论文标题
关于动态内部PCA算法的收敛性
On the Convergence of the Dynamic Inner PCA Algorithm
论文作者
论文摘要
动态内部主成分分析（DIPCA）是分析时间依赖性多元数据的强大方法。 DIPCA提取动态潜在变量，通过解决大规模，密集和非convex非线性程序（NLP）来捕获最主要的时间趋势。最近在文献中提出了可扩展的分解算法来解决这些具有挑战性的NLP。分解算法在实践中的表现良好，但其收敛属性尚不清楚。在这项工作中，我们表明该算法是坐标最大化算法的专门变体。该观察结果使我们能够解释为什么分解算法在实践中可能（或不起作用），并且可以指导改进。我们将分解策略的性能与现成的求解器IPOPT的性能进行了比较。结果表明，分解更可扩展，令人惊讶的是提供更高质量的解决方案。
Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale, dense, and nonconvex nonlinear program (NLP). A scalable decomposition algorithm has been recently proposed in the literature to solve these challenging NLPs. The decomposition algorithm performs well in practice but its convergence properties are not well understood. In this work, we show that this algorithm is a specialized variant of a coordinate maximization algorithm. This observation allows us to explain why the decomposition algorithm might work (or not) in practice and can guide improvements. We compare the performance of the decomposition strategies with that of the off-the-shelf solver Ipopt. The results show that decomposition is more scalable and, surprisingly, delivers higher quality solutions.
