Recurrence network modeling and analysis of spatial data

Estimation of Carleman operator from a univariate time series

Reconstructing a nonlinear dynamical system from empirical time series is a fundamental task in data-driven analysis. One of the main challenges is the existence of hidden variables; we only have records for some variables, and those for hidden variables are unavailable. In this work, the techniques for Carleman linearization, phase-space embedding, and dynamic mode decomposition are integrated to rebuild an optimal dynamical system from time series for one specific variable. Using the Takens theorem, the embedding dimension is determined, which is adopted as the dynamical system's dimension. The Carleman linearization is then used to transform this finite nonlinear system into an infinite linear system, which is further truncated into a finite linear system using the dynamic mode decomposition technique. We illustrate the performance of this integrated technique using data generated by the well-known Lorenz model, the Duffing oscillator, and empirical records of electrocardiogram, electroencephalogram, and measles outbreaks. The results show that this solution accurately estimates the operators of the nonlinear dynamical systems. This work provides a new data-driven method to estimate the Carleman operator of nonlinear dynamical systems.

A novel methodology for emotion recognition through 62-lead EEG signals: multilevel heterogeneous recurrence analysis

Objective

Recognizing emotions from electroencephalography (EEG) signals is a challenging task due to the complex, nonlinear, and nonstationary characteristics of brain activity. Traditional methods often fail to capture these subtle dynamics, while deep learning approaches lack explainability. In this research, we introduce a novel three-phase methodology integrating manifold embedding, multilevel heterogeneous recurrence analysis (MHRA), and ensemble learning to address these limitations in EEG-based emotion recognition.

Approach

The proposed methodology was evaluated using the SJTU-SEED IV database. We first applied uniform manifold approximation and projection (UMAP) for manifold embedding of the 62-lead EEG signals into a lower-dimensional space. We then developed MHRA to characterize the complex recurrence dynamics of brain activity across multiple transition levels. Finally, we employed tree-based ensemble learning methods to classify four emotions (neutral, sad, fear, happy) based on the extracted MHRA features.

Main results

Our approach achieved high performance, with an accuracy of 0.7885 and an AUC of 0.7552, outperforming existing methods on the same dataset. Additionally, our methodology provided the most consistent recognition performance across different emotions. Sensitivity analysis revealed specific MHRA metrics that were strongly associated with each emotion, offering valuable insights into the underlying neural dynamics.

Significance

This study presents a novel framework for EEG-based emotion recognition that effectively captures the complex nonlinear and nonstationary dynamics of brain activity while maintaining explainability. The proposed methodology offers significant potential for advancing our understanding of emotional processing and developing more reliable emotion recognition systems with broad applications in healthcare and beyond.

Synthetic Genitourinary Image Synthesis via Generative Adversarial Networks: Enhancing Artificial Intelligence Diagnostic Precision

INTRODUCTION

In the realm of computational pathology, the scarcity and restricted diversity of genitourinary (GU) tissue datasets pose significant challenges for training robust diagnostic models. This study explores the potential of Generative Adversarial Networks (GANs) to mitigate these limitations by generating high-quality synthetic images of rare or underrepresented GU tissues. We hypothesized that augmenting the training data of computational pathology models with these GAN-generated images, validated through pathologist evaluation and quantitative similarity measures, would significantly enhance model performance in tasks such as tissue classification, segmentation, and disease detection.

METHODS

To test this hypothesis, we employed a GAN model to produce synthetic images of eight different GU tissues. The quality of these images was rigorously assessed using a Relative Inception Score (RIS) of 1.27 ± 0.15 and a Fréchet Inception Distance (FID) that stabilized at 120, metrics that reflect the visual and statistical fidelity of the generated images to real histopathological images. Additionally, the synthetic images received an 80% approval rating from board-certified pathologists, further validating their realism and diagnostic utility. We used an alternative Spatial Heterogeneous Recurrence Quantification Analysis (SHRQA) to assess the quality of prostate tissue. This allowed us to make a comparison between original and synthetic data in the context of features, which were further validated by the pathologist's evaluation. Future work will focus on implementing a deep learning model to evaluate the performance of the augmented datasets in tasks such as tissue classification, segmentation, and disease detection. This will provide a more comprehensive understanding of the utility of GAN-generated synthetic images in enhancing computational pathology workflows.

RESULTS

This study not only confirms the feasibility of using GANs for data augmentation in medical image analysis but also highlights the critical role of synthetic data in addressing the challenges of dataset scarcity and imbalance.

CONCLUSIONS

Future work will focus on refining the generative models to produce even more diverse and complex tissue representations, potentially transforming the landscape of medical diagnostics with AI-driven solutions.

Recurrence Network Analysis of Histopathological Images for the Detection of Invasive Ductal Carcinoma in Breast Cancer

The histopathological image analysis is one of the most crucial diagnostic procedures to identify Invasive ductal carcinoma (IDC) in breast cancers. However, this diagnosis process is currently time-consuming and heavily dependent on human expertise. Prior research has shown that different degrees of tumors present various microstructures in the histopathological images. However, very little has been done to utilize spatial recurrence features of microstructures for identifying IDC. This paper presents a novel recurrence analysis methodology for automatic image-guided IDC detection. We first utilize wavelet decomposition to delineate the subtle information in the images. Then, we model the patches with a weighted recurrence network approach to characterize the recurrence patterns of the histopathological images. Finally, we develop automated IDC detection models leveraging machine learning methods with spatial recurrence features extracted. The developed recurrence analysis models successfully characterize the complex microstructures of histopathological images and achieve the IDC detection performances of at least AUC = 0.96. This research developed a spatial recurrence analysis methodology to effectively identify IDC regions in histopathological images for BC. It shows a high potential to assist physicians in the decision-making process. The proposed methodology can further be applicable to image processing for other medical or biological applications.

Recurrence network analysis of design-quality interactions in additive manufacturing

Powder bed fusion (PBF) additive manufacturing (AM) provides a great level of flexibility in the design-driven build of metal products. However, the more complex the design, the more difficult it becomes to control the quality of AM builds. The quality challenge persistently hampers the widespread application of AM technology. Advanced imaging (e.g., X-ray computed tomography scans and high-resolution optical images) has been increasingly explored to enhance the visibility of information and improve the AM quality control. Realizing the full potential of imaging data depends on the advent of information processing methodologies for the analysis of design-quality interactions. This paper presents a design of AM experiment to investigate how design parameters (e.g., build orientation, thin-wall width, thin-wall height, and contour space) interact with quality characteristics in thin-wall builds. Note that the build orientation refers to the position of thin-walls in relation to the recoating direction on the plate, and the contour space indicates the width between rectangle hatches. First, we develop a novel generalized recurrence network (GRN) to represent the AM spatial image data. Then, GRN quantifiers, namely degree, betweenness, pagerank, closeness, and eigenvector centralities, are extracted to characterize the quality of layerwise builds. Further, we establish a regression model to predict how the design complexity impacts GRN behaviors in each layer of thin-wall builds. Experimental results show that network features are sensitive to build orientations, width, height, and contour space under the significant level α = 0.05. Thin-walls with the width bigger than 0.1 mm printed under orientation 0° are found to yield better quality compared to 60° and 90°. Also, thin-walls build with orientation 60° are more sensitive to the changes in contour space compare to the other two orientations. As a result, the orientation 60° should be avoided while printing thin-wall structures. The proposed design-quality analysis shows great potential to optimize engineering design and enhance the quality of PBF-AM builds.

Frequency spectrum recurrence analysis

In this paper, we present the new frequency spectrum recurrence analysis technique by means of electro-encephalon signals (EES) analyses. The technique is suitable for time series analysis with noise and disturbances. EES were collected, and alpha waves of the occipital region were analysed by comparing the signals from participants in two states, eyes open and eyes closed. Firstly, EES were characterized and analysed by means of techniques already known to compare with the results of the innovative technique that we present here. We verified that, standard recurrence quantification analysis by means of EES time series cannot statistically distinguish the two states. However, the new frequency spectrum recurrence quantification exhibit quantitatively whether the participants have their eyes open or closed. In sequence, new quantifiers are created for analysing the recurrence concentration on frequency bands. These analyses show that EES with similar frequency spectrum have different recurrence levels revealing different behaviours of the nervous system. The technique can be used to deepen the study on depression, stress, concentration level and other neurological issues and also can be used in any complex system.

Heterogeneous recurrence analysis of spatial data

Nonlinear dynamical systems often generate significant amounts of observational data such as time series, as well as high-dimensional spatial data. To delineate recurrence dynamics in the spatial data, prior efforts either extended the recurrence plot, which is a widely used tool for time series, to a four-dimensional hyperspace or utilized the network approach for recurrence analysis. However, very little has been done to differentiate heterogeneous types of recurrences in the spatial data (e.g., recurrence variations of state transitions in the spatial domain). Therefore, we propose a novel heterogeneous recurrence approach for spatial data analysis. First, spatial data are traversed with the Hilbert Space-Filling Curve to transform the variations of recurrence patterns from the spatial domain to the state-space domain. Second, we design an Iterated Function System to derive the fractal representation for the state-space trajectory of spatial data. Such a fractal representation effectively captures self-similar behaviors of recurrence variations and multi-state transitions in the spatial data. Third, we develop the Heterogeneous Recurrence Quantification Analysis of spatial data. Experimental results in both simulation and real-world case studies show that the proposed approach yields superior performance in the extraction of salient features to characterize and quantify heterogeneous recurrence dynamics in spatial data.

Heterogeneous Recurrence Analysis of Disease-Altered Spatiotemporal Patterns in Multi-Channel Cardiac Signals

Heart diseases alter the rhythmic behaviors of cardiac electrical activity. Recent advances in sensing technology bring the ease to acquire space-time electrical activity of the heart such as vectorcardiogram (VCG) signals. Recurrence analysis of successive heartbeats is conducive to detect the disease-altered cardiac activities. However, conventional recurrence analysis is more concerned about homogeneous recurrences, and overlook heterogeneous types of recurrence variations in VCG signals (i.e., in terms of state properties and transition dynamics). This paper presents a new framework of heterogeneous recurrence analysis for the characterization and modeling of disease-altered spatiotemporal patterns in multi-channel cardiac signals. Experimental results show that the proposed approach yields an accuracy of 96.9%, a sensitivity of 95.0%, and a specificity of 98.7% for the identification of myocardial infarctions. The proposed method of heterogeneous recurrence analysis shows strong potential to be further extended for the analysis of other physiological signals such as electroencephalogram (EEG) and electromyography (EMG) signals towards medical decision making.