quantitative attributes are numeric and their values display an ordering relationship, for example, <. Items_bought is an example of a categori- cal attribute and Transaction_id and Time are quantitative.
One approach to handling a quantitative attribute is to partition its values into nonoverlapping intervals that are assigned labels. This can be done in a static man- ner based on domain-specific knowledge. For example, a concept hierarchy may group values for Salary into three distinct classes: low income (0 < Salary < 29,999), middle income (30,000 < Salary < 74,999), and high income ( Salary > 75,000). From here, the typical Apriori-type algorithm or one of its variants can be used for the rule mining since the quantitative attributes now look like categorical attributes. Another approach to partitioning is to group attribute values based on data distri- bution, for example, equi-depth partitioning, and to assign integer values to each partition. The partitioning at this stage may be relatively fine, that is, a larger num- ber of intervals. Then during the mining process, these partitions may combine with other adjacent partitions if their support is less than some predefined maxi- mum value. An Apriori-type algorithm can be used here as well for the data mining.
Negative Associations. The problem of discovering a negative association is harder than that of discovering a positive association. A negative association is of the following type: 60 percent of customers who buy potato chips do not buy bottled water. (Here, the 60 percent refers to the confidence for the negative association rule.) In a database with 10,000 items, there are 210,000 possible combinations of items, a majority of which do not appear even once in the database. If the absence of
a certain item combination is taken to mean a negative association, then we poten- tially have millions and millions of negative association rules with RHSs that are of no interest at all. The problem, then, is to find only interesting negative rules. In gen- eral, we are interested in cases in which two specific sets of items appear very rarely in the same transaction. This poses two problems.
1. For a total item inventory of 10,000 items, the probability of any two being bought together is (1/10,000) * (1/10,000) = 10 –8 . If we find the actual sup-
port for these two occurring together to be zero, that does not represent a significant departure from expectation and hence is not an interesting (neg- ative) association.
2. The other problem is more serious. We are looking for item combinations with very low support, and there are millions and millions with low or even
zero support. For example, a data set of 10 million transactions has most of the 2.5 billion pairwise combinations of 10,000 items missing. This would generate billions of useless rules.
Therefore, to make negative association rules interesting, we must use prior knowl-
1050 Chapter 28 Data Mining Concepts
Soft drinks
Chips
Figure 28.4
Simple hierarchy of soft drinks and chips.
Nightos Party’Os
A strong positive association has been shown between soft drinks and chips. If we find a large support for the fact that when customers buy Days chips they predomi- nantly buy Topsy and not Joke and not Wakeup, that would be interesting because we would normally expect that if there is a strong association between Days and Topsy, there should also be such a strong association between Days and Joke or Days and Wakeup. 5
In the frozen yogurt and bottled water groupings shown in Figure 28.3, suppose the Reduce versus Healthy-brand division is 80–20 and the Plain and Clear brands divi- sion is 60–40 among respective categories. This would give a joint probability of Reduce frozen yogurt being purchased with Plain bottled water as 48 percent among the transactions containing a frozen yogurt and bottled water. If this sup- port, however, is found to be only 20 percent, it would indicate a significant negative association among Reduce yogurt and Plain bottled water; again, that would be interesting.
The problem of finding negative association is important in the above situations given the domain knowledge in the form of item generalization hierarchies (that is, the beverage given and desserts hierarchies shown in Figure 28.3), the existing posi- tive associations (such as between the frozen yogurt and bottled water groups), and the distribution of items (such as the name brands within related groups). The scope of discovery of negative associations is limited in terms of knowing the item hierarchies and distributions. Exponential growth of negative associations remains
a challenge.
Parts
» Fundamentals_of_Database_Systems,_6th_Edition
» Characteristics of the Database Approach
» Advantages of Using the DBMS Approach
» A Brief History of Database Applications
» Schemas, Instances, and Database State
» The Three-Schema Architecture
» The Database System Environment
» Centralized and Client/Server Architectures for DBMSs
» Classification of Database Management Systems
» Domains, Attributes, Tuples, and Relations
» Key Constraints and Constraints on NULL Values
» Relational Databases and Relational Database Schemas
» Integrity, Referential Integrity, and Foreign Keys
» Update Operations, Transactions, and Dealing with Constraint Violations
» SQL Data Definition and Data Types
» Specifying Constraints in SQL
» The SELECT-FROM-WHERE Structure of Basic SQL Queries
» Ambiguous Attribute Names, Aliasing, Renaming, and Tuple Variables
» Substring Pattern Matching and Arithmetic Operators
» INSERT, DELETE, and UPDATE Statements in SQL
» Comparisons Involving NULL and Three-Valued Logic
» Nested Queries, Tuples, and Set/Multiset Comparisons
» The EXISTS and UNIQUE Functions in SQL
» Joined Tables in SQL and Outer Joins
» Grouping: The GROUP BY and HAVING Clauses
» Discussion and Summary of SQL Queries
» Specifying General Constraints as Assertions in SQL
» Introduction to Triggers in SQL
» Specification of Views in SQL
» View Implementation, View Update, and Inline Views
» Schema Change Statements in SQL
» Sequences of Operations and the RENAME Operation
» The UNION, INTERSECTION, and MINUS Operations
» The CARTESIAN PRODUCT (CROSS PRODUCT) Operation
» Variations of JOIN: The EQUIJOIN and NATURAL JOIN
» Additional Relational Operations
» Examples of Queries in Relational Algebra
» The Tuple Relational Calculus
» The Domain Relational Calculus
» Using High-Level Conceptual Data Models
» Entity Types, Entity Sets, Keys, and Value Sets
» Relationship Types, Relationship Sets, Roles, and Structural Constraints
» ER Diagrams, Naming Conventions, and Design Issues
» Example of Other Notation: UML Class Diagrams
» Relationship Types of Degree Higher than Two
» Subclasses, Superclasses, and Inheritance
» Constraints on Specialization and Generalization
» Specialization and Generalization Hierarchies
» Modeling of UNION Types Using Categories
» A Sample UNIVERSITY EER Schema, Design Choices, and Formal Definitions
» Data Abstraction, Knowledge Representation, and Ontology Concepts
» ER-to-Relational Mapping Algorithm
» Discussion and Summary of Mapping for ER Model Constructs
» Mapping EER Model Constructs
» The Role of Information Systems
» The Database Design and Implementation Process
» Use of UML Diagrams as an Aid to Database Design Specification 6
» Rational Rose: A UML-Based Design Tool
» Automated Database Design Tools
» Introduction to Object-Oriented Concepts and Features
» Object Identity, and Objects versus Literals
» Complex Type Structures for Objects and Literals
» Encapsulation of Operations and Persistence of Objects
» Type Hierarchies and Inheritance
» Other Object-Oriented Concepts
» Object-Relational Features: Object Database Extensions to SQL
» Overview of the Object Model of ODMG
» Built-in Interfaces and Classes in the Object Model
» Atomic (User-Defined) Objects
» Extents, Keys, and Factory Objects
» The Object Definition Language ODL
» Differences between Conceptual Design of ODB and RDB
» Mapping an EER Schema to an ODB Schema
» Query Results and Path Expressions
» Overview of the C++ Language Binding in the ODMG Standard
» Structured, Semistructured, and Unstructured Data
» XML Hierarchical (Tree) Data Model
» Well-Formed and Valid XML Documents and XML DTD
» XPath: Specifying Path Expressions in XML
» XQuery: Specifying Queries in XML
» Extracting XML Documents from
» Database Programming: Techniques
» Retrieving Single Tuples with Embedded SQL
» Retrieving Multiple Tuples with Embedded SQL Using Cursors
» Specifying Queries at Runtime Using Dynamic SQL
» SQLJ: Embedding SQL Commands in Java
» Retrieving Multiple Tuples in SQLJ Using Iterators
» Database Programming with SQL/CLI Using C
» JDBC: SQL Function Calls for Java Programming
» Database Stored Procedures and SQL/PSM
» PHP Variables, Data Types, and Programming Constructs
» Overview of PHP Database Programming
» Imparting Clear Semantics to Attributes in Relations
» Redundant Information in Tuples and Update Anomalies
» Normal Forms Based on Primary Keys
» General Definitions of Second and Third Normal Forms
» Multivalued Dependency and Fourth Normal Form
» Join Dependencies and Fifth Normal Form
» Inference Rules for Functional Dependencies
» Minimal Sets of Functional Dependencies
» Properties of Relational Decompositions
» Dependency-Preserving Decomposition
» Dependency-Preserving and Nonadditive (Lossless) Join Decomposition into 3NF Schemas
» Problems with NULL Values and Dangling Tuples
» Discussion of Normalization Algorithms and Alternative Relational Designs
» Further Discussion of Multivalued Dependencies and 4NF
» Other Dependencies and Normal Forms
» Memory Hierarchies and Storage Devices
» Hardware Description of Disk Devices
» Magnetic Tape Storage Devices
» Placing File Records on Disk
» Files of Unordered Records (Heap Files)
» Files of Ordered Records (Sorted Files)
» External Hashing for Disk Files
» Hashing Techniques That Allow Dynamic File Expansion
» Other Primary File Organizations
» Parallelizing Disk Access Using RAID Technology
» Types of Single-Level Ordered Indexes
» Some General Issues Concerning Indexing
» Algorithms for External Sorting
» Implementing the SELECT Operation
» Implementing the JOIN Operation
» Algorithms for PROJECT and Set
» Notation for Query Trees and Query Graphs
» Heuristic Optimization of Query Trees
» Catalog Information Used in Cost Functions
» Examples of Cost Functions for SELECT
» Examples of Cost Functions for JOIN
» Example to Illustrate Cost-Based Query Optimization
» Factors That Influence Physical Database Design
» Physical Database Design Decisions
» An Overview of Database Tuning in Relational Systems
» Transactions, Database Items, Read and Write Operations, and DBMS Buffers
» Why Concurrency Control Is Needed
» Transaction and System Concepts
» Desirable Properties of Transactions
» Serial, Nonserial, and Conflict-Serializable Schedules
» Testing for Conflict Serializability of a Schedule
» How Serializability Is Used for Concurrency Control
» View Equivalence and View Serializability
» Types of Locks and System Lock Tables
» Guaranteeing Serializability by Two-Phase Locking
» Dealing with Deadlock and Starvation
» Concurrency Control Based on Timestamp Ordering
» Multiversion Concurrency Control Techniques
» Validation (Optimistic) Concurrency
» Granularity of Data Items and Multiple Granularity Locking
» Using Locks for Concurrency Control in Indexes
» Other Concurrency Control Issues
» Recovery Outline and Categorization of Recovery Algorithms
» Caching (Buffering) of Disk Blocks
» Write-Ahead Logging, Steal/No-Steal, and Force/No-Force
» Transaction Rollback and Cascading Rollback
» NO-UNDO/REDO Recovery Based on Deferred Update
» Recovery Techniques Based on Immediate Update
» The ARIES Recovery Algorithm
» Recovery in Multidatabase Systems
» Introduction to Database Security Issues 1
» Discretionary Access Control Based on Granting and Revoking Privileges
» Mandatory Access Control and Role-Based Access Control for Multilevel Security
» Introduction to Statistical Database Security
» Introduction to Flow Control
» Encryption and Public Key Infrastructures
» Challenges of Database Security
» Distributed Database Concepts 1
» Types of Distributed Database Systems
» Distributed Database Architectures
» Data Replication and Allocation
» Example of Fragmentation, Allocation, and Replication
» Query Processing and Optimization in Distributed Databases
» Overview of Transaction Management in Distributed Databases
» Overview of Concurrency Control and Recovery in Distributed Databases
» Current Trends in Distributed Databases
» Distributed Databases in Oracle 13
» Generalized Model for Active Databases and Oracle Triggers
» Design and Implementation Issues for Active Databases
» Examples of Statement-Level Active Rules
» Time Representation, Calendars, and Time Dimensions
» Incorporating Time in Relational Databases Using Tuple Versioning
» Incorporating Time in Object-Oriented Databases Using Attribute Versioning
» Temporal Querying Constructs and the TSQL2 Language
» Spatial Database Concepts 24
» Multimedia Database Concepts
» Clausal Form and Horn Clauses
» Datalog Programs and Their Safety
» Evaluation of Nonrecursive Datalog Queries
» Introduction to Information Retrieval
» Types of Queries in IR Systems
» Evaluation Measures of Search Relevance
» Web Analysis and Its Relationship to Information Retrieval
» Analyzing the Link Structure of Web Pages
» Approaches to Web Content Analysis
» Trends in Information Retrieval
» Data Mining as a Part of the Knowledge
» Goals of Data Mining and Knowledge Discovery
» Types of Knowledge Discovered during Data Mining
» Market-Basket Model, Support, and Confidence
» Frequent-Pattern (FP) Tree and FP-Growth Algorithm
» Other Types of Association Rules
» Approaches to Other Data Mining Problems
» Commercial Data Mining Tools
» Data Modeling for Data Warehouses
» Difficulties of Implementing Data Warehouses
» Grouping, Aggregation, and Database Modification in QBE
Show more