Clustering and Dimensionality Reduction in MerQur: Unsupervised Learning from K-Means to UMAP

Abstract

Unsupervised learning methods — clustering and dimensionality reduction — are the two main ways of extracting structure from unlabelled data. Clustering groups similar observations, while dimensionality reduction transforms high-dimensional data into a low-dimensional (typically 2D or 3D) representation. This study introduces in detail the 7 analyses offered in MerQur’s Clustering category: K-Means Clustering, Hierarchical Clustering, DBSCAN, Principal Component Analysis (PCA), t-Distributed Stochastic Neighbour Embedding (t-SNE), Multidimensional Scaling (MDS), and Uniform Manifold Approximation and Projection (UMAP). For each: (i) the basis of the method and its place in unsupervised learning, (ii) hyperparameters and selection strategies, (iii) form fields and options in MerQur, (iv) reported statistics and visualisation outputs, and (v) interpretation guidance for a typical research question. The distinction between geometric distance-based methods (K-Means, Hierarchical) and density-based approaches (DBSCAN); the design differences between linear (PCA, MDS) and non-linear dimensionality reductions (t-SNE, UMAP) are discussed. Overall, MerQur’s Clustering category brings together within a single graphical interface a spectrum spanning classical statistical dimensionality reduction, modern manifold learning, geometric grouping methods, and density-based clustering algorithms capable of outlier detection.