Logistic Regression vs K Nearest Neighbors in Machine Learning

Machine learning algorithms play a crucial role in training the data and decision-making processes. Logistic Regression and K Nearest Neighbors (KNN) are two popular algorithms in machine learning used for classification tasks. In this article, we’ll delve into the concepts of Logistic Regression and KNN and understand their functions and their differences.

What is Logistic Regression?

Logistic Regression is a statistical approach used in binary classification, forecasting the likelihood of a binary result depending on independent variables. Unlike linear regression, it models the connection between the independent variables and the log odds of the result utilizing the logistic function. This technique finds application in various domains like healthcare, finance, and advertising, aiding in tasks such as predicting customer attrition, disease onset, or spam detection in emails. Logistic Regression employs the sigmoid function to map the output of a linear equation to a probability score between 0 and 1, for classifying data into binary outcomes. The probability f(x) of the positive class is determined by [Tex]f(x)=\frac{1}{1+e^x}[/Tex]​, where x is a linear combination of input features and their weights.

What is K Nearest Neighbors (KNN)?

K-nearest neighbors (KNN) is a machine learning algorithm categorized as lazy learning, employed in both classification and regression tasks. It works by assigning a data point to the class most common among its k nearest neighbors in the feature space. KNN is simple to understand and implement, making it a popular choice for beginners and for tasks where interpretability is important. However, it can be computationally expensive, especially with large datasets, as it requires storing all training data and computing distances for each prediction.

Key Difference between Logistic Regression and K Nearest Neighbors (KNN)

Parameters	Logistic Regression	K Nearest Neighbors
Algorithm	Logistic function (sigmoid) is used.	Nearest neighbors are computed using distance metrics.
Working	Predicts the likelihood of an instance belonging to a particular category.	Classifies datapoints based on the class of their k-nearest neighbors.
Nature	Suitable for binary and multiclass classification.	Used for both classification and regression.
Training	It involves estimating the parameters by minimizing the logistic loss function using techniques like gradient descent.	The training process in KNN is minimal, as the algorithm essentially memorizes the training data.
Assumptions	Assumes a linear relationship between features and the log of odds of variables.	KNN makes no assumptions about the underlying data distribution and is non-linear.
Model	It is a parametric model.	It is a non-parametric model.
Handling Outliers	It can be sensitive to outliers which may affect the estimated coefficients.	It is not affected by outliers as the prediction is based on neighbors.
Decision Boundary	It is a linear function in feature space, creating a hyperplane that separates the classes.	It is non-linear and the decision boundary is determined by the distribution of data points.
Training Time	Faster training times, especially for large datasets.	Training time is negligible as it follows lazy learning approach.
High-Dimensional Data	Can perform well in high-dimension spaces but regularization may be necessary to avoid overfitting.	Is affected by the curse of dimensionality. Feature reduction techniques are employed.
Boundary Smoothness	Smooth decision boundary.	Decision boundary can be jagged.
Scalability	Performs well with large dataset.	Computationally expensive as the size of the dataset increases.

When to use?

The choice between Logistic Regression and K Nearest Neighbors (KNN) hinges on data characteristics and task requirements. Logistic Regression is suitable for linear relationships, offering interpretability crucial in fields like finance or medicine, especially when the decision boundary is clear. Conversely, KNN excels with diverse, non-linear data, adapting well to changing patterns and dynamic datasets due to its simplicity and real-time adaptability. Understanding the nature of the data, interpretability needs, and adaptability requirements guides the selection process, ensuring alignment with specific machine learning objectives. Ultimately, Logistic Regression is best suited for transparent, linear scenarios, while KNN thrives in complex, dynamic environments.