三维非负矩阵因子分解代谢组学数据解析

Three dimension non-negative matrix factorization for metabolomic data analysis

多维数据解析方法越来越引起人们的重视,非负矩阵因子分解算法已较广泛地用于图像分析。基于PARAFAC模型,将非负矩阵因子分解算法拓展为三维非负矩阵因子分解算法(three dimension non-negative matrix factorization,NMF3)。其原理简明,算法易于执行。与基于向量计算的其他三维化学计量学算法不同,NMF3基于矩阵计算单个元素,所以不必将三维数据平铺处理,就可直接解析,为三维数据解析研究提供了一种全新的思路和方法。应用NMF3解析模拟三维数据和代谢组学数据,结果令人满意。

Non-negative matrix factorization （NMF） is a technique for dimensionality reduction by placing non-negativity constraints on the matrix. It has been widely used in image analysis. The factorization matrices obtained from NMF are non-negative and can be understood and interpreted directly. Based on the PARAFAC model, NMF was extended for three-way data decomposition. The three dimension non-negative matrix factorization （NMF3） algorithm, which was concise and easy to implement, was given in this paper. It has been applied to decomposition of the simulated data array and metabolomic data array, the results were reasonable. The NMF3 algorithm implementation is based on elements but not on vectors. It can decompose a data array directly without unfolding, which is not similar to that the traditional algorithms do. It will give us a novel enlightenment for the decomposition of chemical three dimension data array.