Assignment 3: 100 Points - Students Are Required To Submit

Assignment 3 100 Pointstudentsare Required To Submit The Assignmen

Consider the following assignment tasks:

1. Analyze a data set from Table 5 (Chapter 5). Calculate the support for itemsets {e}, {b, d}, and {b, d, e} by treating each transaction ID as a market basket. Use these support values to compute the confidence for the association rules {b, d} → {e} and {e} → {b, d}. Determine whether confidence is a symmetric measure.

2. Examine transactions from Table 6.15 with an item taxonomy from Figure 6 (Chapter 6). Identify the main challenges of mining association rules with item taxonomy. Then, consider two different approaches:

• First approach: Replace each transaction with an extended transaction containing all items and their ancestors; for example, {Chips, Cookies} becomes {Chips, Cookies, Snack Food, Food}. Use this to derive all frequent itemsets up to size 4 with support ≥ 70%.
• Second approach: Generate frequent itemsets one level at a time, starting with items at the highest hierarchy level, and then use higher-level frequent itemsets to generate candidates at lower levels. Derive all frequent itemsets up to size 4 with support ≥ 70%.

3. For a dataset of 220 vectors each with 32 components (each component 4 bytes), where 216 prototype vectors are used for vector quantization, calculate:

• The total storage size before compression.
• The total storage size after compression.
• The compression ratio.

Sample Paper For Above instruction

Introduction

Data mining techniques, particularly association rule mining, play a crucial role in uncovering meaningful patterns within large datasets. These methods enable understanding of the relationships among items in transaction datasets and help optimize decision-making processes in retail, marketing, and other sectors. This paper addresses three key tasks: calculating support and confidence of specific itemsets, exploring hierarchical item taxonomy challenges, and analyzing data storage implications of vector quantization, thereby providing comprehensive insights into advanced data mining practices.

Support and Confidence Calculation in Market Basket Data

The initial task involves analyzing a dataset from Table 5, which, although not explicitly provided here, typically contains transactional data representing market baskets. Computing support involves determining the proportion of transactions that contain specific itemsets. For instance, support for {e} reflects the fraction of transactions including item e, support for {b, d} measures the presence of both items b and d in transactions, and support for {b, d, e} accounts for transactions containing all three items.

Assuming total transactions are N, support calculations follow:

• Support({e}) = (Number of transactions with e) / N
• Support({b, d}) = (Number of transactions with both b and d) / N
• Support({b, d, e}) = (Number of transactions with b, d, and e) / N

For example, if 30 transactions include e out of 100 total transactions, support({e}) = 0.3. Similarly, support for {b, d} might be 0.4, and support for {b, d, e} could be 0.2 based on transaction counts.

Confidence measures the likelihood of item e being purchased given items b and d, and vice versa. Specifically:

• Confidence({b, d} → {e}) = Support({b, d, e}) / Support({b, d})
• Confidence({e} → {b, d}) = Support({b, d, e}) / Support({e})

This analysis helps identify strong association rules, essential for targeted marketing and cross-selling strategies. Notably, confidence is not symmetric because Confidence({b, d} → {e}) ≠ Confidence({e} → {b, d}), highlighting the directional nature of association rules.

Hierarchical Item Taxonomy Challenges in Association Rule Mining

The second task considers the complexities introduced by hierarchical item taxonomies in association rule mining. Incorporating item taxonomy enables capturing more generalized relationships but introduces challenges such as:

• Data Sparsity: More generalized categories may dilute significant patterns.
• Computational Complexity: Hierarchical structures increase the number of candidate itemsets, requiring advanced pruning techniques.
• Support Calculation: Extended transactions necessitate careful inclusion of ancestor items, complicating support counting.

To address these challenges, approaches are developed that either flatten the hierarchy by extending transactions or generate frequent itemsets level-by-level. The initial approach involves replacing each transaction with an extended version including ancestor items, thus enabling frequent itemsets derivation up to size 4 with support thresholds, such as ≥70%. For example, a transaction containing {Chips, Cookies} is extended to {Chips, Cookies, Snack Food, Food}, enabling more comprehensive pattern detection.

Hierarchical Approach: Level-by-Level Generation

Alternatively, hierarchical frequent itemsets are generated sequentially:

• First, generate frequent itemsets consisting of top-level categories, such as “Food” or “Snack Food.”
• Next, use these to generate candidate itemsets at lower levels, like specific snack types, only if their higher-level itemsets are frequent, ensuring computational efficiency and reducing search space.

This bottom-up approach allows capturing hierarchical dependencies effectively, aiding in building a structured understanding of item relationships. Deriving frequent itemsets up to size 4 with support ≥70% enables identifying core patterns that are statistically significant.

Data Storage and Compression in Vector Quantization

The third task explores data size considerations involving vector quantization. For 220 data vectors, each with 32 components of 4 bytes, the raw data size is calculated as:

Raw data size = Total vectors × Components per vector × Bytes per component

= 220 × 32 × 4 bytes = 28,160 bytes.

Using vector quantization with 216 prototype vectors allows representing each data vector by an index pointing to one of these prototypes. The number of bits required per index is:

Bits per index = log2(216) ≈ 8 bits (since 2^8=256, which is sufficient for 216 prototypes).

Thus, after compression, each vector consumes 1 byte (8 bits), resulting in total storage:

Compressed data size = Number of vectors × bits per index / 8 = 220 × 1 byte = 220 bytes.

The compression ratio is calculated as:

Compression ratio = Original size / Compressed size = 28,160 / 220 ≈ 128.0

This indicates the storage size reduces significantly when applying vector quantization, facilitating efficient storage and transmission of large datasets.

Conclusion

This comprehensive review demonstrates the importance of support and confidence calculations in market basket analysis, elucidates the complexities introduced by hierarchical item taxonomies, and highlights the substantial benefits of vector quantization in data compression. Mastery of these techniques enhances data analysts' ability to extract meaningful insights and optimize storage solutions, thereby contributing to more efficient and effective data mining practices.

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