Evolving factor analysis (EFA) investigates the evolution of the singular values of matrices formed by a series of measured spectra, typically, resulting from the spectral observation of an ongoing chemical process. In the original EFA, the logarithms of the singular values are plotted for submatrices that include an increasing number of spectra. A typical observation in these plots is that pairs of trajectories of the singular values are on a collision course, but finally, the curves seem to repel each other and then run in different directions. For parameter‐dependent square matrices, such a behaviour is known for the eigenvalues under the keyword of an avoidance of crossing. Here, we adjust the explanation of this avoidance of crossing to the curves of singular values of EFA. Further, a condition is studied that breaks this avoidance of crossing. We demonstrate that the understanding of this noncrossing allows us to design model data sets with a predictable crossing behaviour.

中文翻译：

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关于演化因子分析中奇异值交叉的避免

演化因子分析 (EFA) 研究由一系列测量光谱形成的矩阵奇异值的演化，通常由对正在进行的化学过程的光谱观察产生。在原始 EFA 中，针对包含越来越多光谱的子矩阵绘制了奇异值的对数。这些图中的一个典型观察是奇异值的成对轨迹在碰撞过程中，但最终，这些曲线似乎相互排斥，然后向不同的方向运行。对于依赖于参数的方阵，这种行为对于避免交叉关键字下的特征值是已知的。在这里，我们将这种避免交叉的解释调整到 EFA 的奇异值曲线。更多，研究了打破这种避免交叉的条件。我们证明了对这种非交叉的理解使我们能够设计具有可预测交叉行为的模型数据集。