基于流形学习的全球创新指数降维与聚类分析

Dimensionality Reduction and Clustering Analysis of the Global Innovation Index Based on Manifold Learning

摘要: 全球创新指数(Global Innovation Index, GII)作为衡量国家创新能力的高维多指标体系，其复杂性对深入分析与直观可视化构成了挑战。传统线性降维方法在处理其非线性数据结构时存在局限，而现有流形学习方法未充分考虑特征重要性差异。为此，本研究提出一种融合特征权重的改进UMAP方法，旨在更有效地揭示全球创新格局的内在结构与集群特征。以2013~2022年118个经济体的GII数据为基础，首先通过熵权法计算特征权重，并将其融入UMAP的距离度量中以构建加权降维模型；进而使用K-Means聚类，结合多种评估指标量化聚类效果，最终采用TOPSIS方法进行综合评价排序。实验结果显示，熵权UMAP在聚类数为5时取得最优综合性能，其TOPSIS排名第一，较采用的PCA降维方法具有更优的结构识别能力，为全球创新格局分析提供了更鲁棒的数据处理工具，也为类似多指标综合评价体系的降维与聚类问题提供了新的方法参考。

Abstract: As a high-dimensional, multi-indicator system for measuring national innovation capabilities, the Global Innovation Index (GII) poses challenges for in-depth analysis and intuitive visualization due to its complexity. Traditional linear dimensionality reduction methods have limitations in handling its non-linear data structure, while existing manifold learning approaches have not fully considered differences in feature importance. To address this, this study proposes an improved UMAP method that integrates feature weights, aiming to more effectively reveal the intrinsic structure and cluster characteristics of the global innovation landscape. Based on GII data from 118 economies between 2013 and 2022, feature weights are first calculated using the entropy weight method and incorporated into UMAP’s distance metric to construct a weighted dimensionality reduction model. Subsequently, K-Means clustering is applied, and multiple evaluation metrics are used to quantify clustering performance. Finally, the TOPSIS method is employed for comprehensive evaluation and ranking. Experimental results show that entropy-weighted UMAP achieves optimal comprehensive performance when the number of clusters is set to 5, ranking first in the TOPSIS evaluation. Compared to the PCA dimensionality reduction method used, it demonstrates superior structural recognition capabilities. This study provides a more robust data processing tool for analyzing the global innovation landscape and offers a new methodological reference for dimensionality reduction and clustering in similar multi-indicator comprehensive evaluation systems.