Which unsupervised machine learning algorithm reduces the dimensionality of a dataset while retaining information?

Principal Component Analysis (PCA) is an unsupervised machine learning algorithm designed specifically for dimensionality reduction. It works by transforming the original dataset into a new coordinate system where the largest variance by any projection lies on the first coordinate (first principal component), the second largest variance on the second coordinate, and so forth. This transformation allows PCA to capture the most significant underlying patterns in the data while diminishing the less important features.

The primary goal of PCA is to reduce the number of variables in a dataset while retaining as much information (variance) as possible, making it easier to visualize and analyze high-dimensional data effectively. By projecting the data into a lower-dimensional space, PCA enables the retention of essential insights and relationships in the dataset, especially useful in exploratory data analysis and preprocessing steps for machine learning.

Other methods mentioned, such as t-SNE, are often used for visualization rather than general dimensionality reduction; while they preserve local structures well, they don't focus on explaining global variance in the data in the way PCA does. K-means Clustering and Hierarchical Clustering are clustering algorithms that do not inherently perform dimensionality reduction, as their main task is to group data points into clusters based on similarity rather than transforming feature representations.