Open The Assignment 3 Ms Word File And Answer The Following

Open The Assignment 3 Ms Word File And Answerthe Following Questions

Open the assignment #3 MS word file and answer the following questions. If you complete it, please upload into the blackboard. 1. Draw the full decision tree for the parity function of four Boolean attributes, A, B, C, and D. Assignment #. Consider the training examples show in the table for binary classification problem. Assignment #) Compute the Gini index for the overall collection of training examples. 2) Compute the Gini index for the Customer ID attribute. 3) Compute the Gini index for the Gender attribute. 4) Compute the Gini index for the Car Type attribute using multiway split. 5) Compute the Gini index for the Shirt Size attribute using multiway split. 6) Which attribute is better, Gender, Car, Type, or Shirt Size? Assignment #3

Paper For Above instruction

Introduction

The assignment encompasses several critical tasks in the realm of data mining and machine learning, including constructing a decision tree for a parity function and calculating Gini indices for various attributes in a classification dataset. These exercises are fundamental in understanding decision tree algorithms, especially concepts like entropy, Gini impurity, and attribute selection strategies. This paper aims to systematically address each question, providing detailed explanations, calculations, and visualizations where appropriate.

Part 1: Decision Tree for the Parity Function of Four Boolean Attributes

The parity function of four Boolean attributes A, B, C, and D outputs 'true' if an odd number of attributes are true and 'false' otherwise. To construct the full decision tree, we examine all possible combinations of the attributes and their corresponding outputs. The total number of combinations is 2^4 = 16.

For the decision tree, the root node tests one attribute, say A. Depending on A's value, subsequent nodes test B, C, and D, following a systematic approach to account for every combination. Since the parity function flips value with each true attribute, the tree structure involves alternating outputs at each level, leading to a comprehensive tree with depth 4, covering all input combinations.

Constructing this decision tree involves recursive splitting: At each node, test an attribute, and branch to subtrees based on true or false. The leaves represent the output value of the parity function for that specific combination.

Part 2: Gini Index Calculations

The Gini index measures the impurity of a dataset, and lower values indicate purer splits. We analyze a given set of training examples, summarized in a table (not provided explicitly here), to compute several Gini indices:

Overall Gini Index

Calculate the Gini index for the entire dataset by determining the proportion of each class and applying the formula:

Gini(S) = 1 - Σ (p_i)^2, where p_i is the proportion of class i in the dataset.

This provides a baseline measure of impurity before any attribute-based splits.

Gini Index for Specific Attributes

• Customer ID Attribute: Typically unique for each record; thus, its Gini index will be 0, indicating pure segmentation if each customer ID is unique.
• Gender Attribute: Calculate the Gini index by partitioning the dataset into groups based on gender and computing the weighted sum of impurity within each group.
• Car Type Attribute: Using multiway split, partition the dataset by car types and compute the Gini index for each group, then aggregate.
• Shirt Size Attribute: Similarly, partition by shirt sizes using multiway split and compute the overall Gini index.

These calculations inform which attribute best reduces impurity and thus is most suitable for decision node splits.

Part 3: Attribute Selection

Compare the Gini indices obtained for Gender, Car Type, and Shirt Size attributes to determine which attribute most effectively separates the classes. The attribute with the lowest Gini index after partitioning is considered the best candidate for the decision node, as it provides the most homogeneous splits.

In practice, this step guides the decision tree construction by selecting the attribute that maximizes information gain or minimizes impurity, ultimately leading to a more accurate and efficient model.

Conclusion

This assignment integrates key concepts in decision tree learning and attribute selection. Constructing the full decision tree for the parity function illustrates the binary logic underlying Boolean functions, while the Gini index calculations demonstrate how to evaluate and compare attribute effectiveness in classification tasks. Understanding these foundational processes enhances the development of robust machine learning models for various data-driven applications.

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