Hybrid algorithm based initialization for 2-D convolutive non-negative matrix factorization

To solve the problem that the two-dimensional convolutive non-negative matrix factorization (2-DCNMF) algorithm is sensitive to the initial value, and the traditional random initialization is easy to converge to the relatively poor local optimal value, this paper proposes a hybrid algorithm by combining k-means clustering algorithm and singular value decomposition (SVD) algorithm. Through using k-means clustering method, clustering center was calculated as the initial value of the coefficient matrix H, which avoids the non-unity problem of the traditional decomposition result. Considering that the number of base matrix W of the 2-DCNMF algorithm is more than that of the one-dimensional convolution non-negative matrix decomposition, the singular value decomposition and the principal component analysis method were applied iteratively to obtain initial W matrix, which eliminates the initialization error from a single algorithm. Under the same parameter environment, experiments demonstrate that the proposed method has better separation performance and better convergence compared with other similar algorithms. The experimental results show that the method is capable of separating relatively independent signals in SNR environments from -1 dB to 10 dB accurately and has high robustness to noise data, which further proves that the use of hybrid algorithm is beneficial for the realization of real-time and high-performance of 2-DCNMF. © 2019, Editorial Board of Journal of Harbin Institute of Technology. All right reserved.