A MixedInteger Programming Approach to Customer Segmentation Problem

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A Mixed-Integer Programming Approach to
Customer Segmentation Problem

• Burcu Saglam, F.Sibel Salman, Metin Türkay
• bsaglam,ssalman,mturkay_at_ku.edu.tr
• Dept. of Industrial Engineering
• Serpil Sayin
• ssayin_at_ku.edu.tr
• Dept. of Business Administration
• June 20, 2004
• ESI 2004, METU, Ankara

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Koç University, Istanbul
www.ku.edu.tr www.eng.ku.edu.tr
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Outline

• Introduction
• Clustering Problem
• Clustering Approaches
• Motivation of the Study
• Proposed Model
• Illustrative Example
• Evaluation in Real World Scenario
• Conclusions and Future Work

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Introduction

• This study presents one new mathematical
  programming-based segmentation model that is
  applied to a digital platform companys customer
  database

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Digiturk

• Private digital platform
• Eager to find out opportunities in customer
  relationship management, such as onetoone
  marketing

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Digiturk

• Pay-Per-View Services
• Vision halls
• Football matches
• Erotic channels
• Interactive Events
• Banking
• TV Games, etc...

• Products
• Standard package
• Sports package
• Cinema package
• Super package
• Mega package

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Why Data Mining, Segmentation?

• Analysis of large data collections, huge
  databases
• Understanding needs, desires, and expectations of
  the customers
• Grouping the ongoing and potential customers
• Hidden patterns and knowledge within the data
• Segmentation is applied when there is a need to
  partition the instances into natural groups

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Clustering Analysis

• A data mining technique developed for the purpose
  of identifying groups of entities that are
  similar to each other with respect to certain
  characteristics
• Dividing heterogeneous sets of data into smaller
  and homogeneous ones
• Evaluating the result and performance of a
  supervised learning model
• Analyzing the set of input attributes
• Determining outliers

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Clustering Problem

• Given a data set with n data items in
  m-dimensions
• Partition the data into k clusters
• In an optimization setting, an objective function
  can be defined such as the minimization of the
  sum of 1-norm distances between each data point
  and the center of the cluster which it belongs to
  (Bradley et al., 1997)

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Main Considerations

• The term similarity
• Exclusive, overlapping, probabilistic or fuzzy
  clusters
• Iterative or non-iterative
• Hierarchical or non-hierarchical
• Distance-based, probability-based approaches,
  graph theoretic methods, continuous-discrete
  optimization, ...

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Analytical Clustering Methods

• Hierarchical - number of clusters is not assumed
  to be known a priori
• Divisive and agglomerative methods
• Once an assigment is made, it is irrevocable
• Well known BIRCH algorithm

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Analytical Clustering Methods

• Nonhierarchical - number of clusters is known a
  priori
• Initially data is divided into k partitions where
  each partition represents a cluster
• Two main decisions
• Selection of the initial cluster centroids
• Assignment of the instances to clusters
• Sensitive to initial partitions
• Too many local minima
• K-Means, K-Medoids, CLARANS, etc. ...

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Classical K-Means

• Iterative distance-based
• Works in numeric domains
• Partitions instances into disjoint clusters
• Two steps
• Assignment
• Updating the cluster centers
• Works well when the candidate clusters are
  approximately equal size

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Shortcomings of K-Means

• Solution is local minima
• Convergence to a local optima is proved
• Sensitivity to initially selected cluster centers
• Worst case time complexity is stated to be
  exponential
• To find a global minima, the algorithm has to be
  repeated several times
• Impossible to interpret which attributes are
  significant

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Motivation of the Study

• Considering the limitations of existing
  clustering approaches and algorithms, an exact
  non-hierarchical distance-based clustering
  algorithm is proposed

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Proposed Approach

• Given a data set of n data items in m-dimensions
• Aim is to find the optimum partitioning of the
  data set into k exclusive clusters
• Objective function Minimization of the maximum
  diameter of the generated clusters
• Number of clusters is known a priori

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MIP-Max Model
Minimize
s.t.
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MIP-Max

• O(kn) variables and O(kn2) constraints
• Non-hierarchical
• Not iterative
• No need for an initial solution
• Global optimum

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Illustrative Example
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Comparisons with the Results of the K-Means
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Comparisons with the Results of the K-Means
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Evaluation in Real World Scenario

• Data set includes demographic and transactional
  information
• Each row represents a unique customer
• 18 real-valued and categorical attributes

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Experiments with MIP-Max Model
k 2
CPU times are reported for a computer with a
Pentium IV processor at 2.56 GHz and 1GB memory.
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Comparison of MIP-Max with K-Means and
Interpretations

• The result of the approach is compared with the 3
  cluster solution and 100 data items
• MIP-Max model grouped 39 instances in the first
  cluster, 34 instances in the second cluster and
  27 instances in the third cluster
• K-Means generated clusters 1, 2 and 3
  respectively with 59, 22, and 19 instances
• Interpretations based on predictiveness score

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Predictiveness Score

• Given class C and attribute A with values v1,
  v2, v3vn, an attribute-value predictiveness
  score for vi is defined as the probability an
  instance resides in C given the instance has
  value vi for A.
• Between-class measure
• Actually for categorical attibutes, most of our
  attributes are in nominal form
• An attribute has a distinguishing power in one
  cluster if its predictiveness scores are higher
  than 75

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Predictiveness Score
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Conclusions and Future work

• The sensitivity of the K-Means to initial
  solution is analyzed
• The interpretations of MIP-Max model is more
  meaningful than K-Means, sports package
  subscriber grouped in one group, etc. ...
• MIP-Max is significantly better than K-Means in
  terms of quality and stability of the solutions
• Future Work
• Improvement of run times
• Determination of number of clusters

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Thanks ? Welcome to Any Questions ?
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Clustering Approaches

• Hierarchical and non-hierarchical clustering
  methods
• Classical K-Means
• Cobweb
• Clarans
• Birch
• Advantages and disadvantages
• Motivation of the study

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COBWEB

• Conceptual clustering technique
• Forms a hierarchy to capture knowledge
• Deals only with categorical (nominal) data
• Cluster quality namely Category Utility
• Expensive to compute this measurement
• Instance ordering have impact on the resulting
  clustering.

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CLARANS

• A type of K-Medoids algorithm, differs by its
  randomized partial search strategy,
• Clustering problem is represented by graph,
• Limitations
• Convergence to a definite local minimum,
• Efficiency considerations.

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BIRCH

• Stemmed from the fact that available memory is
  limited,
• One iteration ends with a successful clustering,
• Applicable to large data sets,
• But, sensitive to parameters settings.

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Experimental Results of MIP-Max
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Comparisons with the Results of the K-Means