Linearly Separable Data Analysis

Requirements Clarification & Assessment

Before diving into the solution, it is essential to clarify and assess the requirements of the problem at hand:

1. Understanding Linearly Separable Data:

   • Definition: Data is said to be linearly separable if there exists a hyperplane that can perfectly separate the data points of different classes without any overlap.
   • Implications: In such datasets, the classes can be perfectly divided by a straight line (in 2D), a plane (in 3D), or a hyperplane (in higher dimensions).

2. Logistic Regression Basics:

   • Purpose: Logistic regression is a binary classification algorithm that predicts the probability of a binary outcome based on one or more predictor variables.
   • Mechanism: It models the relationship using a logistic function, outputting probabilities between 0 and 1.

3. Objective:

   • To understand what happens when logistic regression is applied to perfectly linearly separable data.
   • To explore how this affects model convergence, coefficient estimates, and overall performance.

4. Constraints:

   • The dataset is assumed to be perfectly linearly separable with no noise or overlapping data points.
   • The focus is on logistic regression without any regularization initially.

5. Expectations:

   • Identify potential issues with logistic regression on such data.
   • Explore solutions to mitigate these issues, if any.