Fast Orthogonal Nonnegative Matrix Tri-Factorization for Simultaneous Clustering

Orthogonal Nonnegative Matrix Tri-Factorization (ONMTF), a dimension reduction method using three small matrices to approximate an input data matrix, clusters the rows and columns of an input data matrix simultaneously. However, ONMTF is computationally expensive due to an intensive computation of the Lagrangian multipliers for the orthogonal constraints. In this paper, we introduce Fast Orthogonal Nonnegative Matrix Tri-Factorization (FONT), which uses approximate constants instead of computing the Lagrangian multipliers. As a result, FONT reduces the computational complexity significantly. Experiments on document datasets show that FONT outperforms ONMTF in terms of clustering quality and running time. Moreover, FONT is further accelerated by incorporating Alternating Least Squares, and can be much faster than ONMTF.