High-Dimensional Impedance Spectroscopy Analysis of Homeopathic Medicines: A Machine Learning Approach

The impedance spectroscopy is a well-established technique for studying the electrical characteristics of materials, especially in the biomedical and chemical fields. Impedance spectroscopy produces complex information as a result of its multi-frequency readings. The high-dimensional characteristics of impedance data pose difficulties in display, understanding and interpretation. Manually discerning patterns among various substances with linked properties may result in analytical redundancy. Efficient visualization and dimensionality reduction methods can substantially improve data interpretation and pattern identification. Data-Driven dimensionality reduction techniques, like Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), and Uniform Manifold Approximation and Projection (UMAP), offer solutions by converting complex datasets into lower-dimensional representations. This work provides insights on using these three methodologies on impedance spectroscopy data obtained from 27 different medicinal samples used in homeopathy over a range of frequencies. PCA is a linear method that effectively captures variance but has limitations operating with non-linear data interactions. t-SNE effectively clusters data while preserving local structures; however, it involves considerable processing costs and compromises global structure. UMAP provides balance by maintaining both local and global structures while reducing processing resources. We applied these techniques to impedance spectroscopy data to evaluate their strengths and weaknesses, demonstrating that UMAP is the most suitable for revealing meaningful patterns for our impedance data set. PCA, efficiently maintained global variance, enabling K-Means grouping into discrete categories, whereas t-SNE and UMAP demonstrated enhanced preservation of local structures. This research contributes to improving data interpretation in material science and biomedical diagnostics.