用截断SVD降维建模变道行为，发现效率提升有限且信息损失严重。
Analysis of Truncated Singular Value Decomposition for Koopman Operator-Based Lane Change Model
- 用截断SVD压缩数据，构建基于柯普曼算子的变道模型
- 实际训练时间减少不明显，信息丢失显著
- 适合关注降维代价与模型精度权衡的研究者
理解与建模复杂动态系统对提升车辆性能与安全至关重要，尤其在自动驾驶背景下。近年来，柯普曼算子及其近似方法——扩展动态模态分解（EDMD）因其能将强非线性系统行为转化为线性表示而受到关注，便于与传统线性控制器结合。为此，奇异值分解（SVD），特别是截断SVD，被用于从大规模数据集中高效逼近柯普曼算子。本研究评估了不同基函数在EDMD中用于截断SVD表示变道行为模型的效果，旨在平衡计算效率与信息损失。结果表明，截断SVD并未带来显著的训练时间降低，反而造成明显的信息丢失。
原文摘要 · Abstract (English)
Understanding and modeling complex dynamic systems is crucial for enhancing vehicle performance and safety, especially in the context of autonomous driving. Recently, popular methods such as Koopman operators and their approximators, known as Extended Dynamic Mode Decomposition (EDMD), have emerged for their effectiveness in transforming strongly nonlinear system behavior into linear representations. This allows them to be integrated with conventional linear controllers. To achieve this, Singular Value Decomposition (SVD), specifically truncated SVD, is employed to approximate Koopman operators from extensive datasets efficiently. This study evaluates different basis functions used in EDMD and ranks for truncated SVD for representing lane change behavior models, aiming to balance computational efficiency with information loss. The findings, however, suggest that the technique of truncated SVD does not necessarily achieve substantial reductions in computational training time and results in significant information loss.
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