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1.Data Mining: Concepts and Techniques
2.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
3.What is Cluster Analysis?
Cluster: a collection of data objects
Similar to one another within the same cluster
Dissimilar to the objects in other clusters
Cluster analysis
Grouping a set of data objects into clusters
Clustering is unsupervised classification: no predefined classes
Typical applications
As a stand-alone tool to get insight into data distribution
As a preprocessing step for other algorithms
Cluster: a collection of data objects
Similar to one another within the same cluster
Dissimilar to the objects in other clusters
Cluster analysis
Grouping a set of data objects into clusters
Clustering is unsupervised classification: no predefined classes
Typical applications
As a stand-alone tool to get insight into data distribution
As a preprocessing step for other algorithms
4.General Applications of Clustering
Pattern Recognition
Spatial Data Analysis
create thematic maps in GIS by clustering feature spaces
detect spatial clusters and explain them in spatial data mining
Image Processing
Economic Science (especially market research)
WWW
Document classification
Cluster Weblog data to discover groups of similar access patterns
Pattern Recognition
Spatial Data Analysis
create thematic maps in GIS by clustering feature spaces
detect spatial clusters and explain them in spatial data mining
Image Processing
Economic Science (especially market research)
WWW
Document classification
Cluster Weblog data to discover groups of similar access patterns
5.Examples of Clustering Applications
Marketing: Help marketers discover distinct groups in their customer bases, and then use this knowledge to develop targeted marketing programs
Land use: Identification of areas of similar land use in an earth observation database
Insurance: Identifying groups of motor insurance policy holders with a high average claim cost
City-planning: Identifying groups of houses according to their house type, value, and geographical location
Earth-quake studies: Observed earth quake epicenters should be clustered along continent faults
Marketing: Help marketers discover distinct groups in their customer bases, and then use this knowledge to develop targeted marketing programs
Land use: Identification of areas of similar land use in an earth observation database
Insurance: Identifying groups of motor insurance policy holders with a high average claim cost
City-planning: Identifying groups of houses according to their house type, value, and geographical location
Earth-quake studies: Observed earth quake epicenters should be clustered along continent faults
6.What Is Good Clustering?
A good clustering method will produce high quality clusters with
high intra-class similarity
low inter-class similarity
The quality of a clustering result depends on both the similarity measure used by the method and its implementation.
The quality of a clustering method is also measured by its ability to discover some or all of the hidden patterns.
A good clustering method will produce high quality clusters with
high intra-class similarity
low inter-class similarity
The quality of a clustering result depends on both the similarity measure used by the method and its implementation.
The quality of a clustering method is also measured by its ability to discover some or all of the hidden patterns.
7.Requirements of Clustering in Data Mining
Scalability
Ability to deal with different types of attributes
Discovery of clusters with arbitrary shape
Minimal requirements for domain knowledge to determine input parameters
Able to deal with noise and outliers
Insensitive to order of input records
High dimensionality
Incorporation of user-specified constraints
Interpretability and usability
Scalability
Ability to deal with different types of attributes
Discovery of clusters with arbitrary shape
Minimal requirements for domain knowledge to determine input parameters
Able to deal with noise and outliers
Insensitive to order of input records
High dimensionality
Incorporation of user-specified constraints
Interpretability and usability
8.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
9.Data Structures
10.Measure the Quality of Clustering
11.Type of data in clustering analysis
Interval-scaled variables:
Binary variables:
Nominal, ordinal, and ratio variables:
Variables of mixed types:
Interval-scaled variables:
Binary variables:
Nominal, ordinal, and ratio variables:
Variables of mixed types:
12.Interval-valued variables
13.Similarity and Dissimilarity Between Objects
14.Binary Variables
15.Dissimilarity between Binary Variables
16.Nominal Variables
17.Ordinal Variables
18.Ratio-Scaled Variables
19.Variables of Mixed Types
20.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
21.Major Clustering Approaches
Partitioning algorithms: Construct various partitions and then evaluate them by some criterion
Hierarchy algorithms: Create a hierarchical decomposition of the set of data (or objects) using some criterion
Density-based: based on connectivity and density functions
Grid-based: based on a multiple-level granularity structure
Model-based: A model is hypothesized for each of the clusters and the idea is to find the best fit of that model to each other
Partitioning algorithms: Construct various partitions and then evaluate them by some criterion
Hierarchy algorithms: Create a hierarchical decomposition of the set of data (or objects) using some criterion
Density-based: based on connectivity and density functions
Grid-based: based on a multiple-level granularity structure
Model-based: A model is hypothesized for each of the clusters and the idea is to find the best fit of that model to each other
22.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
23.Partitioning Algorithms: Basic Concept
Partitioning method: Construct a partition of a database D of n objects into a set of k clusters
Given a k, find a partition of k clusters that optimizes the chosen partitioning criterion
Global optimal: exhaustively enumerate all partitions
Heuristic methods: k-means and k-medoids algorithms
k-means (MacQueen’67): Each cluster is represented by the center of the cluster
k-medoids or PAM (Partition around medoids) (Kaufman & Rousseeuw’87): Each cluster is represented by one of the objects in the cluster
Partitioning method: Construct a partition of a database D of n objects into a set of k clusters
Given a k, find a partition of k clusters that optimizes the chosen partitioning criterion
Global optimal: exhaustively enumerate all partitions
Heuristic methods: k-means and k-medoids algorithms
k-means (MacQueen’67): Each cluster is represented by the center of the cluster
k-medoids or PAM (Partition around medoids) (Kaufman & Rousseeuw’87): Each cluster is represented by one of the objects in the cluster
24.The K-Means Clustering Method
Given k, the k-means algorithm is implemented in 4 steps:
Partition objects into k nonempty subsets
Compute seed points as the centroids of the clusters of the current partition. The centroid is the center (mean point) of the cluster.
Assign each object to the cluster with the nearest seed point.
Go back to Step 2, stop when no more new assignment.
Given k, the k-means algorithm is implemented in 4 steps:
Partition objects into k nonempty subsets
Compute seed points as the centroids of the clusters of the current partition. The centroid is the center (mean point) of the cluster.
Assign each object to the cluster with the nearest seed point.
Go back to Step 2, stop when no more new assignment.
25.The K-Means Clustering Method
26.Comments on the K-Means Method
27.Variations of the K-Means Method
A few variants of the k-means which differ in
Selection of the initial k means
Dissimilarity calculations
Strategies to calculate cluster means
Handling categorical data: k-modes (Huang’98)
Replacing means of clusters with modes
Using new dissimilarity measures to deal with categorical objects
Using a frequency-based method to update modes of clusters
A mixture of categorical and numerical data: k-prototype method
A few variants of the k-means which differ in
Selection of the initial k means
Dissimilarity calculations
Strategies to calculate cluster means
Handling categorical data: k-modes (Huang’98)
Replacing means of clusters with modes
Using new dissimilarity measures to deal with categorical objects
Using a frequency-based method to update modes of clusters
A mixture of categorical and numerical data: k-prototype method
28.The K-Medoids Clustering Method
Find representative objects, called medoids, in clusters
PAM (Partitioning Around Medoids, 1987)
starts from an initial set of medoids and iteratively replaces one of the medoids by one of the non-medoids if it improves the total distance of the resulting clustering
PAM works effectively for small data sets, but does not scale well for large data sets
CLARA (Kaufmann & Rousseeuw, 1990)
CLARANS (Ng & Han, 1994): Randomized sampling
Focusing + spatial data structure (Ester et al., 1995)
Find representative objects, called medoids, in clusters
PAM (Partitioning Around Medoids, 1987)
starts from an initial set of medoids and iteratively replaces one of the medoids by one of the non-medoids if it improves the total distance of the resulting clustering
PAM works effectively for small data sets, but does not scale well for large data sets
CLARA (Kaufmann & Rousseeuw, 1990)
CLARANS (Ng & Han, 1994): Randomized sampling
Focusing + spatial data structure (Ester et al., 1995)
29.PAM (Partitioning Around Medoids) (1987)
PAM (Kaufman and Rousseeuw, 1987), built in Splus
Use real object to represent the cluster
Select k representative objects arbitrarily
For each pair of non-selected object h and selected object i, calculate the total swapping cost TCih
For each pair of i and h,
If TCih < 0, i is replaced by h
Then assign each non-selected object to the most similar representative object
repeat steps 2-3 until there is no change
PAM (Kaufman and Rousseeuw, 1987), built in Splus
Use real object to represent the cluster
Select k representative objects arbitrarily
For each pair of non-selected object h and selected object i, calculate the total swapping cost TCih
For each pair of i and h,
If TCih < 0, i is replaced by h
Then assign each non-selected object to the most similar representative object
repeat steps 2-3 until there is no change
30.CLARA (Clustering Large Applications) (1990)
CLARA (Kaufmann and Rousseeuw in 1990)
Built in statistical analysis packages, such as S+
It draws multiple samples of the data set, applies PAM on each sample, and gives the best clustering as the output
Strength: deals with larger data sets than PAM
Weakness:
Efficiency depends on the sample size
A good clustering based on samples will not necessarily represent a good clustering of the whole data set if the sample is biased
CLARA (Kaufmann and Rousseeuw in 1990)
Built in statistical analysis packages, such as S+
It draws multiple samples of the data set, applies PAM on each sample, and gives the best clustering as the output
Strength: deals with larger data sets than PAM
Weakness:
Efficiency depends on the sample size
A good clustering based on samples will not necessarily represent a good clustering of the whole data set if the sample is biased
31.CLARANS (“Randomized” CLARA) (1994)
CLARANS (A Clustering Algorithm based on Randomized Search) (Ng and Han’94)
CLARANS draws sample of neighbors dynamically
The clustering process can be presented as searching a graph where every node is a potential solution, that is, a set of k medoids
If the local optimum is found, CLARANS starts with new randomly selected node in search for a new local optimum
It is more efficient and scalable than both PAM and CLARA
Focusing techniques and spatial access structures may further improve its performance (Ester et al.’95)
CLARANS (A Clustering Algorithm based on Randomized Search) (Ng and Han’94)
CLARANS draws sample of neighbors dynamically
The clustering process can be presented as searching a graph where every node is a potential solution, that is, a set of k medoids
If the local optimum is found, CLARANS starts with new randomly selected node in search for a new local optimum
It is more efficient and scalable than both PAM and CLARA
Focusing techniques and spatial access structures may further improve its performance (Ester et al.’95)
32.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
33.Hierarchical Clustering
Use distance matrix as clustering criteria. This method does not require the number of clusters k as an input, but needs a termination condition
Use distance matrix as clustering criteria. This method does not require the number of clusters k as an input, but needs a termination condition
34.AGNES (Agglomerative Nesting)
Introduced in Kaufmann and Rousseeuw (1990)
Implemented in statistical analysis packages, e.g., Splus
Use the Single-Link method and the dissimilarity matrix.
Merge nodes that have the least dissimilarity
Go on in a non-descending fashion
Eventually all nodes belong to the same cluster
Introduced in Kaufmann and Rousseeuw (1990)
Implemented in statistical analysis packages, e.g., Splus
Use the Single-Link method and the dissimilarity matrix.
Merge nodes that have the least dissimilarity
Go on in a non-descending fashion
Eventually all nodes belong to the same cluster
35.A Dendrogram Shows How the Clusters are Merged Hierarchically
36.DIANA (Divisive Analysis)
37.More on Hierarchical Clustering Methods
Major weakness of agglomerative clustering methods
do not scale well: time complexity of at least O(n2), where n is the number of total objects
can never undo what was done previously
Integration of hierarchical with distance-based clustering
BIRCH (1996): uses CF-tree and incrementally adjusts the quality of sub-clusters
CURE (1998): selects well-scattered points from the cluster and then shrinks them towards the center of the cluster by a specified fraction
CHAMELEON (1999): hierarchical clustering using dynamic modeling
Major weakness of agglomerative clustering methods
do not scale well: time complexity of at least O(n2), where n is the number of total objects
can never undo what was done previously
Integration of hierarchical with distance-based clustering
BIRCH (1996): uses CF-tree and incrementally adjusts the quality of sub-clusters
CURE (1998): selects well-scattered points from the cluster and then shrinks them towards the center of the cluster by a specified fraction
CHAMELEON (1999): hierarchical clustering using dynamic modeling
38.BIRCH (1996)
Birch: Balanced Iterative Reducing and Clustering using Hierarchies, by Zhang, Ramakrishnan, Livny (SIGMOD’96)
Incrementally construct a CF (Clustering Feature) tree, a hierarchical data structure for multiphase clustering
Phase 1: scan DB to build an initial in-memory CF tree (a multi-level compression of the data that tries to preserve the inherent clustering structure of the data)
Phase 2: use an arbitrary clustering algorithm to cluster the leaf nodes of the CF-tree
Scales linearly: finds a good clustering with a single scan and improves the quality with a few additional scans
Weakness: handles only numeric data, and sensitive to the order of the data record.
Birch: Balanced Iterative Reducing and Clustering using Hierarchies, by Zhang, Ramakrishnan, Livny (SIGMOD’96)
Incrementally construct a CF (Clustering Feature) tree, a hierarchical data structure for multiphase clustering
Phase 1: scan DB to build an initial in-memory CF tree (a multi-level compression of the data that tries to preserve the inherent clustering structure of the data)
Phase 2: use an arbitrary clustering algorithm to cluster the leaf nodes of the CF-tree
Scales linearly: finds a good clustering with a single scan and improves the quality with a few additional scans
Weakness: handles only numeric data, and sensitive to the order of the data record.
39.Clustering Feature Vector
40.CF Tree
41.CURE (Clustering Using REpresentatives )
42.Drawbacks of Distance-Based Method
Drawbacks of square-error based clustering method
Consider only one point as representative of a cluster
Good only for convex shaped, similar size and density, and if k can be reasonably estimated
Drawbacks of square-error based clustering method
Consider only one point as representative of a cluster
Good only for convex shaped, similar size and density, and if k can be reasonably estimated
43.Cure: The Algorithm
Draw random sample s.
Partition sample to p partitions with size s/p
Partially cluster partitions into s/pq clusters
Eliminate outliers
By random sampling
If a cluster grows too slow, eliminate it.
Cluster partial clusters.
Label data in disk
Draw random sample s.
Partition sample to p partitions with size s/p
Partially cluster partitions into s/pq clusters
Eliminate outliers
By random sampling
If a cluster grows too slow, eliminate it.
Cluster partial clusters.
Label data in disk
44.Data Partitioning and Clustering
45.Cure: Shrinking Representative Points
46.Shrink the multiple representative points towards the gravity center by a fraction of ?.
Multiple representatives capture the shape of the cluster
Multiple representatives capture the shape of the cluster
47.Clustering Categorical Data: ROCK
ROCK: Robust Clustering using linKs, by S. Guha, R. Rastogi, K. Shim (ICDE’99).
Use links to measure similarity/proximity
Not distance based
ROCK: Robust Clustering using linKs, by S. Guha, R. Rastogi, K. Shim (ICDE’99).
Use links to measure similarity/proximity
Not distance based
48.Rock: Algorithm
49.CHAMELEON
CHAMELEON: hierarchical clustering using dynamic modeling, by G. Karypis, E.H. Han and V. Kumar’99
Measures the similarity based on a dynamic model
Two clusters are merged only if the interconnectivity and closeness (proximity) between two clusters are high relative to the internal interconnectivity of the clusters and closeness of items within the clusters
A two phase algorithm
1. Use a graph partitioning algorithm: cluster objects into a large number of relatively small sub-clusters
2. Use an agglomerative hierarchical clustering algorithm: find the genuine clusters by repeatedly combining these sub-clusters
CHAMELEON: hierarchical clustering using dynamic modeling, by G. Karypis, E.H. Han and V. Kumar’99
Measures the similarity based on a dynamic model
Two clusters are merged only if the interconnectivity and closeness (proximity) between two clusters are high relative to the internal interconnectivity of the clusters and closeness of items within the clusters
A two phase algorithm
1. Use a graph partitioning algorithm: cluster objects into a large number of relatively small sub-clusters
2. Use an agglomerative hierarchical clustering algorithm: find the genuine clusters by repeatedly combining these sub-clusters
50.Overall Framework of CHAMELEON
51.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
53.Density-Based Clustering Methods
Clustering based on density (local cluster criterion), such as density-connected points
Major features:
Discover clusters of arbitrary shape
Handle noise
One scan
Need density parameters as termination condition
Several interesting studies:
DBSCAN: Ester, et al. (KDD’96)
OPTICS: Ankerst, et al (SIGMOD’99).
DENCLUE: Hinneburg & D. Keim (KDD’98)
CLIQUE: Agrawal, et al. (SIGMOD’98)
Clustering based on density (local cluster criterion), such as density-connected points
Major features:
Discover clusters of arbitrary shape
Handle noise
One scan
Need density parameters as termination condition
Several interesting studies:
DBSCAN: Ester, et al. (KDD’96)
OPTICS: Ankerst, et al (SIGMOD’99).
DENCLUE: Hinneburg & D. Keim (KDD’98)
CLIQUE: Agrawal, et al. (SIGMOD’98)
54.Density-Based Clustering: Background
55.Density-Based Clustering: Background (II)
56.DBSCAN: Density Based Spatial Clustering of Applications with Noise
57.DBSCAN: The Algorithm
Arbitrary select a point p
Retrieve all points density-reachable from p wrt Eps and MinPts.
If p is a core point, a cluster is formed.
If p is a border point, no points are density-reachable from p and DBSCAN visits the next point of the database.
Continue the process until all of the points have been processed.
Arbitrary select a point p
Retrieve all points density-reachable from p wrt Eps and MinPts.
If p is a core point, a cluster is formed.
If p is a border point, no points are density-reachable from p and DBSCAN visits the next point of the database.
Continue the process until all of the points have been processed.
58.OPTICS: A Cluster-Ordering Method (1999)
OPTICS: Ordering Points To Identify the Clustering Structure
Ankerst, Breunig, Kriegel, and Sander (SIGMOD’99)
Produces a special order of the database wrt its density-based clustering structure
This cluster-ordering contains info equiv to the density-based clusterings corresponding to a broad range of parameter settings
Good for both automatic and interactive cluster analysis, including finding intrinsic clustering structure
Can be represented graphically or using visualization techniques
OPTICS: Ordering Points To Identify the Clustering Structure
Ankerst, Breunig, Kriegel, and Sander (SIGMOD’99)
Produces a special order of the database wrt its density-based clustering structure
This cluster-ordering contains info equiv to the density-based clusterings corresponding to a broad range of parameter settings
Good for both automatic and interactive cluster analysis, including finding intrinsic clustering structure
Can be represented graphically or using visualization techniques
59.OPTICS: Some Extension from DBSCAN
60.Reachability-distance
61.DENCLUE: using density functions
DENsity-based CLUstEring by Hinneburg & Keim (KDD’98)
Major features
Solid mathematical foundation
Good for data sets with large amounts of noise
Allows a compact mathematical description of arbitrarily shaped clusters in high-dimensional data sets
Significant faster than existing algorithm (faster than DBSCAN by a factor of up to 45)
But needs a large number of parameters
DENsity-based CLUstEring by Hinneburg & Keim (KDD’98)
Major features
Solid mathematical foundation
Good for data sets with large amounts of noise
Allows a compact mathematical description of arbitrarily shaped clusters in high-dimensional data sets
Significant faster than existing algorithm (faster than DBSCAN by a factor of up to 45)
But needs a large number of parameters
62.Denclue: Technical Essence
Uses grid cells but only keeps information about grid cells that do actually contain data points and manages these cells in a tree-based access structure.
Influence function: describes the impact of a data point within its neighborhood.
Overall density of the data space can be calculated as the sum of the influence function of all data points.
Clusters can be determined mathematically by identifying density attractors.
Density attractors are local maximal of the overall density function.
Uses grid cells but only keeps information about grid cells that do actually contain data points and manages these cells in a tree-based access structure.
Influence function: describes the impact of a data point within its neighborhood.
Overall density of the data space can be calculated as the sum of the influence function of all data points.
Clusters can be determined mathematically by identifying density attractors.
Density attractors are local maximal of the overall density function.
63.Gradient: The steepness of a slope
64.Density Attractor
65.Center-Defined and Arbitrary
66.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
67.Grid-Based Clustering Method
Using multi-resolution grid data structure
Several interesting methods
STING (a STatistical INformation Grid approach) by Wang, Yang and Muntz (1997)
WaveCluster by Sheikholeslami, Chatterjee, and Zhang (VLDB’98)
A multi-resolution clustering approach using wavelet method
CLIQUE: Agrawal, et al. (SIGMOD’98)
Using multi-resolution grid data structure
Several interesting methods
STING (a STatistical INformation Grid approach) by Wang, Yang and Muntz (1997)
WaveCluster by Sheikholeslami, Chatterjee, and Zhang (VLDB’98)
A multi-resolution clustering approach using wavelet method
CLIQUE: Agrawal, et al. (SIGMOD’98)
68.STING: A Statistical Information Grid Approach
Wang, Yang and Muntz (VLDB’97)
The spatial area area is divided into rectangular cells
There are several levels of cells corresponding to different levels of resolution
Wang, Yang and Muntz (VLDB’97)
The spatial area area is divided into rectangular cells
There are several levels of cells corresponding to different levels of resolution
69.STING: A Statistical Information Grid Approach
Wang, Yang and Muntz (VLDB’97)
The spatial area area is divided into rectangular cells
There are several levels of cells corresponding to different levels of resolution
Wang, Yang and Muntz (VLDB’97)
The spatial area area is divided into rectangular cells
There are several levels of cells corresponding to different levels of resolution
70.STING: A Statistical Information Grid Approach (2)
Each cell at a high level is partitioned into a number of smaller cells in the next lower level
Statistical info of each cell is calculated and stored beforehand and is used to answer queries
Parameters of higher level cells can be easily calculated from parameters of lower level cell
count, mean, s, min, max
type of distribution—normal, uniform, etc.
Use a top-down approach to answer spatial data queries
Start from a pre-selected layer—typically with a small number of cells
For each cell in the current level compute the confidence interval
Each cell at a high level is partitioned into a number of smaller cells in the next lower level
Statistical info of each cell is calculated and stored beforehand and is used to answer queries
Parameters of higher level cells can be easily calculated from parameters of lower level cell
count, mean, s, min, max
type of distribution—normal, uniform, etc.
Use a top-down approach to answer spatial data queries
Start from a pre-selected layer—typically with a small number of cells
For each cell in the current level compute the confidence interval
71.STING: A Statistical Information Grid Approach (3)
Remove the irrelevant cells from further consideration
When finish examining the current layer, proceed to the next lower level
Repeat this process until the bottom layer is reached
Advantages:
Query-independent, easy to parallelize, incremental update
O(K), where K is the number of grid cells at the lowest level
Disadvantages:
All the cluster boundaries are either horizontal or vertical, and no diagonal boundary is detected
Remove the irrelevant cells from further consideration
When finish examining the current layer, proceed to the next lower level
Repeat this process until the bottom layer is reached
Advantages:
Query-independent, easy to parallelize, incremental update
O(K), where K is the number of grid cells at the lowest level
Disadvantages:
All the cluster boundaries are either horizontal or vertical, and no diagonal boundary is detected
72.WaveCluster (1998)
Sheikholeslami, Chatterjee, and Zhang (VLDB’98)
A multi-resolution clustering approach which applies wavelet transform to the feature space
A wavelet transform is a signal processing technique that decomposes a signal into different frequency sub-band.
Both grid-based and density-based
Input parameters:
# of grid cells for each dimension
the wavelet, and the # of applications of wavelet transform.
Sheikholeslami, Chatterjee, and Zhang (VLDB’98)
A multi-resolution clustering approach which applies wavelet transform to the feature space
A wavelet transform is a signal processing technique that decomposes a signal into different frequency sub-band.
Both grid-based and density-based
Input parameters:
# of grid cells for each dimension
the wavelet, and the # of applications of wavelet transform.
73.What is Wavelet (1)?
74.WaveCluster (1998)
How to apply wavelet transform to find clusters
Summaries the data by imposing a multidimensional grid structure onto data space
These multidimensional spatial data objects are represented in a n-dimensional feature space
Apply wavelet transform on feature space to find the dense regions in the feature space
Apply wavelet transform multiple times which result in clusters at different scales from fine to coarse
How to apply wavelet transform to find clusters
Summaries the data by imposing a multidimensional grid structure onto data space
These multidimensional spatial data objects are represented in a n-dimensional feature space
Apply wavelet transform on feature space to find the dense regions in the feature space
Apply wavelet transform multiple times which result in clusters at different scales from fine to coarse
75.What Is Wavelet (2)?
76.Quantization
77.Transformation
78.CLIQUE (Clustering In QUEst)
Agrawal, Gehrke, Gunopulos, Raghavan (SIGMOD’98).
Automatically identifying subspaces of a high dimensional data space that allow better clustering than original space
CLIQUE can be considered as both density-based and grid-based
It partitions each dimension into the same number of equal length interval
It partitions an m-dimensional data space into non-overlapping rectangular units
A unit is dense if the fraction of total data points contained in the unit exceeds the input model parameter
A cluster is a maximal set of connected dense units within a subspace
Agrawal, Gehrke, Gunopulos, Raghavan (SIGMOD’98).
Automatically identifying subspaces of a high dimensional data space that allow better clustering than original space
CLIQUE can be considered as both density-based and grid-based
It partitions each dimension into the same number of equal length interval
It partitions an m-dimensional data space into non-overlapping rectangular units
A unit is dense if the fraction of total data points contained in the unit exceeds the input model parameter
A cluster is a maximal set of connected dense units within a subspace
79.CLIQUE: The Major Steps
Partition the data space and find the number of points that lie inside each cell of the partition.
Identify the subspaces that contain clusters using the Apriori principle
Identify clusters:
Determine dense units in all subspaces of interests
Determine connected dense units in all subspaces of interests.
Generate minimal description for the clusters
Determine maximal regions that cover a cluster of connected dense units for each cluster
Determination of minimal cover for each cluster
Partition the data space and find the number of points that lie inside each cell of the partition.
Identify the subspaces that contain clusters using the Apriori principle
Identify clusters:
Determine dense units in all subspaces of interests
Determine connected dense units in all subspaces of interests.
Generate minimal description for the clusters
Determine maximal regions that cover a cluster of connected dense units for each cluster
Determination of minimal cover for each cluster
80.Strength and Weakness of CLIQUE
Strength
It automatically finds subspaces of the highest dimensionality such that high density clusters exist in those subspaces
It is insensitive to the order of records in input and does not presume some canonical data distribution
It scales linearly with the size of input and has good scalability as the number of dimensions in the data increases
Weakness
The accuracy of the clustering result may be degraded at the expense of simplicity of the method
Strength
It automatically finds subspaces of the highest dimensionality such that high density clusters exist in those subspaces
It is insensitive to the order of records in input and does not presume some canonical data distribution
It scales linearly with the size of input and has good scalability as the number of dimensions in the data increases
Weakness
The accuracy of the clustering result may be degraded at the expense of simplicity of the method
81.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
82.Model-Based Clustering Methods
Attempt to optimize the fit between the data and some mathematical model
Statistical and AI approach
Conceptual clustering
A form of clustering in machine learning
Produces a classification scheme for a set of unlabeled objects
Finds characteristic description for each concept (class)
COBWEB (Fisher’87)
A popular a simple method of incremental conceptual learning
Creates a hierarchical clustering in the form of a classification tree
Each node refers to a concept and contains a probabilistic description of that concept
Attempt to optimize the fit between the data and some mathematical model
Statistical and AI approach
Conceptual clustering
A form of clustering in machine learning
Produces a classification scheme for a set of unlabeled objects
Finds characteristic description for each concept (class)
COBWEB (Fisher’87)
A popular a simple method of incremental conceptual learning
Creates a hierarchical clustering in the form of a classification tree
Each node refers to a concept and contains a probabilistic description of that concept
83.COBWEB Clustering Method
84.More on Statistical-Based Clustering
Limitations of COBWEB
The assumption that the attributes are independent of each other is often too strong because correlation may exist
Not suitable for clustering large database data – skewed tree and expensive probability distributions
CLASSIT
an extension of COBWEB for incremental clustering of continuous data
suffers similar problems as COBWEB
AutoClass (Cheeseman and Stutz, 1996)
Uses Bayesian statistical analysis to estimate the number of clusters
Popular in industry
Limitations of COBWEB
The assumption that the attributes are independent of each other is often too strong because correlation may exist
Not suitable for clustering large database data – skewed tree and expensive probability distributions
CLASSIT
an extension of COBWEB for incremental clustering of continuous data
suffers similar problems as COBWEB
AutoClass (Cheeseman and Stutz, 1996)
Uses Bayesian statistical analysis to estimate the number of clusters
Popular in industry
85.Other Model-Based Clustering Methods
Neural network approaches
Represent each cluster as an exemplar, acting as a “prototype” of the cluster
New objects are distributed to the cluster whose exemplar is the most similar according to some dostance measure
Competitive learning
Involves a hierarchical architecture of several units (neurons)
Neurons compete in a “winner-takes-all” fashion for the object currently being presented
Neural network approaches
Represent each cluster as an exemplar, acting as a “prototype” of the cluster
New objects are distributed to the cluster whose exemplar is the most similar according to some dostance measure
Competitive learning
Involves a hierarchical architecture of several units (neurons)
Neurons compete in a “winner-takes-all” fashion for the object currently being presented
86.Model-Based Clustering Methods
87.Self-organizing feature maps (SOMs)
Clustering is also performed by having several units competing for the current object
The unit whose weight vector is closest to the current object wins
The winner and its neighbors learn by having their weights adjusted
SOMs are believed to resemble processing that can occur in the brain
Useful for visualizing high-dimensional data in 2- or 3-D space
Clustering is also performed by having several units competing for the current object
The unit whose weight vector is closest to the current object wins
The winner and its neighbors learn by having their weights adjusted
SOMs are believed to resemble processing that can occur in the brain
Useful for visualizing high-dimensional data in 2- or 3-D space
88.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
89.What Is Outlier Discovery?
What are outliers?
The set of objects are considerably dissimilar from the remainder of the data
Example: Sports: Michael Jordon, Wayne Gretzky, ...
Problem
Find top n outlier points
Applications:
Credit card fraud detection
Telecom fraud detection
Customer segmentation
Medical analysis
What are outliers?
The set of objects are considerably dissimilar from the remainder of the data
Example: Sports: Michael Jordon, Wayne Gretzky, ...
Problem
Find top n outlier points
Applications:
Credit card fraud detection
Telecom fraud detection
Customer segmentation
Medical analysis
90.Outlier Discovery: Statistical Approaches
Assume a model underlying distribution that generates data set (e.g. normal distribution)
Use discordancy tests depending on
data distribution
distribution parameter (e.g., mean, variance)
number of expected outliers
Drawbacks
most tests are for single attribute
In many cases, data distribution may not be known
Assume a model underlying distribution that generates data set (e.g. normal distribution)
Use discordancy tests depending on
data distribution
distribution parameter (e.g., mean, variance)
number of expected outliers
Drawbacks
most tests are for single attribute
In many cases, data distribution may not be known
91.Outlier Discovery: Distance-Based Approach
Introduced to counter the main limitations imposed by statistical methods
We need multi-dimensional analysis without knowing data distribution.
Distance-based outlier: A DB(p, D)-outlier is an object O in a dataset T such that at least a fraction p of the objects in T lies at a distance greater than D from O
Algorithms for mining distance-based outliers
Index-based algorithm
Nested-loop algorithm
Cell-based algorithm
Introduced to counter the main limitations imposed by statistical methods
We need multi-dimensional analysis without knowing data distribution.
Distance-based outlier: A DB(p, D)-outlier is an object O in a dataset T such that at least a fraction p of the objects in T lies at a distance greater than D from O
Algorithms for mining distance-based outliers
Index-based algorithm
Nested-loop algorithm
Cell-based algorithm
92.Outlier Discovery: Deviation-Based Approach
Identifies outliers by examining the main characteristics of objects in a group
Objects that “deviate” from this description are considered outliers
sequential exception technique
simulates the way in which humans can distinguish unusual objects from among a series of supposedly like objects
OLAP data cube technique
uses data cubes to identify regions of anomalies in large multidimensional data
Identifies outliers by examining the main characteristics of objects in a group
Objects that “deviate” from this description are considered outliers
sequential exception technique
simulates the way in which humans can distinguish unusual objects from among a series of supposedly like objects
OLAP data cube technique
uses data cubes to identify regions of anomalies in large multidimensional data
93.Cluster Analysis
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
What is Cluster Analysis?
Types of Data in Cluster Analysis
A Categorization of Major Clustering Methods
Partitioning Methods
Hierarchical Methods
Density-Based Methods
Grid-Based Methods
Model-Based Clustering Methods
Outlier Analysis
Summary
94.Problems and Challenges
Considerable progress has been made in scalable clustering methods
Partitioning: k-means, k-medoids, CLARANS
Hierarchical: BIRCH, CURE
Density-based: DBSCAN, CLIQUE, OPTICS
Grid-based: STING, WaveCluster
Model-based: Autoclass, Denclue, Cobweb
Current clustering techniques do not address all the requirements adequately
Constraint-based clustering analysis: Constraints exist in data space (bridges and highways) or in user queries
Considerable progress has been made in scalable clustering methods
Partitioning: k-means, k-medoids, CLARANS
Hierarchical: BIRCH, CURE
Density-based: DBSCAN, CLIQUE, OPTICS
Grid-based: STING, WaveCluster
Model-based: Autoclass, Denclue, Cobweb
Current clustering techniques do not address all the requirements adequately
Constraint-based clustering analysis: Constraints exist in data space (bridges and highways) or in user queries
95.Constraint-Based Clustering Analysis
Clustering analysis: less parameters but more user-desired constraints, e.g., an ATM allocation problem
Clustering analysis: less parameters but more user-desired constraints, e.g., an ATM allocation problem
96.Summary
Cluster analysis groups objects based on their similarity and has wide applications
Measure of similarity can be computed for various types of data
Clustering algorithms can be categorized into partitioning methods, hierarchical methods, density-based methods, grid-based methods, and model-based methods
Outlier detection and analysis are very useful for fraud detection, etc. and can be performed by statistical, distance-based or deviation-based approaches
There are still lots of research issues on cluster analysis, such as constraint-based clustering
Cluster analysis groups objects based on their similarity and has wide applications
Measure of similarity can be computed for various types of data
Clustering algorithms can be categorized into partitioning methods, hierarchical methods, density-based methods, grid-based methods, and model-based methods
Outlier detection and analysis are very useful for fraud detection, etc. and can be performed by statistical, distance-based or deviation-based approaches
There are still lots of research issues on cluster analysis, such as constraint-based clustering
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