Inference with K-means

TL;DR

This thesis explores new inference methods for k-means clustering, demonstrating that increasing cluster count reduces errors and highlighting the need for specialized inference techniques to improve accuracy.

Contribution

It introduces novel approaches for inference with k-means, emphasizing the impact of cluster number and dataset size on inference accuracy and proposing directions for future improvements.

Findings

More clusters lead to lower inference errors

Increasing assigned data points does not significantly reduce errors

Reducing learning losses does not affect inference accuracy

Abstract

This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates centroids based on the mean of assigned points. This process continues until convergence, forming k clusters where each point belongs to the closest centroid. This research investigates the prediction of the last component of data points obtained from a distribution of clustered data using the online balanced k-means approach. Through extensive experimentation and analysis, key findings have emerged. It is observed that a larger number of clusters or partitions tends to yield lower errors while increasing the number of assigned data points does not significantly improve inference errors. Reducing losses in the learning process does not significantly impact overall inference errors. Indicating that as learning is going on inference errors remain unchanged. Recommendations include the need for specialized inference techniques to estimate better data points derived from multi-clustered data and exploring methods that yield improved results with larger assigned datasets. By addressing these recommendations, this research advances the accuracy and reliability of inferences made with the k-means algorithm, bridging the gap between clustering and non-parametric density estimation and inference.