Connection Between PCA and K-Means

Requirements Clarification & Assessment

Before diving into the relationship between Principal Component Analysis (PCA) and K-means clustering, it's crucial to clarify the requirements and assess the context in which these techniques are applied:

1. Understanding the Techniques:

   • Principal Component Analysis (PCA): A dimensionality reduction technique that transforms data into a lower-dimensional space while retaining as much variance as possible.
   • K-means Clustering: A clustering algorithm that partitions data into K clusters by minimizing the variance within each cluster.

2. Objective:

   • To explore how PCA and K-means clustering can be used together to enhance clustering performance.
   • To understand the mathematical and operational relationship between the two techniques.

3. Contextual Considerations:

   • High-dimensional Data: Both techniques are often applied to datasets with many features, where PCA can help reduce dimensionality before clustering.
   • Computational Efficiency: Assessing how PCA can make K-means more computationally feasible by reducing the number of dimensions.
   • Interpretability: Understanding how PCA simplifies data and how K-means interprets these simplified features.