Browsing by Author "Mirza, Fuat Kaan"

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Citation - WoS: 2
Citation - Scopus: 2
Decoding Rhythmic Complexity: a Nonlinear Dynamics Approach via Visibility Graphs for Classifying Asymmetrical Rhythmic Frameworks of Turkish Classical Music
(Elsevier Science inc, 2025) Mirza, Fuat Kaan; Baykas, Tuncer; Hekimoglu, Mustafa; Pekcan, Onder; Tuncay, Gonul Pacaci
The non-isochronous, hierarchical rhythmic cycles (usuls) of Turkish Classical Music (TCM) exhibit emergent temporal structures that challenge conventional rhythm analysis based on metrical regularity. To address this challenge, this study presents a complexity-oriented framework for usul classification, grounded in nonlinear time series analysis and network-based representations. Rhythmic signals are processed through energy envelope extraction, diffusion entropy analysis, and spectral transformations to capture multiscale temporal dynamics. Visibility graphs (VGs) are constructed from these representations to encode underlying structural complexity and temporal dependencies. Features derived from VG adjacency matrices serve as complexity-sensitive descriptors and enable high-accuracy classification (0.99) across 40 usul classes and 628 compositions. Energy envelope-derived graphs provide the most discriminative information, highlighting the importance of amplitude modulation in encoding rhythmic structure. Beyond classification, the analysis reveals self-organizing patterns and signatures of complexity, such as quasi-periodicity, scale-dependent variability, and entropy saturation, suggesting that usuls function as adaptive, nonlinear systems rather than metrically constrained patterns. The topological features extracted from the resulting graphs align with theoretical constructs from complexity science, such as modularity and long-range temporal correlations. This positions usul as an exemplary case for studying structured temporal complexity in cultural artifacts through the lens of dynamical systems. These findings contribute to computational rhythm analysis by demonstrating the efficacy of complexity measures in characterizing culturally specific rhythmic systems.
A Novel Multiscale Graph Signal Processing and Network Dynamics Approach to Vibration Analysis for Stone Size Discrimination via Nonlinear Manifold Embeddings and a Convolutional Self-Attention Model
(Springer Wien, 2025) Mirza, Fuat Kaan; Oz, Usame; Hekimoglu, Mustafa; Aydemir, Mehmet Timur; Pural, Yusuf Enes; Baykas, Tuncer; Pekcan, Onder
Understanding nonlinear dynamics is critical for analyzing the hidden complexities of vibrational behavior in real-world systems. This study introduces a graph-theoretic approach to analyze the complex nonlinear temporal patterns in vibrational signals, utilizing the Tri-Axial Vibro-Dynamic Stone Classification dataset. This dataset captures high-resolution acceleration signals from controlled stone-crushing experiments, providing a unique opportunity to investigate temporal dynamics associated with distinct stone sizes. A 12-level Maximal Overlap Discrete Wavelet Transform is employed to perform multiscale signal decomposition, enabling the construction of transition graphs that encode transient and stable structural characteristics. Conceptually, transition graphs are analyzed as dynamic networks to uncover the interactions and temporal patterns embedded within vibrational signals. These networks are studied using a comprehensive suite of complexity metrics derived from information theory, graph theory, network science, and dynamical systems analysis. Metrics such as Shannon and Von Neumann's entropy evaluate signal dynamics' stochasticity and information retention. At the same time, the spectral radius measures the network's stability and structural robustness. Lyapunov exponents and fractal dimensions, informed by chaos theory and fractal geometry, further capture the degree of nonlinearity and temporal complexity. Complementing these dynamic measures, static network metrics-including the clustering coefficient, modularity, and the static Kuramoto index-offer critical discernment into the network's community structures, synchronization phenomena, and connectivity efficiency. Manifold learning techniques address the high-dimensional feature space derived from complexity metrics, with UMAP outperforming ISOMAP, Spectral Embedding, and PCA in preserving critical data structures. The reduced features are input into a convolutional self-attention model, combining localized feature extraction with long-term sequence modeling, achieving 100% classification accuracy across stone-size categories. This study presents a comprehensive framework for vibrational signal analysis, integrating multiscale graph-based representations, nonlinear dynamics quantification, and UMAP-based dimensionality reduction with a convolutional self-attention classifier. The proposed approach supports accurate classification and contributes to the development of data-driven tools for automated diagnostics and predictive maintenance in industrial and engineering contexts.
Citation - WoS: 11
Citation - Scopus: 14
Residual Lstm Neural Network for Time Dependent Consecutive Pitch String Recognition From Spectrograms: a Study on Turkish Classical Music Makams
(Springer, 2023) Mirza, Fuat Kaan; Gursoy, Ahmet Fazil; Baykas, Tuncer; Hekimoglu, Mustafa; Pekcan, Onder
Turkish classical music, characterized by 'makam', specific melodic configurations delineated by sequential pitches and intervals, is rich in cultural significance and poses a considerable challenge in identifying a musical piece's particular makam. This identification complexity remains an issue even for experienced musical experts, emphasizing the need for automated and accurate classification techniques. In response, we introduce a residual LSTM neural network model that classifies makams by leveraging the distinct sequential pitch patterns discerned within various audio segments over spectrogram-based inputs. This model's design uniquely merges the spatial capabilities of two-dimensional convolutional layers with the temporal understanding of one-dimensional convolutional and LSTM mechanisms embedded within a residual framework. Such an integrated approach allows for detailed temporal analysis of shifting frequencies, as revealed in logarithmically scaled spectrograms, and is adept at recognizing consecutive pitch patterns within segments. Employing stratified cross-validation on a comprehensive dataset encompassing 1154 pieces spanning 15 unique makams, we found that our model demonstrated an accuracy of 95.60% for a subset of 9 makams and 89.09% for all 15 makams. Our approach demonstrated consistent precision even when distinguishing makam pairs known for their closely related pitch sequences. To further validate our model's prowess, we conducted benchmark tests against established methodologies found in current literature, providing a comparative assessment of our proposed workflow's abilities.
Citation - WoS: 6
Citation - Scopus: 7
Decoding Compositional Complexity: Identifying Composers Using a Model Fusion-Based Approach With Nonlinear Signal Processing and Chaotic Dynamics
(Pergamon-elsevier Science Ltd, 2024) Mirza, Fuat Kaan; Baykas, Tuncer; Hekimoglu, Mustafa; Pekcan, Onder; Tuncay, Gonul Pacaci
Music, a universal medium that effortlessly transcends the confines of language and culture, serves as a vessel for the distinctive expression of a composer's ingenuity, particularly palpable through the elaborate symphony of melodies, harmonies, and rhythms. This phenomenon is acutely observable in the realm of Turkish Classical Music, where the identification of individual composers poses a formidable challenge due to a confluence of diverse stylistic expressions and sophisticated techniques. Shaped by centuries of cultural interchanges, this genre is celebrated for its convoluted rhythmic frameworks and deep melodic modes, often exhibiting fractal characteristics that compound the complexity of composer classification based on mere audio signals. In response to these complexities, this study introduces an advanced analytical paradigm that amalgamates Multi-resolution analysis, spectral entropy assessments, and a spectrum of multidimensional chaotic and statistical descriptors. By invoking chaos theory, the research delineates distinct patterns and features inherent to musical compositions, subsequently deploying these discoveries for composer categorization. Employing a model fusion-based strategy, the approach utilizes esteemed base estimators for section-level probabilistic determinations, subsequently amalgamated at the song level through a Long Short-Term Memory (LSTM) neural network model to classify a corpus of 380 compositions from 15 distinct composers. The results of this study not only highlight the efficacy of chaos-based approaches in Musical Information Retrieval but also provide a nuanced understanding of the unique characteristics of Turkish Classical Music, thus advancing the boundaries of how musicological data is scrutinized and conceptualized within scholarly discourse.