Solution Manual for Data Mining and Machine Learning Fundamental Concepts and Algorithms 2nd Edition

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Contents

1

Contents

1

Data Mining and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.7

3

PART I

2

3

4

5

6

7

9

DATA ANALYSIS FOUNDATIONS

5

Numeric Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.7

7

Exercises

Categorical Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

3.7

16

Exercises

Graph Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

4.6

20

Exercises

Kernel Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

5.6

26

Exercises

High-dimensional Data . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

6.9

29

Exercises

Dimensionality Reduction . . . . . . . . . . . . . . . . . . . . . . . . .

39

7.6

39

PART II

8

Exercises

Exercises FREQUENT PATTERN MINING

45

Itemset Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

8.5

47

Exercises

Summarizing Itemsets . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

9.6

56

Exercises

1

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2

10

11

12

Contents

Sequence Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

10.5

63

Graph Pattern Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

11.5

75

14

15

16

17

84

12.4

84

19

20

21

22

Exercises CLUSTERING

89

Representative-based Clustering . . . . . . . . . . . . . . . . . . . . . .

91

13.5

91

Exercises

Hierarchical Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

14.4

99

Exercises

Density-based Clustering . . . . . . . . . . . . . . . . . . . . . . . . . .

106

15.5

106

Exercises

Spectral and Graph Clustering . . . . . . . . . . . . . . . . . . . . . . .

111

16.5

111

Exercises

Clustering Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

118

17.5

118

PART IV

18

Exercises

Pattern and Rule Assessment . . . . . . . . . . . . . . . . . . . . . . . .

PART III

13

Exercises

Exercises CLASSIFICATION

123

Probabilistic Classification . . . . . . . . . . . . . . . . . . . . . . . . .

125

18.5

125

Exercises

Decision Tree Classifier . . . . . . . . . . . . . . . . . . . . . . . . . . .

129

19.4

129

Exercises

Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . . . . . . .

137

20.4

137

Exercises

Support Vector Machines . . . . . . . . . . . . . . . . . . . . . . . . . .

141

21.7

141

Exercises

Classification Assessment . . . . . . . . . . . . . . . . . . . . . . . . . .

145

22.5

145

Exercises

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CHAPTER 1

Data Mining and Analysis

1.7 EXERCISES Q1. Show that the mean of the centered data matrix Z in Eq. (1.5) is 0.

Answer: Each centered point is given as: zi = xi − µ. Their mean is therefore: n

n

i=0

i=0

1X 1X zi = (xi − µ) n n n

=

1X 1 xi − · n · µ n n i=0

= µ−µ= 0 Q2. Prove that for the Lp -distance in Eq. (1.2), we have d δ∞ (x, y) = lim δp (x, y) = max |xi − yi | p→∞

for x, y ∈ Rd .

i=1

Answer: We have to show that lim

p→∞

d X i=1

|xi − yi |p

! p1

d = max |xi − yi | i=1

Assume that dimension a is the max, and let m = |xa − ya |. For simplicity, we assume that |xi − yi | < m for all i 6= a.

If we divide and multiply the left hand side with mp we get:

m

p

d X |xi − yi | p i=1

m

! p1



= m 1 +

X |xi − yi | p i6=a

m

1

p



3

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4

Data Mining and Analysis

p −yi | As p → ∞, each term |xi m → 0, since m > |xi − yi | for all i 6= a. The finite P |xi −yi | p converges to 0 as p → ∞, as does 1/p. summation i6=a m

Thus δ∞ (x, y) = m × 10 = m = |xa − ya | = maxdi=1 {|xi − yi |} Note that the same result is obtained even if we assume that dimensions other than a achieve the maximum value m. In the worst case, we have m = |xi − yi | for all d dimensions. In this case, the expression on LHS becomes lim m

p→∞

d X i=1

p

1

!1/p

= lim md 1/p = lim md 0 = m p→∞

p→∞

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