“A Comparative Study between Clustering Algorithms”

Pattern Discovery for Categorical Cross-Cultural Data in the Market Research

DomainSeptember, 2015

Supervisor : Reviewer: - Industry Partner:

Professor: Plamen Angelov Professor: Nigel Davies Bonamy Finch

Author: Ahmed Hamada

INDUSTRY PARTNER

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THE CHALLENGE

Cross-cultural attitudinal segmentation studies using rating scales are

seriously a challengeable tasks within the market research domain as there are

a lot of shared views with fuzzy boundaries in these studies, unlike clustering

on demographics. The dilemma of having meaningful clusters that can

realistically reflect the respondents segments with good geometrical cluster

properties is also a demanding subject in the market research domain

GAP ANALYSIS

• 76% used K-means as a partitioning method for their segmentation

• 93% of the segmentation studies Euclidean distance.

• More 60% of the examined market research studies didn’t include an

evaluation criteria for the developed clusters

In a multi variate survey study, studying 243 market segmentation publications in the tourism domain (Dolnicar, 2003)

K-MEANS PROBLEMS

Data Dimensionality

• Distances between points become relatively uniform, therefore the concept of the nearest neighbour of a point becomes meaningless

Dissimilarity Measure

• it isn't just about distances, but about computing the mean. But there is no reasonable mean on categorical data

Non-Convex Shaped Clusters

• In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object

Local Minima

• differentiating the objective function w.r.t. to the centroids, to find a local minimum. More paths and more initiation points can result in a global minima

EXPERIMENTS

PARTITIONING METHODS HIERARCHICAL METHODS

K-means K-modes ROCKKernel K-means

K-m

eans

on

raw

dat

a

K-m

eans

on

stan

dard

ized

row

s

MCA

on

raw

dat

a +

K-m

eans

Kern

el K

-mea

ns o

n ra

w d

ata

Kern

el K

-mea

ns o

n st

anda

rdize

d ro

ws

K-m

odes

on

raw

dat

a

ROCK

on

raw

dat

a

Euclidean Distance

Matching Measure

Arbitrary shaped clusters

Non-convex shaped clusters

21

experiments

7 X 3

DETERMINING THE NUMBER OF CLUSTERS

______________________________________________Gap Statistic for 10 clusters

_____________________________________________Within Sum of Squares for 10 clusters

? 5, 6 & 7 Clusters Models

7-CLUSTER MODEL GEOMETRICAL COMPARISON

0

100,000

200,000

300,000

117,604 87,2321,644

283,904224,892

0%20%40%60%80%

21% 18%

59%

0% 0%

Within cluster sum of squares Cluster closeness index

INTERNAL MEASURES COMPARISON

K-means

K-means o

d standard

ised ro

ws

MCA + K-means

Kernel K

-means

Kernel K

-means o

n standard

ised ro

ws0

0.1

0.2

0.3

0.4

0.1020.05

0.09 0.08 0.07

0.125

0.05

0.1

00.05

0.109

0.05

0.1

0.08 0.05

5 clusters 6 clusters 7 clusters

K-means

K-means o

d standard

ised ro

ws

MCA + K-means

Kernel K

-means

Kernel K

-means o

n standard

ised ro

ws

-0.1

0

0.1

0.2

0.050.03

-0.02 -0.01 -0.01

0.05

0.03

-0.02

0.01 0.01

0.04

0.03

-0.03

-0.010.02

5 clusters 6 clusters 7 clusters

Dunn index Silhouette measure

INDUSTRY EVALUATIONAlgorithm K-means on standardised rows Kernel K-means on standardised

rowsNo. Clusters 5 6 7 5 6 7Response Bias Freedom

1 79% 86% 79% 70% 59% 58%2 81% 77% 67% 93% 61% 71%3 90% 61% 79% 77% 64% 75%4 72% 81% 71% 74% 79% 83%5 80% 70% 75% 79% 67% 67%6 71% 71% 61% 79%7 71% 79%

Reportability 1 71% 62% 67% 62% 76% 71%2 38% 19% 19% 90% 24% 19%3 19% 29% 81% 48% 81% 71%4 43% 52% 29% 71% 33% 62%5 62% 52% 43% 10% 33% 43%6 71% 57% 33% 43%7 62% 52%

5-CLUSTERS MODEL SCATTER PLOT MATRIX FOR THE FIRST 4 VARIABLES

K-means on standardised rows Kernel K-means on standardised rows

CONCLUSION

1. The results of this research revealed that the standardisation of the respondents developed better segments from the pragmatic point of view.

2. From the overall evaluation analysis, the results of the 5 clusters model using the K-means and the kernel K-means on standardised rows revealed more meaningful segments than the other methods.

3. The results illustrated that the ROCK algorithm and the application of MCA then K-means was not suitable for multiscale categorical data and resulted in meaningless clusters.

FURTHER RESEARCH

• Evaluate the stability of the classification accuracy using different algorithms

• Study other clustering methods available in the literature

• Evaluate the same algorithms on various cross-cultural multiscale data sets and test the hypothesis whether the multi-scaled data (i.e. Likert scale) develop better clusters from the geometrical point of view.

• Evaluate the clustering algorithms on a different type of response scales rather than using the multi point biased response scales

Thank You