Learning-Augmented K-Means Clustering Using Dimensional Reduction

Abstract: Learning augmented is a machine learning concept built to improve the performance of a method or model, such as enhancing its ability to predict and generalize data or features, or testing the reliability of the method by introducing noise and other factors. On the other hand, clustering is a fundamental aspect of data analysis and has long been used to understand the structure of large datasets. Despite its long history, the k-means algorithm still faces challenges. One approach, as suggested by Ergun et al,is to use a predictor to minimize the sum of squared distances between each data point and a specified centroid. However, it is known that the computational cost of this algorithm increases with the value of k, and it often gets stuck in local minima. In response to these challenges, we propose a solution to reduce the dimensionality of the dataset using Principal Component Analysis (PCA). It is worth noting that when using k values of 10 and 25, the proposed algorithm yields lower cost results compared to running it without PCA. "Principal component analysis (PCA) is the problem of fitting a low-dimensional affine subspace to a set of data points in a high-dimensional space. PCA is well-established in the literature and has become one of the most useful tools for data modeling, compression, and visualization."