Sound signals analysis and classification using geometric methods

Sound signals are one-dimensional temporal waveforms that represent implicitly hidden complex features. Their sophisticated computational processing is essential for classification tasks spanning speaker identification, accent recognition, and medical diagnosis based on sound biomarkers. This thesis presents a novel approach for sound signal classification based on geometric analysis of their spectrogram surfaces. Including demonstrating applications to speech accent classification and detection of common lung diseases. Traditional spectral features such as Mel-Frequency Cepstral Coefficients (MFCCs) represent the spectral envelope as energy vectors but do not account for the intrinsic geometric shape and topological structure of the time-frequency-magnitude surface. We propose treating spectrograms as three-dimensional geometric surfaces represented by triangular meshes. Our methodology employs the previously-developed Adaptive Block Coordinate Descent (ABCD) algorithm to compute an optimal two-dimensional projection which minimizes geometric distortion. The resulting distortion measures, quantifying local changes in scale, area, and angles, constitute our geometric feature vectors. We evaluate this approach using Support Vector Machines (SVMs) applied on the L2-ARCTIC speech database, and a combined lung sound dataset comprised of ICBHI, KAUH, and lung disease data recorded at the Rambam Medical Center (RMC). Results, demonstrating task-specific geometric signatures: scale distortions (Dirichlet energy and Conformal Factor) achieve 91\% accuracy in accent classification, while conformal distortions (MIPS) achieve 80\% recall for multi-class lung disease classification and 0.84 AUROC for asthma detection. Geometric features exhibit also superior noise robustness, outperforming the MFCCs significantly in F1 score for asthma detection in noisy environments. This work highlights the potential of geometric surface
distortion analysis as a robust tool for audio signal processing and classification.

M.Sc. student under the supervision of Prof. Emeritus Yehoshua Y. Zeevi.