Abstract: Aiming at  the problem that the traditional fuzzy C-means (FCM) algorithm  produced a large amount of computation  when dealing with high-dimensional data sets with complex structures, which led to the decline of clustering effect, we proposed a modified fuzzy clustering algorithm based on non-negative matrix factorization. Firstly, the algorithm proposed a new objective function, which was solved by alternating iterations. Secondly, in the iterative process, triangular inequalities were used to filter out samples that met the inequality conditions, and at the same time,  a new membership updating formula was used to reduce the amount of calculation and  improve the clustering performance. Finally,  experiments were carried ou on the UCI dataset and image dataset, and compared with other classical FCM algorithms. The experimental results show that the algorithm  improves the clustering effect.

Key words: fuzzy C-means, clustering, non-negative matrix factorization, alternate iteration, triangular inequality