Improving Decomposition by Eliminating Spurious Components Using KL Divergence and Correlation Coefficient

EMD (Empirical Mode Decomposition) is a widely used decomposition method in signal processing that breaks down complex signals into multiple Intrinsic Mode Functions (IMFs). However, under certain conditions, the decomposition results may contain spurious components—artifacts that don't genuinely reflect the physical characteristics of the signal but rather represent noise or redundant elements introduced by the algorithm itself. To improve EMD decomposition and eliminate these false components, KL Divergence and correlation coefficients can be employed as screening tools. From an implementation perspective, KL Divergence (Kullback-Leibler Divergence) measures the difference between two probability distributions. In EMD decomposition, KL Divergence can be computationally applied to evaluate the distribution similarity between each IMF component and the original signal. A Python implementation might use scipy.stats.entropy() to calculate KL divergence values. If a component exhibits excessively high KL divergence, it indicates significant dissimilarity from the original signal, suggesting it may be a spurious component that should be flagged for removal. Correlation coefficients serve to quantify the linear relationship between IMF components and either the original signal or adjacent components. In practice, Pearson correlation coefficients can be calculated using numpy.corrcoef() or similar functions. Higher correlation coefficients typically indicate that a component contains more meaningful information, while lower values may signify noise or irrelevant artifacts. By establishing appropriate thresholds through statistical analysis or domain knowledge, components with weak correlations can be systematically identified and excluded. Combining these two methodologies allows for optimized EMD decomposition results through the removal of spurious components, thereby enhancing the accuracy and reliability of subsequent analyses. This improvement strategy proves particularly valuable in signal processing scenarios with significant noise interference, such as biomedical signal analysis, financial time series processing, and industrial vibration monitoring. The algorithm can be implemented by first calculating KL divergence and correlation metrics for all IMFs, then applying dual-criteria filtering based on predefined thresholds to automatically eliminate components failing both tests.