Data Mining & Association Analysis – Answers

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1. Answer the following with proper explanation

a) Impact of Normalization in Data Preprocessing

Normalization rescales data into a common range (e.g., 0–1 or −1 to 1).

Impact:

• Prevents attributes with large values from dominating
• Improves performance of distance-based algorithms (k-means, k-NN)
• Speeds up convergence of machine learning models
• Ensures fair comparison among features

Example:
Income (₹10,000–₹1,000,000) and Age (1–100).
Without normalization, income dominates distance calculations.

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b) Does FP-Growth Maintain Downward Closure Property?

Yes, FP-Growth maintains the downward closure property implicitly.

Explanation:

• Downward closure: If an itemset is frequent, all its subsets must be frequent
• FP-Growth avoids candidate generation
• It uses conditional FP-trees to ensure only frequent subsets are explored

Search Space Reduction:

• No candidate generation
• Compact FP-tree structure
• Recursive mining on conditional databases

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c) What is a Null Transaction? How Does Cosine Similarity Reduce Its Impact?

A null transaction is a transaction where none of the items under comparison appear.

Problem:

• Null transactions increase similarity artificially in some measures

Cosine Similarity: [ \text{Cosine}(A,B) = \frac{A \cdot B}{|A||B|} ]

Advantages:

• Ignores transactions where both items are absent
• Focuses only on co-occurrence
• Reduces noise from null transactions

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2. Chi-Square Test and Association Rule

Given Contingency Table

Gender	Yes	No	Total
Male	90	170	260
Female	250	50	300
Total	340	220	560

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a) Chi-Square Test

Null Hypothesis (H₀): Gender and bird lover are independent
Alternative Hypothesis (H₁): Gender and bird lover are correlated

Expected Frequency Formula: [ E = \frac{(Row\ Total \times Column\ Total)}{Grand\ Total} ]

Expected values:

• Male–Yes = 157.86
• Male–No = 102.14
• Female–Yes = 182.14
• Female–No = 117.86

[ \chi^2 = \sum \frac{(O - E)^2}{E} ]

[ \chi^2 = 138.61 ]

Degrees of Freedom: (2−1)(2−1) = 1
Critical Value (α = 0.05): 3.84

Decision:
138.61 > 3.84 ⇒ Reject H₀

Conclusion:
Gender and bird lover are correlated.

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b) Association Rule: Female → Yes

• Support = 250 / 560 = 44.64%
• Confidence = 250 / 300 = 83.33%

Thresholds:

• Minimum Support = 50%
• Minimum Confidence = 60%

Conclusion:
Rule is not strong because it fails minimum support condition.

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3. FP-Tree Construction (Min Support = 50%)

Transaction Dataset

T1: P Q R S T
T2: P S T X
T3: T
T4: X Y Z
T5: P S T

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Step 1: Item Frequency Count

Item	Count
T	4
P	3
S	3
X	2
Q	1
R	1
Y	1
Z	1

Minimum support count = 50% of 5 = 3

Frequent items: T, P, S

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Step 2: Remove Infrequent Items & Sort

T1: P S T
T2: P S T
T3: T
T4: — (removed)
T5: P S T

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Step 3: FP-Tree Construction

Root └── T:4 └── P:3 └── S:3

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4. Mining Frequent Patterns (Min Support = 50%)

Frequent Itemsets

Single Items:

• {T}, {P}, {S}

Two-Item Sets:

• {T,P}, {T,S}, {P,S}

Three-Item Set:

• {T,P,S}

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Final Frequent Patterns

{T}
{P}
{S}
{T,P}
{T,S}
{P,S}
{T,P,S}

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