二维卷积非负矩阵分解的初值确定混合算法

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

摘要:

为解决二维卷积非负矩阵分解算法存在初值敏感,且传统随机初始化确定的初始值容易使算法收敛到结果相对不好的局部最优值的问题,通过结合K均值聚类、奇异值分解和主成分分析方法,提出了一种适用于二维卷积非负矩阵分解初始值确定的混合算法.首先,利用K均值聚类方法得到聚类中心作为系数矩阵（H矩阵）的初始值,避开了传统初始化不确定系数矩阵带来的分解结果不唯一问题；其次,考虑到相比一维卷积非负矩阵分解算法,二维卷积非负矩阵分解算法的基矩阵（W矩阵）个数更多,利用奇异值分解和主成分分析方法交替产生基矩阵的初始值,克服了单个算法产生的初始化误差问题.在相同参数环境下将本文算法和现有初始化算法的分解收敛性能进行对比实验,结果表明本文算法相比其他同类算法具有更好的分解性能并具有更好的收敛性.进一步加入噪声进行实验,在白噪声为-1 dB~10 dB的不同信噪比环境下,本文算法均能快速实现信号的分离,对于噪声数据具有很强的鲁棒性.采用混合算法确定初值,更有利于实现二维卷积非负矩阵分解的实时性和高性能.

Abstract:

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.