Descriptive Data Mining

Clustering

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Business Analytics

Lecture # 08

TOPICS to be COVERED

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CLUSTER ANALYSIS

• It Used to classify objects (cases) into homogeneous groups called clusters.
• Objects in each cluster tend to be similar and dissimilar to objects in the other clusters

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• The goal of clustering is to segment observations into similar groups based on the observed variables. Clustering can be employed during the data-preparation step to identify variables or observations that can be aggregated or removed from consideration.

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CLUSTER ANALYSIS continued.…

• Cluster analysis is commonly used in marketing to divide consumers into different homogeneous groups, a process known as market segmentation.

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An Ideal Clustering Situation

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Example

• we consider the use of cluster analysis to assist a company called Know Thy Customer (KTC), a financial advising company that provides personalized financial advice to its clients

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• Age = age of the customer in whole years
• Female = 1 if female, 0 if not
• Income = annual income in dollars
• Married = 1 if married, 0 if not
• Children = number of children
• Loan = 1 if customer has a car loan, 0 if not
• Mortgage = 1 if customer has a mortgage, 0 if not

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Measuring Similarity Between Observations

• we need explicit measurements of similarity or, conversely, dissimilarity.
• Some metrics track similarity between observations, and a clustering method using such a metric would seek to maximize the similarity between observations.
• Other metrics measure dissimilarity, or distance, between observations, and a clustering method using one of these metrics would seek to minimize the distance between observations in a cluster.

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Euclidean Distance

• Euclidean distance is the most common method to measure dissimilarity between observations.
• Let observations
• u =(u1,u2 ,…,uq) and v = (v1, v2 ,…, vq) each comprise measurements of q variables. The Euclidean distance between observations u and v is

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Matching Coefficient

• When clustering observations solely on the basis of categorical variables encoded as 0–1 (or dummy variables), a better measure of similarity between two observations can be achieved by counting the number of variables with matching values.
• The simplest overlap measure is called the matching coefficient and is computed as follows:

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Weakness of SMC

• One weakness of the matching coefficient is that if two observations both have a 0 entry for a categorical variable, this is counted as a sign of similarity between the two observations.

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• However, matching 0 entries do not necessarily imply similarity. For instance, if the categorical variable is Own A Minivan, then a 0 entry in two different observations does not mean that these two people own the same type of car; it means only that neither owns a minivan.

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Jaccard’s Coefficient

• To avoid this similarity due to the absence of a feature,
• a similarity measure called Jaccard’s coefficient does not count matching zero entries and is computed as follows:

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Types of clustering

• Hierarchical clustering
• k-mean clustering

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Hierarchical Clustering

• Hierarchical clustering consider bottom-up approach that starts with each observation belonging to its own cluster and then sequentially merges the most similar clusters to create a series of nested clusters.

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Hierarchical Clustering

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b

d

c

e

a

a b

d e

c d e

a b c d e

Initialization:

Each object is a cluster

Iteration:

Merge two clusters which are

most similar to each other;

Until all objects are merged

into a single cluster

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Thank You !

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