The paper presents UTOPIAN, a visual analytics system for interactive topic modelling using Nonnegative Matrix Factorization (NMF). The workflow begins by applying NMF to decompose a term-document matrix into two representations: topics as weighted combinations of keywords, and documents as weighted combinations of topics. A modified t-SNE algorithm creates a 2D layout visualizing documents as points coloured by their topic assignments, with enhanced cluster separation for clarity. The core of UTOPIAN is an iterative refinement loop where users assess topic quality and interact with the model through multiple mechanisms: keyword refinement adjusts weights of terms within topics; topic merging combines similar topics; topic splitting divides topics based on semantic differences; document-induced topic creation builds topics from exemplar documents; and keyword-induced topic creation generates topics from selected terms. Each interaction produces reference specifications (V and G matrices with supervision weights) that guide subsequent topic modelling through semi-supervised NMF, which regularizes the solution toward user specifications while maintaining fit to the data. Through iterative exploration and refinement, analysts progressively improve topic quality and interpretability, discovering meaningful semantic structures in document collections. The approach was demonstrated on research papers, product reviews, and newsgroup data, revealing topic relationships and document organization.