Dictionary-Learning-Based Data Pruning for System Identification

System identification is normally involved in augmenting time series data by time shifting and nonlinearisation (via polynomial basis), which introduce redundancy both feature-wise and sample-wise. Many research works focus on reducing redundancy feature-wise, while less attention is paid to sample-wise redundancy. This paper proposes a novel data pruning method, called (mini-batch) FastCan, to reduce sample-wise redundancy based on dictionary learning. Time series data is represented by some representative samples, called atoms, via dictionary learning. The useful samples are selected based on their correlation with the atoms. The method is tested on one simulated dataset and two benchmark datasets. The R-squared between the coefficients of models trained on the full and the coefficients of models trained on pruned datasets is adopted to evaluate the performance of data pruning methods. It is found that the proposed method significantly outperforms the random pruning method.

Canonical-Correlation-Based Fast Feature Selection

This paper proposes a canonical-correlation-based filter method for feature selection. The sum of squared canonical correlation coefficients is adopted as the feature ranking criterion. The proposed method boosts the computational speed of the ranking criterion in greedy search. The supporting theorems developed for the feature selection method are fundamental to the understanding of the canonical correlation analysis. In empirical studies, a synthetic dataset is used to demonstrate the speed advantage of the proposed method, and eight real datasets are applied to show the effectiveness of the proposed feature ranking criterion in both classification and regression. The results show that the proposed method is considerably faster than the definition-based method, and the proposed ranking criterion is competitive compared with the seven mutual-information-based criteria.