增量非线性降维方法实现流数据实时分析与可视化。
An Incremental Non-Linear Manifold Approximation Method
- 基于几何多分辨率分析框架，增量更新聚类图、主成分向量和小波系数。
- 小样本初始下仍能准确逼近非线性流形，性能接近批量算法。
- 适合需要自适应高维数据表示的实时可视化与交互图形应用。
高维数据分析受“维度诅咒”影响，计算成本高昂。线性与非线性降维技术可简化此类数据，其中非线性方法在交互式与图形化应用中对复杂数据结构的高效可视化与处理尤为重要。本研究提出一种基于几何多分辨率分析（GMRA）框架的增量式非线性降维方法，适用于流数据场景。该方法通过增量更新聚类图、主成分分析（PCA）基向量和小波系数，支持实时数据分析与可视化。数值实验表明，即使初始样本量较小，增量式GMRA仍能准确表示非线性流形，且与批量GMRA结果高度一致，验证了其高效更新能力与多尺度结构保持性。研究结果凸显了增量式GMRA在需自适应高维表示的实时可视化与交互图形应用中的潜力。
原文摘要 · Abstract (English)
Analyzing high-dimensional data presents challenges due to the "curse of dimensionality'', making computations intensive. Dimension reduction techniques, categorized as linear or non-linear, simplify such data. Non-linear methods are particularly essential for efficiently visualizing and processing complex data structures in interactive and graphical applications. This research develops an incremental non-linear dimension reduction method using the Geometric Multi-Resolution Analysis (GMRA) framework for streaming data. The proposed method enables real-time data analysis and visualization by incrementally updating the cluster map, PCA basis vectors, and wavelet coefficients. Numerical experiments show that the incremental GMRA accurately represents non-linear manifolds even with small initial samples and aligns closely with batch GMRA, demonstrating efficient updates and maintaining the multiscale structure. The findings highlight the potential of Incremental GMRA for real-time visualization and interactive graphics applications that require adaptive high-dimensional data representations.
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