DATA MINING WITH
CLUSTERING AND
Overview
• Definition of Clustering
• Existing clustering methods
• Clustering examples
• Classification
Definition
• Clustering can be considered the most important
unsupervised learning
technique; so, as every
other problem of this kind, it deals with finding a
structure
in a collection of unlabeled data.
• Clustering is “the process of organizing objects into
groups whose members are similar in some way”.
• A
cluster
is therefore a collection of objects which
are “similar” between them and are “dissimilar” to
the objects belonging to other clusters.
Why clustering?
A few good reasons ...
• Simplifications
• Pattern detection
Where to use clustering?
• Data mining
• Information retrieval
• text mining
• Web analysis
• marketing
Which method should I
use?
• Type of attributes in data
• Scalability to larger dataset
• Ability to work with irregular data
• Time cost
• complexity
Major Existing clustering
methods
• Distance-based
• Hierarchical
Measuring Similarity
• Dissimilarity/Similarity metric: Similarity is expressed
in terms of a distance function, which is typically
metric:
d
(
i, j
)
• There is a separate “quality” function that measures
the “goodness” of a cluster.
• The definitions of distance functions are usually very
different for interval-scaled, boolean, categorical,
ordinal and ratio variables.
• Weights should be associated with different variables
based on applications and data semantics.
• It is hard to define “similar enough” or “good enough”
– the answer is typically highly subjective.
Distance based method
Hierarchical clustering
Agglomerative (bottom up)
1. start with 1 point (singleton)
2. recursively add two or more appropriate
clusters
3. Stop when k number of clusters is
achieved.
Divisive (top down)
1. Start with a big cluster 2. Recursively divide into
smaller clusters
general steps of hierarchical
clustering
Given a set of N items to be clustered, and an N*N distance (or similarity) matrix, the basic process of hierarchical clustering (defined by S.C. Johnson in 1967) is this:
• Start by assigning each item to a cluster, so that if you have N items, you now have N clusters, each containing just one item. Let the distances (similarities) between the clusters the same as the distances (similarities) between the items they contain.
• Find the closest (most similar) pair of clusters and merge them into a single cluster, so that now you have one
cluster less.
• Compute distances (similarities) between the new cluster and each of the old clusters.
• Repeat steps 2 and 3 until all items are clustered into K number of clusters
Exclusive vs. non
exclusive clustering
• In the first case data are grouped in an
exclusive way, so that if a certain
datum belongs to a definite cluster
then it could not be included in
another cluster. A simple example of
that is shown in the figure below,
where the separation of points is
achieved by a straight line on a
bi-dimensional plane.
• On the contrary the second type, the
overlapping clustering, uses fuzzy sets
to cluster data, so that each point may
belong to two or more clusters with
Partitioning clustering
1.
Divide data into proper subset
2.
recursively go through each subset
and relocate points between
clusters (opposite to visit-once
approach in Hierarchical approach)
Probabilistic clustering
1. Data are picked from mixture of
probability distribution.
2. Use the mean, variance of each
distribution as parameters for
cluster
Single-Linkage
Clustering(hierarchical)
• The N*N proximity matrix is D = [d(i,j)]
• The clusterings are assigned sequence
numbers 0,1,..., (n-1)
• L(k) is the level of the kth clustering
• A cluster with sequence number m is
denoted (m)
• The proximity between clusters (r) and
(s) is denoted d [(r),(s)]
The algorithm is composed of
the following steps:
•
Begin with the disjoint clustering having
level L(0) = 0 and sequence number m = 0.
•
Find the least dissimilar pair of clusters in
the current clustering, say pair (r), (s),
according to
d[(r),(s)] = min d[(i),(j)]
The algorithm is composed of the
following steps:(cont.)
•
Increment the sequence number : m = m +1. Merge
clusters (r) and (s) into a single cluster to form the
next clustering m. Set the level of this clustering to
L(m) = d[(r),(s)]
•
Update the proximity matrix, D, by deleting the rows
and columns corresponding to clusters (r) and (s) and
adding a row and column corresponding to the newly
formed cluster. The proximity between the new
cluster, denoted (r,s) and old cluster (k) is defined in
this way:
d[(k), (r,s)] = min d[(k),(r)], d[(k),(s)]
Hierarchical clustering example
• Let’s now see a simple example: a hierarchical
clustering of distances in kilometers between some
Italian cities. The method used is single-linkage.
• The nearest pair of cities is MI and TO, at distance 138. These
are merged into a single cluster called "MI/TO". The level of
the new cluster is L(MI/TO) = 138 and the new sequence
number is m = 1.
Then we compute the distance from this new compound object
to all other objects.
In single link clustering the rule is that
the distance from the compound object to another object is
equal to the shortest distance from any member of the
• min d(i,j) = d(NA,RM) = 219 => merge NA and RM into a
new cluster called NA/RM
• min d(i,j) = d(BA,NA/RM) = 255 => merge BA and NA/RM
into a new cluster called BA/NA/RM
• min d(i,j) = d(BA/NA/RM,FI) = 268 => merge BA/NA/RM and
FI into a new cluster called BA/FI/NA/RM
• Finally, we merge the last two clusters at level 295.
K-mean algorithm
1. It accepts the
number of clusters
to group
data into, and the
dataset
to cluster as input
values.
2. It then creates the first
K initial clusters
(K=
number of clusters needed) from the dataset by
choosing K rows of data randomly from the
dataset.
For Example
, if there are 10,000 rows
of data in the dataset and 3 clusters need to be
formed, then the first
K=3 initial clusters
will
be created by selecting 3 records randomly
3. The K-Means algorithm calculates the Arithmetic Mean of each cluster formed in the dataset. The
Arithmetic Mean of a cluster is the mean of all the
individual records in the cluster. In each of the first K initial clusters, their is only one record. The Arithmetic Mean of a cluster with one record is the set of values that make up that record. For Example if the dataset we are discussing is a set of Height, Weight and Age measurements for
students in a University, where a record P in the dataset S
is represented by a Height, Weight and Age
measurement, then P = {Age, Height, Weight). Then
a record containing the measurements of a student John, would be represented as John = {20, 170, 80} where
John's Age = 20 years, Height = 1.70 metres and Weight = 80 Pounds. Since there is only one record in each
4. Next, K-Means assigns each record in the dataset to only one of the initial clusters. Each record is assigned to the nearest cluster (the cluster which it is most similar to) using a measure of distance or
similarity like the Euclidean Distance Measure or Manhattan/City-Block Distance Measure.
5. K-Means re-assigns each record in the dataset to the most
similar cluster and re-calculates the arithmetic mean of all the clusters in the dataset. The arithmetic mean of a cluster is the arithmetic mean of all the records in that cluster. For Example, if a cluster contains two records where the record of the set of measurements for John = {20, 170, 80} and Henry = {30, 160, 120}, then the arithmetic mean Pmean
is represented as Pmean= {Agemean, Heightmean, Weightmean).
6. K-Means re-assigns each record in the dataset to only one of the new clusters formed. A record or data point is assigned to the nearest cluster (the cluster which it is most similar to) using a measure of distance or similarity
7. The preceding steps are repeated until stable clusters are formed and the K-Means clustering procedure is completed. Stable clusters are formed when new iterations or repetitions of the K-Means clustering algorithm does not create new
clusters as the cluster center or Arithmetic Mean of each cluster formed is the same as the old cluster center. There are different techniques for determining when a stable
Classification
• Classification Problem Overview
• Classification Techniques
classification problem and introduce some of
classification problem and introduce some of
the basic algorithms
Classification Examples
• Teachers classify students’ grades
as A, B, C, D, or F.
• Identify mushrooms as poisonous
or edible.
• Predict when a river will flood.
• Identify individuals with credit risks.
• Speech recognition
Classification Ex: Grading
• If x >= 90 then grade
=A.
• If 80<=x<90 then
grade =B.
• If 70<=x<80 then
grade =C.
Classification Techniques
• Approach:
1.
Create specific model by
evaluating training data (or using
domain experts’ knowledge).
2.
Apply model developed to new
data.
• Classes must be predefined
Defining Classes
Partitioning
Based
Classification Using
Regression
•
Division:
Use regression function
to divide area into regions.
•
Prediction
: Use regression
function to predict a class
Height Example Data
Name
Gender Height Output1 Output2
Classification Using
Distance
• Place items in class to which they are
“closest”.
• Must determine distance between an
item and a class.
• Classes represented by
–
Centroid:
Central value.
–
Medoid:
Representative point.
– Individual points
K Nearest Neighbor
(KNN):
• Training set includes classes.
• Examine K items near item to be
classified.
• New item placed in class with the
most number of close items.
• O(q) for each tuple to be classified.
(Here q is the size of the training
Classification Using
Decision Trees
•
Partitioning based:
Divide search
space into rectangular regions.
• Tuple placed into class based on the
region within which it falls.
• DT approaches differ in how the tree is
built:
DT Induction
Decision Tree
Given:
– D = {t
1, …, t
n} where t
i=<t
i1, …, t
ih>
– Database schema contains {A
1, A
2, …, A
h}
– Classes C={C
1, …., C
m}
Decision or Classification Tree
is a tree
associated with D such that
– Each internal node is labeled with attribute, A
i– Each arc is labeled with predicate which can
be applied to attribute at parent
Comparing DTs
Balanced
ID3
• Creates tree using information theory concepts and
tries to reduce expected number of comparison..
Conclusion
• very useful in data mining
• applicable for both text and
graphical based data
• Help simplify data complexity
• classification
Reference
• Dr. M.H. Dunham -
http://engr.smu.edu/~mhd/dmbook/part2.ppt. • Dr. Lee, Sin-Min – San Jose State University • Mu-Yu Lu, SJSU
