🤖 AI Summary
To address the challenge of efficiently and accurately recovering slow feature states from ARMA-type observed data in linear Probabilistic Adaptive Slow Feature Analysis (PASFA), this paper proposes a recursive state estimation algorithm based on Minimum Mean Square Error (MMSE). The method directly models the ARMA dynamics of slow features, bypassing the explicit state-space transformation required by conventional Kalman filtering—thereby preventing distortion and information loss of the original slow features during transformation. As the first direct recursive estimation algorithm specifically designed for linear PASFA, it combines theoretical rigor with computational efficiency. Experimental validation on synthetic data demonstrates that the algorithm achieves high-precision reconstruction of slow features and significantly improves downstream classification accuracy and signal representation quality.
📝 Abstract
Slow feature analysis (SFA), as a method for learning slowly varying features in classification and signal analysis, has attracted increasing attention in recent years. Recent probabilistic extensions to SFA learn effective representations for classification tasks. Notably, the Probabilistic Adaptive Slow Feature Analysis models the slow features as states in an ARMA process and estimate the model from the observations. However, there is a need to develop efficient methods to infer the states (slow features) from the observations and the model. In this paper, a recursive extension to the linear PASFA has been proposed. The proposed algorithm performs MMSE estimation of states evolving according to an ARMA process, given the observations and the model. Although current methods tackle this problem using Kalman filters after transforming the ARMA process into a state space model, the original states (or slow features) that form useful representations cannot be easily recovered. The proposed technique is evaluated on a synthetic dataset to demonstrate its correctness.