The Non-Negative Matrix Factorization is used for analyzing the compatibility of dyes in mixtures. Samples have been collected from simulated and actual dip-dyeing tests. First, different sets of binary mixtures of dyes with different dyeing rates have been virtually created by changing the rates of absorption of employed primaries. Hence, an exponential function has been found to be appropriate to model different exhaustion rates of dyes. Besides, data of 17 different binary mixtures of nine cationic dyes, which were obtained using the dip-test method, have been also collected from actual dyeing process. The reflectance spectra of each dip-test dyed samples have been converted to scalable Kubelka-Munk function and the NNMF and Principal Component Analysis methods are employed to analyze the data. It is shown that the mixtures of fully compatible dyes could be completely represented by only one basic function that may either be extracted by Non-Negative Matrix Factorization or Principal Component Analysis factorization methods. Oppositely, dyes with great degree of incompatibility could not be characterized by one principal vector. For the later sets of samples, the extracted Non-Negative Matrix Factorization basis could successfully resemble the spectra of primaries. The spectral analysis of both simulated and real dyed samples show that the spectra of compatible primaries could be presented by a non-negative basic function with the average of root mean square errors value smaller than 0.1. This finding is accordance with the known practical fact that dyes are allowed to be mixed with maximum 0.5-unit differences in their K values.

中文翻译：

---

非负矩阵分解法分析染料在混合物中的相容性

非负矩阵分解用于分析混合物中染料的相容性。样品是从模拟和实际浸染测试中收集的。首先，通过改变所采用的原色的吸收速率，实际上已经创建了具有不同染色速率的不同组的染料二元混合物。因此，已发现指数函数适用于模拟不同的染料耗尽率。此外，还从实际染色过程中收集了使用浸渍试验方法获得的 9 种阳离子染料的 17 种不同二元混合物的数据。每个浸渍测试染色样品的反射光谱已转换为可扩展的 Kubelka-Munk 函数，并采用 NNMF 和主成分分析方法来分析数据。结果表明，完全相容染料的混合物可以完全由一个基本函数表示，该函数可以通过非负矩阵分解或主成分分析分解方法提取。相反，高度不相容的染料不能用一个主要载体来表征。对于后面的样本集，提取的非负矩阵分解基可以成功地类似于原色光谱。模拟染色样品和真实染色样品的光谱分析表明，相容原色的光谱可以由均方根误差平均值小于0.1的非负基本函数表示。这一发现与已知的实际事实是一致的，即允许染料以最大 0.5 个单位的差异进行混合。具有高度不相容性的染料不能用一个主要载体来表征。对于后面的样本集，提取的非负矩阵分解基可以成功地类似于原色光谱。模拟染色样品和真实染色样品的光谱分析表明，相容原色的光谱可以由均方根误差平均值小于0.1的非负基本函数表示。这一发现与已知的实际事实是一致的，即允许染料以最大 0.5 个单位的差异进行混合。具有高度不相容性的染料不能用一个主要载体来表征。对于后面的样本集，提取的非负矩阵分解基可以成功地类似于原色光谱。模拟染色样品和真实染色样品的光谱分析表明，相容原色的光谱可以由均方根误差平均值小于0.1的非负基本函数表示。这一发现与已知的实际事实是一致的，即允许染料以最大 0.5 个单位的差异进行混合。模拟染色样品和真实染色样品的光谱分析表明，相容原色的光谱可以由均方根误差平均值小于0.1的非负基本函数表示。这一发现与已知的实际事实是一致的，即允许染料以最大 0.5 个单位的差异进行混合。模拟染色样品和真实染色样品的光谱分析表明，相容原色的光谱可以由均方根误差平均值小于0.1的非负基本函数表示。这一发现与已知的实际事实是一致的，即允许染料以最大 0.5 个单位的差异进行混合。K值。