Many nonlinear iterative procedures generate high-dimensional trajectories whose early behavior is informative but difficult to compare directly. This paper studies a soft-computing representation problem: how to convert a short early trajectory segment into compact, interpretable, fixed-dimensional fuzzy coordinates that preserve information about subsequent convergence and trajectory geometry. The problem is investigated for iterated Pearson correlation matrices, a nonlinear matrix iteration historically connected with CONCOR-type blockmodeling and repeated-correlation methods. The proposed descriptor uses two logarithmic signals from the early post-transient regime: a step-size signal, measuring contraction magnitude, and a contraction-ratio signal, measuring local contraction evolution. Each signal is projected onto a three-node triangular fuzzy partition using zero-degree F-transform coefficients and one centered first-degree coefficient. This yields an eight-dimensional two-channel representation separating local level from local trend and contraction magnitude from contraction evolution. Across 22 matrix dimensions with 1000 trajectories per dimension, the descriptor is compared with raw trajectory samples, statistical summaries, and PCA-compressed raw features using Random Forest regression for convergence-length approximation. It achieves mean R^2 = 0.6480, close to raw trajectories (0.6518) and statistical summaries (0.6528), while improving over the step-size-only F-transform descriptor (0.5001). Repeated random-split and shifted-window experiments confirm stability. PCA and clustering further show reproducible low-dimensional organization, with the first two principal components explaining 84.26% of variance and k = 3 favored by the mean silhouette criterion.

翻译：许多非线性迭代过程会生成高维轨迹，其早期行为具有信息价值但难以直接比较。本文研究一个软计算表示问题：如何将短早期轨迹片段转换为紧凑、可解释且维度固定的模糊坐标，以保留后续收敛性和轨迹几何结构的信息。该问题针对迭代皮尔逊相关矩阵展开研究，这是一种与CONCOR型分块建模和重复相关方法历史相关的非线性矩阵迭代。所提出的描述符利用早期瞬态后阶段的两个对数信号：步长信号（衡量收缩幅度）和收缩比信号（衡量局部收缩演化）。每个信号通过零阶F-变换系数和一个中心一阶系数投影到三节点三角模糊划分上，从而生成一个八维双通道表示，将局部水平与局部趋势、收缩幅度与收缩演化分离。在22个矩阵维度（每个维度包含1000条轨迹）的实验中，将描述符与原始轨迹样本、统计摘要以及PCA压缩的原始特征进行对比，使用随机森林回归进行收敛长度近似。该描述符的平均R²=0.6480，接近原始轨迹（0.6518）和统计摘要（0.6528），同时优于仅基于步长信号的F-变换描述符（0.5001）。重复随机分割和平移窗口实验证实了其稳定性。PCA和聚类进一步显示出可复现的低维组织结构，其中前两个主成分解释了84.26%的方差，且平均轮廓准则倾向于k=3。