Unified embedding and clustering

This paper investigates the problem of treating embedding and clustering simultaneously to uncover data structure reliably by constraining manifold embedding through clustering. Conversely, most existing methods perform embedding sequentially, followed by clustering, which leads to a clustering that sometimes pushes data towards a direction induced by embedding. Instead, we perform them simultaneously through an original formulation, which allows for preserving the data's original structure in the embedding space and producing a better clustering assignment. To achieve this goal, we introduce a novel algorithm that unifies manifold embedding and clustering (UEC). The proposed UEC algorithm is based on a bi-objective loss function that combines data embedding and clustering, which is optimised using three different ways: (1) Comma Variant, (2) Plus Variant, and (3) Light Plus Variant. The experimental results with several real-world datasets show that UEC is competitive with the state-of-the-art embedding and clustering methods showing in particular that UEC allows for better preservation of the structure of the dataset resulting in better clustering performance.