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Data Mining

Cluster Analysis: Basic Concepts

and Algorithms

Lecture Notes for Chapter 8

Introduction to Data Mining

by

Tan, Steinbach, Kumar

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 1 © Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 2

What is Cluster Analysis?

Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the objects in other groups

Inter-cluster

distances are maximized

Intra-cluster

distances are minimized © Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 3

Applications of Cluster Analysis

Understanding

Group related documents

for browsing, group genes and proteins that have similar functionality, or group stocks with similar price fluctuations

Summarization

Reduce the size of large

data sets

Discovered ClustersIndustry Group

1

Cabletron-Sys-DOWN,CISCO-DOWN,HP-DOWN,

DSC-Comm-DOWN,INTEL-DOWN,LSI-Logic-DOWN,

Sun-DOWN

Technology1-DOWN

2

Apple-Comp-DOWN,Autodesk-DOWN,DEC-DOWN,

ADV-Micro-Device-DOWN,Andrew-Corp-DOWN,

Computer-Assoc-DOWN,Circuit-City-DOWN,

Compaq-DOWN, EMC-Corp-DOWN, Gen-Inst-DOWN,

Technology2-DOWN

3

Fannie-Mae-DOWN,Fed-Home-Loan-DOWN,

MBNA-Corp-DOWN,Morgan-Stanley-DOWN

Financial-DOWN

4

Schlumberger-UP

Oil-UP

Clustering precipitation

in Australia © Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 4

What is not Cluster Analysis?

Supervised classification

Have class label information

Simple segmentation

Dividing students into different registration groups alphabetically, by last name

Results of a query

Groupings are a result of an external specification

Graph partitioning

Some mutual relevance and synergy, but areas are not identical © Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 6

Types of Clusterings

A clustering is a set of clusters

Important distinction between hierarchical and

partitional sets of clusters

Partitional Clustering

A division data objects into non-overlapping subsets (clusters) such that each data object is in exactly one subset

Hierarchical clustering

A set of nested clusters organized as a hierarchical tree © Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 7

Partitional Clustering

Original PointsA Partitional Clustering

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 8

Hierarchical Clustering

p4 p1 p3 p2 p4p1p2p3

Hierarchical ClusteringDendrogram

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 9

Hierarchical Clustering

Hierarchical ClusteringDendrogram

Source: http://cs.jhu.edu/~razvanm/fs-expedition/tux3.html © Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 12

Types of Clusters

Well-separated clusters

Center-based clusters

Contiguous clusters

Density-based clusters

Property or Conceptual

Described by an Objective Function

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 13

Types of Clusters: Well-Separated

Well-Separated Clusters:

A cluster is a set of points such that any point in a cluster is closer (or more similar) to every other point in the cluster than to any point not in the cluster.

3 well-separated clusters

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 14

Types of Clusters: Center-Based

Center-based

A cluster is a set of objects such that an object in a cluster is closer (more similar) to the "center" of a cluster, than to the center of any other cluster The center of a cluster is often a centroid, the average of all the points in the cluster, or a medoid, the most "representative" point of a cluster

4 center-based clusters

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 15

Types of Clusters: Contiguity-Based

Contiguous Cluster (Nearest neighbor or

Transitive)

A cluster is a set of points such that a point in a cluster is closer (or more similar) to one or more other points in the cluster than to any point not in the cluster.

8 contiguous clusters

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 16

Types of Clusters: Density-Based

Density-based

A cluster is a dense region of points, which is separated by low-density regions, from other regions of high density. Used when the clusters are irregular or intertwined, and when noise and outliers are present.

6 density-based clusters

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 20

Characteristics of the Input Data Are Important

Type of proximity or density measure

-This is a derived measure, but central to clustering

Sparseness

Dictates type of similarity

Adds to efficiency

Attribute type

-Dictates type of similarity

Type of Data

Dictates type of similarity

-Other characteristics, e.g., autocorrelation

Dimensionality

Noise and Outliers

Type of Distribution

quotesdbs_dbs20.pdfusesText_26