Exploring Manifold Embedding Techniques for Enhanced Clustering Efficiency

Manifold Embedding (ME) is a fundamental field in machine learning, enabling the effective analysis and visualization of high-dimensional datasets. It plays a crucial role in tasks such as clustering and classification by transforming data into more manageable representations. Recently, deep learning-based and ME methods have shown promise in enhancing clustering performance by preserving local structures while uncovering global relationships within the data. This paper investigates the impact of ME techniques on clustering performance, examining six approaches: Principal Component Analysis (PCA), Denoising Autoencoder (DAE), Convolutional Autoencoder (CAE), Uniform Manifold Approximation and Projection (UMAP), Isometric Mapping (ISOMAP), and t-Distributed Stochastic Neighbor Embedding (t-SNE). We hypothesize that these techniques enable the discovery of lower-dimensional representations that improve clustering effectiveness. To validate this, we incorporate ME as a preprocessing step before applying clustering algorithms, including k-means, Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN), Gaussian Mixture Models (GMM), and Agglomerative Hierarchical Clustering. Our experiments, conducted on benchmark datasets, analyze the clustering performance across varying numbers of dimensions. The results demonstrate that UMAP and t-SNE consistently enhance clustering performance across all datasets, while other ME techniques exhibit fluctuating effectiveness depending on the chosen representation space. These findings highlight the importance of selecting an appropriate ME method for optimizing clustering outcomes.