An online algorithm for contrastive Principal Component Analysis
This work addresses the need for efficient, interpretable low-dimensional representations in large datasets, but it is incremental as it builds on existing cPCA methods.
The authors tackled the problem of cPCA's sensitivity to hyperparameters and lack of an online algorithm by introducing cPCA*, which is more interpretable and less sensitive, and derived an online algorithm that maps to a neural network for potential hardware implementation.
Finding informative low-dimensional representations that can be computed efficiently in large datasets is an important problem in data analysis. Recently, contrastive Principal Component Analysis (cPCA) was proposed as a more informative generalization of PCA that takes advantage of contrastive learning. However, the performance of cPCA is sensitive to hyper-parameter choice and there is currently no online algorithm for implementing cPCA. Here, we introduce a modified cPCA method, which we denote cPCA*, that is more interpretable and less sensitive to the choice of hyper-parameter. We derive an online algorithm for cPCA* and show that it maps onto a neural network with local learning rules, so it can potentially be implemented in energy efficient neuromorphic hardware. We evaluate the performance of our online algorithm on real datasets and highlight the differences and similarities with the original formulation.