The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction

The current era is characterized by a deluge of high-dimensional data. Dimensionality reduction (DR) techniques have emerged as tools for exploratory analysis of such data by visualizing the underlying structure. The most popular methods, t-distributed stochastic neighbor embedding [1] and uniform manifold approximation and projection (UMAP) [2] are grounded in the attraction-repulsion dynamics that bring similar data points closer while pushing dissimilar ones apart. As unsupervised algorithms, these do not rely on labeled data; instead, they identify and preserve the intrinsic structure of high-dimensional data by leveraging local (attractive) and global (repulsive) relationships (forces). This makes these algorithms particularly well-suited for tasks such as clustering [3], exploratory data analysis [4], anomaly detection in semiconductor manufacturing [5], visual search [6], time series analysis [7], studying representation convergence [8], and outlier image detection [9], where visualizing hidden patterns in unlabeled data is critical and meaningful.