On the Convergence of the Dynamic Inner PCA Algorithm
This work addresses convergence issues for a scalable algorithm in time-series data analysis, but it is incremental as it builds on existing decomposition methods.
The paper tackled the convergence analysis of the Dynamic Inner PCA (DiPCA) decomposition algorithm for time-dependent multivariate data, showing it is a specialized coordinate maximization variant, and found that it is more scalable and delivers higher quality solutions than the off-the-shelf solver Ipopt.
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.