Deep Clustering and Representation Learning with Geometric Structure Preservation

In this paper, we propose a novel framework for Deep Clustering and Representation Learning (DCRL) that preserves the geometric structure of data. In the proposed DCRL framework, manifold clustering is done in the latent space guided by a clustering loss. To overcome the problem that clustering-oriented losses may deteriorate the geometric structure of embeddings in the latent space, an isometric loss is proposed for preserving intra-manifold structure locally and a ranking loss for inter-manifold structure globally. Experimental results on various datasets show that the DCRL framework leads to performances comparable to current state-of-the-art deep clustering algorithms, yet exhibits superior performance for downstream tasks. Our results also demonstrate the importance and effectiveness of the proposed losses in preserving geometric structure in terms of visualization and performance metrics. Clustering, a fundamental tool for data analysis and visualization, has been an essential research topic in data science and machine learning. Conventional clustering algorithms such as K -Means (MacQueen, 1965), Gaussian Mixture Models (GMM) (Bishop, 2006), and spectral clustering (Shi & Malik, 2000) perform clustering based on distance or similarity. However, handcrafted distance or similarity measures are rarely reliable for large-scale high-dimensional data, making it increasingly challenging to achieve effective clustering.