Download Data Mining: Tutorial 1

Intelligent Data Analysis and Probabilistic Inference
Data Mining Tutorial 3: Clustering and Associations Rules
1.
i.
ii.
Explain the operation of the k-means clustering algorithm using pseudo code.
Given the following eight points, and assuming initial cluster centroids given by A, B, C,
and that a Euclidean distance function is used for measuring distance between points, use
k-means to show only the three clusters and calculate their new centroids after the second
round of execution.
ID
A
B
C
D
E
F
G
H
X
2
2
8
5
7
6
1
4
Y
10
5
4
8
5
4
2
9
2.
i.
ii.
Explain the meaning of support and confidence in the context of association rule
discovery algorithms and explain how the a priori heuristic can be used to improve the
efficiency of such algorithms.
Given the transactions described below, find all rules between single items that have
support >= 60%. For each rule report both support and confidence.
1: (Beer)
2: (Cola, Beer)
3: (Cola, Beer)
4: (Nuts, Beer)
5: (Nuts, Cola, Beer)
6: (Nuts, Cola, Beer)
7: (Crisps, Nuts, Cola)
8: (Crisps, Nuts, Cola, Beer)
9: (Crisps, Nuts, Cola, Beer)
10:(Crisps, Nuts, Cola, Beer)
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16th Dec2003
3.
a. Explain how hierarchical clustering algorithms work, make sure your answer describes what is
meant by a linkage method and how it is used.
b. Explain the advantages and disadvantages of hierarchical clustering compared to K-means
clustering.
4.
The following table shows the distance matrix between five genes,
G1
G2
G3
G4
G5
i.
ii.
iii.
G1
0
9
3
6
11
G2
G3
G4
G5
0
7
5
10
0
9
2
0
8
0
Based on a complete linkage method show the distance matrix between the first formed
cluster and the other data points.
Draw a dendrogram showing the full hierarchical clustering tree for five points based on
complete linkage.
Draw a dendrogram showing the full hierarchicatree for the five points based on single
linkage.
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16th Dec2003
Data Mining Tutorial 3: Answers
1.
Clusters after 1st iteration
Cluster1: A (2,10), D (5,8), H (4,9)
Cluster2: B: B (2,5), G (1,2)
Cluster3: C (8,4), E (7,5), F (6,4)
Centroids after 1st iteration
Cluster1: centroid: (3.66, 9)
Cluster2: centroid: (1.5, 3.5)
Cluster3: centroid: (7, 4.33)
Clusters after 2nd iteration
(no change)
Cluster1: A (2,10), D (5,8), H (4,9)
Cluster2: B: B (2,5), G (1,2)
Cluster3: C (8,4), E (7,5), F (6,4)
Centroids after 2nd iteration
(no change)
Cluster1: centroid: (3.66, 9)
Cluster2: centroid: (1.5, 3.5)
Cluster3: centroid: (7, 4.33)
2.
Initial Supports
Beer: Support = 9/10
Cola: Support=8/10
Nuts: Support=7/10
Crisps: Support=4/10 (Drop Crisps)
Beer, Cola: Support=7/10
Beer, Nuts: Support=6/10
Cola, Nuts: Support=6/10
Beer->Cola (Support=70%, Confidence= 7/9=77%
Cola->Beer (Support=70%, Confidence= 7/8=87.5
Beer->Nuts (Support=60%, Confidence= 6/9=66%
Nuts->Beer (Support= 60%, Confidence= 6/7=85.7%
Cola->Nuts (Support=60%, Confidence= 6/8=75%
Nuts->Cola (Support=60%, Confidence= 6/7=85.7%
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16th Dec2003
4. The first cluster will be formed from G3 and G5 since they have the minimum distance.
G35
0
11
G1
G35
G1
G2
G4
10
9
9
6
Single Linkage
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G2
G4
0
5
0
0
Complete Linkage
16th Dec2003