Description:FIELD OF THE INVENTION:
The present invention relates to a system and method for detecting Parkinson’s disease using Graph Signal Processing and Deep Learning techniques. More particularly, the present invention relates to a system for detecting Parkinson’s disease by integrating visibility graph models and Pooling techniques for generating vertex-frequency plots from single-channel Electroencephalographic signals which act as optimal feature sets for detecting neurological changes in the brain to accurately classify Parkinson’s disease.

BACKGROUND OF THE INVENTION:
Parkinson’s Disease (PD) is one of the most common neurological diseases that severely affects the quality of life in many ways. It is a progressive disorder that affects the nervous system and the parts of the body controlled by the nerves, causing tremors, stiffness and slow movement. The disease can affect mobility, daily activities, emotional well-being, social support, cognition, communication and causes bodily discomfort. The progressive deterioration of dopamine-producing neurons in the human brain leads to the onset of PD, characterized by motor fluctuations and cognitive damage. Additionally, non-motor symptoms like depression, anxiety, speech disorders, and Rapid Eye Movement (REM) sleep behavior disorder adversely impact the physical and mental health of the people affected by PD. As per the data of the World Health Organization (WHO), globally, the prevalence of Parkinson disease (PD) has doubled in the past 25 years with the estimates of 2019 showing over 8.5 million individuals living with PD. About one percent of the elderly population continues to endure the challenges posed by this disease. The estimated prevalence of PD is expected to double by the year 2030.

Medications are more effective in slowing down the progression of Parkinson’s disease, if administered during the initial stages of PD. Therefore, early detection of Parkinson’s Disease is crucial to facilitate the effective management of neurodegenerative conditions associated with it. However, the early diagnosis of PD is beset with challenges, as the symptoms of PD are similar to those of many other neurological disorders and are less noticeable during the early stages. The diagnosis of PD is traditionally based on the observation of motor symptoms and assessment of clinical signs.

However, traditional diagnostic approaches may suffer from subjectivity as they rely on the evaluation of movements that are sometimes subtle to human eyes and therefore difficult to classify, leading to possible misclassification. In the meantime, early non-motor symptoms of PD may be mild and can be caused by many other conditions. Therefore, these symptoms are often overlooked, making early diagnosis of PD challenging. To address these difficulties and to refine the diagnosis and assessment procedures of PD, machine learning methods have been implemented for the classification of PD and healthy controls or patients with similar clinical presentations. Machine learning also allows for combining different modalities, such as magnetic resonance imaging (MRI) and single-photon emission computed tomography (SPECT) data in the diagnosis of PD. By using machine learning approaches, we may identify relevant features that are not traditionally used in the clinical diagnosis of PD and rely on these alternative measures to detect PD in preclinical stages or atypical forms. Currently, Parkinson’s disease diagnosis is done using various neuroimaging techniques, ranging from Electroencephalogram (EEG) at the basic level to Magnetic Resonance Imaging (MRI) at an advanced level. EEG signals are preferably considered for the early diagnosis of PD since it captures PD-related neural impairments.

Electroencephalography (EEG) is a non-invasive technique that records the electrical activity of the pyramidal neurons of the brain, via small sensors attached to the scalp, thus giving an indirect insight of their function with a great time resolution. A typical EEG display graphs voltages in the vertical domain and time on the horizontal domain, providing a near real-time display of ongoing cerebral activity. Due to its good temporal resolution, EEG data provides dynamic information on the electrical brain activity and connectivity. Early signs of PD can be detected from EEG signals, which capture the associated gradual impairments of cortical layers and subcortical structures of the brain, thus providing a comprehensive understanding of such neural dysfunctions. However, single-channel EEG signal analysis is affected by inter/intra-subjects’ variability and low signal-to-noise ratio as well as the stochastic nature of the signals. Moreover, EEG spectrograms fail to provide brain connectivity details. This calls for the development of diagnostic methods that are built-up on the EEG analysis technology to provide greater details of the brain interconnections for the early detection of the disease.

The field of neurological disorder detection has witnessed a rapid proliferation of techniques based on artificial intelligence (AI). Such computer-assisted AI-based detection systems are based on signal data received from imaging tests such as EEG, Electromyography (EMG), speech, and gait or image data from scans, handwriting, etc. This data is efficiently analyzed and interpreted to extract valuable insights from the complex patterns and features that may not be readily discernible to the human eye. By leveraging machine learning algorithms, AI systems can analyze medical images with speed and precision, aiding in the identification of early-stage diseases that may be difficult to detect through traditional methods. This early detection is crucial as it can lead to timely interventions, potentially saving lives and improving treatment outcomes. However, Traditional machine-learning approaches to PD detection have relied on handcrafted features derived from classical signal processing techniques.

Many works have been attempted in the recent past for detecting PD, by integrating AI with classical signal processing and network features. Jiji et. al., 2023 developed a framework to find a solution for early diagnose of PD by investigating the topological properties of functional brain networks within fMRI and EEG Signals wherein functional connectome is derived by thresholding partial correlation matrices of 160 regions from the Dosenbach brain atlas and subsequently six features were extracted. The extracted features from EEG signals and other inputs were provided as the input to adaboost classifier. The system produced 93.45% accuracy which was significantly higher when compared to earlier works.

Anjum et.al., 2020 developed Linear-predictive-coding EEG Algorithm for PD (LEAPD), a novel EEG-based signal processing approach to distinguish PD and control patients, which encodes EEG time series into features that can detect PD in a computationally fast manner amenable to real time applications.

Lee et.al., 2022 proposed a fast, accurate PD prediction method using the Hjorth parameter and the gradient boosting decision tree (GBDT) algorithm, which distinguished PD patients from controls with an accuracy of 89.3%.

Karakas et.al., 2023 proposed a novel method that utilized the reduced beta activity and amplitude decrease in EEG signals that are associated with PD, wherein, the preprocessed EEG signals were classified using features obtained from gray-level co-occurrence matrix (GLCM) through the Hankelization of EEG signals, which involves projecting a one-dimensional (1D) signal into a two-dimensional (2D) picture. The performance of classifiers with these novel features was evaluated using extensive cross-validations (CV) and leave-one-out cross-validation (LOOCV) schemes. The method gave approximately 90% accuracy in Clinical vs. pathology-confirmed diagnoses.

The aforementioned techniques exhibit limitations in concurrently learning functional and structural information from the data. While Deep Learning (DL) techniques eliminate the need for handcrafted features, they often result in an incomplete data representation. Improved performance has been reported with hybrid models that combine data-derived features with deep learning methods. Recent research has demonstrated that modeling the EEG data as a network yields hitherto unknown insights into the structural connectivity of the data points. Graph theory and network analysis of various networks derived from EEG contribute a number of measures that can effectively predict the alterations in brain functionality.

Notwithstanding, these techniques exhibit limitations in capturing the underlying relationships among the EEG data points. In addition to network modeling of EEG data, EEG can be defined as a graph signal residing on the vertices of a network learned from the signal itself, which can accurately represent the brain’s functional, structural connectivity, and electrical activities. EEG can be effectively represented as graphs, with each data point as a node and their pairwise interconnection as edges. Typically, nodes represent brain regions and edges represent synapses, pathways, or statistical dependencies between neural units. The strength of each interconnection is reflected in the associated weights, representing the similarity between the nodes to which it is connected. The resulting network representation and EEG signals are complementary and ideally should be analyzed together, though this has remained a challenge due to the lack of appropriate techniques.

In view of the deficiencies of the previously reported techniques in efficient early diagnosis of PD, we disclose herein a novel system and method for early PD detection integrating Graph Signal Processing (GSP) and DL techniques. The proposed research focuses on the relatively unexplored domain of GSP-based EEG features and the application of such features for PD detection using DL models. Graph Signal Processing (GSP) is, as its name implies, signal processing applied on graphs. GSP is an emerging field which provides a flexible framework to model and analyze Electroencephalogram (EEG) signals that exhibit intricate relationships and dependencies that traditional signal processing methods may not effectively capture. Of late, GSP has forayed into multiple domains ranging from detecting stress in smart grids to detecting neural disorders such as attention deficit hyperactivity disorders (ADHD), epilepsy, and brain activity analysis.

OBJECT OF THE INVENTION:
In order to obviate the drawbacks of the existing state of the art, the present invention discloses a system and method for early detection of Parkinson’s disease by integrating Graph Signal Processing (GSP) and Deep Learning (DL) techniques.

The main object of the present invention is to develop a system for detecting Parkinson’s disease by defining and analyzing graph signals from single-channel Electroencephalogram data using an optimal combination of visibility graph algorithms and pooling techniques.

Another object of the invention is to develop a system and program for converting single-channel EEG signals to graph signals and deriving GSP-based features that effectively combine structural and functional neurological information of the brain.

Another object of the invention is to develop a system for the identification of an optimal combination of visibility graph and pooling techniques for deriving graph signals from single-channel EEG signals, namely, Weighted Natural Visibility Graph with Maximum-Pooling (WNVG-Max) graph signal modeling algorithm, which offers superior results.

Another object of the invention is to develop a system for deriving vertex-frequency plots from graph signals, which serve as an optimal Graph Signal Processing (GSP)-based feature set for enhancing classification accuracy.

Another object of the invention is to develop a system and method for the identification of optimal channels for Parkinson’s Disease detection using the novel GSP-based feature set.

Another object of the invention is to develop a system for benchmarking the performance of classical signal processing (Time-frequency spectrograms) and network-based approaches (Adjacency matrix heatmaps) on the optimized channels.

Another object of the invention is to develop a system for validation of GSP-based feature set for Parkinson’s Disease detection using Deep Learning techniques.

SUMMARY OF THE INVENTION:
The present invention discloses a system and method for early detection of Parkinson’s disease by integrating Graph Signal Processing (GSP) and Deep Learning (DL) techniques. Graph signals are derived from single-channel Electroencephalographs by a novel generic algorithm combining visibility graph algorithms and pooling techniques. Vertex-frequency plots are generated from the derived graph signals which act as GSP-based features that effectively combine structural and functional neurological information. The performance of these newly derived vertex-frequency features was evaluated on Parkinsons disease datasets of the University of New Mexico and the University of Iowa using Deep Learning (DL) architectures such as Vision Transformer and Residual Network-50. An optimal combination of visibility graph and pooling techniques namely Weighted Natural Visibility Graph with Maximum-Pooling (WNVG-Max) graph signal modeling algorithm was identified to accurately classify Parkinson’s disease based on neurological changes detected in the brain.
The novel system of the present invention for early detection of Parkinson’s disease comprises of a series of interconnected modules, synergistically extracting relevant neurological information from single-channel EEG signals which are converted into graph signals and subsequently represented as vertex-frequency plots which act as GSP-based features for accurate classification of Parkinson’s disease.

The performance of features based on classical signal processing and network-based features were evaluated on the same datasets using the DL models. Vertex-frequency features derived using WNVG-Max algorithm outperformed the other techniques by yielding a classification accuracy of 99.5%. The novel methodology used in the invention which integrates Graph Signal Processing with Deep Learning techniques, offers promising results with enhanced accuracy and facilitates early intervention strategies. Use of vertex-frequency plots derived from single-channel graph signals, utilizing a combination of visibility graph algorithms and pooling techniques, presents the key novel aspect of the invention. Since these graph signals encapsulate structural and functional information, vertex-frequency spectrograms provide superior insights into neural activities than ordinary time-frequency spectrograms. Leveraging GSP techniques, the invention also proposes a set of optimal top-performing channels that yield superior results for PD detection. As a result, this GSP-based PD detection integrating DL models exhibits superior performance when compared to existing methodologies.

BRIEF DESCRIPTION OF THE DRAWINGS:
Fig. 1: depicts Block diagram representation of proposed methodology.
Fig. 2: depicts Graph signals derived from Health Control (HC) EEG.
Fig. 3: depicts Graph signals derived from Parkinson’s Disease (PD) EEG.
Fig. 4: depicts the ViT architecture.
Fig. 5: depicts Vertex-frequency plots of Graph Signals of HC and PD.
Fig. 6: depicts Accuracy vs. Epoch curves of ViT and ResNet-50 using vertex-
frequency plots derived from WNVG-Maxpooling graph signals of UI dataset and WNVG-Minpooling graph signals of UNM dataset.
Fig. 7: depicts the confusion matrix of ViT and Residual Network-50 when trained
with vertex-frequency plots.
Fig. 8: depicts the Top-performing channels and channel positions of UNM and UI
datasets.
Fig. 9: depicts HC and PD EEG Spectrograms of TP8, the top-performing channel
of UI dataset.
Fig. 10: depicts adjacency matrix Heatmaps of WNVG Max-pooling graph signal
derived from channel TP8 of HC and PD EEG
Fig. 11: depicts Comparison of PD classification performance based on GSP-based
vertex-frequency features, CSP-based time-frequency spectrograms, and network-based adjacency matrix heatmaps derived from UNM and UI datasets using Vision Transformer (b) ResNet-50.
Fig. 12: depicts the Flow Chart of GSP-based PD detection system

DETAILED DESCRIPTION OF THE INVENTION:
Parkinson’s disease (PD) is a chronic and progressive movement disorder that affects the nervous system, and the parts of the body controlled by the nerves. The progressive deterioration of dopamine-producing neurons in the human brain leads to the onset of PD characterized by motor as well as non-motor symptoms. Symptoms of the disease start slowly, and often begin on one side of the body with noticeable tremor in just one hand and usually remain worse on that side, even after symptoms begin to affect the limbs on both sides. Tremors are common, but the disorder also may cause stiffness or slowing of movement. The progressive symptoms of PD may vary from person to person, but some common symptoms include tremors, bradykinesia, rigid muscles, impaired posture and balance, loss of automatic movements, speech changes, dementia, sleep disorders and involuntary movements. Symptoms get worse over time and there is no cure for the disease, but therapies and medicines can reduce symptoms. However, medications are more effective in slowing down the progression of this disease, when administered during the initial stages. Therefore, early detection of PD is crucial to facilitate the effective management of this neurodegenerative condition. However, the early diagnosis of PD is beset with challenges, as the symptoms of PD are similar to those of many other neurological disorders and are less noticeable during the early stages as well.

Currently, disease diagnosis is done using various neuroimaging techniques, ranging from Electroencephalogram (EEG) at the basic level to Magnetic Resonance Imaging (MRI) at the advanced level. Early signs of PD can be detected from EEG signals, which capture the associated impairments of cortical layers and subcortical structures of the brain. Thus, EEG spectrograms provide a comprehensive understanding of neural dysfunctions which is a hallmark of the degeneration of brain caused by PD. However, EEG fails to provide the intricate, dynamic, and nonlinear interactions between the anatomical constituents of the brain which remain hidden within the EEG recordings, surpassing the observational capabilities of even highly trained physicians in the field. These connectivity details give insights into the neurological degradation of the brain causing loss in neural connectivity which are manifested even in the early stages of PD. To mitigate this shortcoming, EEGs have been represented as graphs, with each data point as a node and their pairwise interconnection as edges. Nodes represent brain regions and edges represent synapses, pathways, or statistical dependencies between neural units. The strength of each interconnection (edges) is reflected in the associated weights, representing the similarity between the nodes to which it is connected. Since EEG signals and the network representation as graphs are complementary, their simultaneous analysis is presumed to provide a wholesome view encompassing both structural as well as functional changes in the brain. Graph signal processing (GSP) is a vibrant branch of signal processing models and algorithms that aims at handling data supported on graphs. GSP has been used to study the EEG signals which are represented as graphs. Recent advances in Graph Signal Processing (GSP) heralded a new era of potent techniques for analyzing signals defined over networks in a domain-agnostic manner. As a result, GSP can capture the underlying data pattern, which helps to unveil the hidden relationships among the data points. However, there is a lack of technology which could adequately reproduce the EEG signals as complementary graphs which accurately represent brain interconnections.

To mitigate these challenges, the present invention discloses a system and method for detecting Parkinson’s disease integrating Graph Signal Processing (GSP) and Deep Learning (DL) techniques to extract relevant information of the changes in neural interconnections of the brain which manifest as Parkinson’s disease (PD). More particularly, the present invention discloses a system for detecting PD by integrating visibility graph algorithms or models (VGA/VGM) and Pooling techniques (PT) for generating vertex-frequency plots (VFP) from single-channel Electroencephalographic (EEG) signals. The vertex-frequency plots are generated using a novel graph signal modeling algorithm and act as optimal feature sets for detecting neurological changes in the brain to accurately classify Parkinson’s disease (PD).

The system of the invention comprises of a series of interconnected modules which extract relevant features from single-channel EEG signals. EEG signals are captured using a Brain Vision system with 64 Ag/AgCl electrodes at a sampling rate of 500 Hz. Preprocessing operations are performed with EEGLAB software, Python programming environment is used for Graph signal modeling from single-channel EEG signals. Further, vertex frequency plots are generated from these graph signals using MATLAB R2021a. Finally, these derived vertex-frequency plots are classified into PD and HC using DL models such as ViT and ResNet-50. DL models are implemented using Python software.

Conventional electroencephalogram (EEG) signals are transformed to EEG graph signals using a novel graph signal modeling algorithm, where EEG amplitudes are defined over the vertices of the associated network representation. Vertex-frequency plots (VFP) which are joint representations of vertex and spectral domain of graph signals, are generated from the EEG graph signals. These offer a new set of potential features which are leveraged for the detection of neurological symptoms of PD.

An optimized algorithm, WNVG-Max, developed in the course of the invention, maximizes the classification accuracy of PD detection and provides insights about the top-performing EEG channels that capture significant neurological variations associated with PD. Vertex-frequency features are obtained from these graph signals which are classified using various deep learning (DL) models such as Vision Transformer (ViT) and Residual Network-50 (ResNet-50). In order to assess the efficacy of the GSP-based features obtained by using the system of the present invention, a comparative evaluation of PD detection was done using classical features that are not GSP-based, such as time-frequency spectrograms, and adjacency matrix heatmaps derived from the top performing channels. The Vertex-frequency features derived using WNVG-Max algorithm outperformed the other techniques by yielding a classification accuracy of 99.5%. The novel system and method of the present invention which integrates GSP with DL techniques, offers promising results with enhanced accuracy for facilitating early intervention strategies.

The system of the present invention is designed to achieving the following outputs:
Defining graph signals by combining structural and functional information from EEG data using an optimal combination of visibility graph algorithms or models (VGA/VGM) and pooling techniques: WNVG-Max Algorithm.
Using graph signals to derive vertex-frequency plots (VFP), which serve as optimal features with enhanced accuracy by precisely capturing the neurological changes from EEG.
Validating GSP-based feature set for Parkinson’s Disease (PD) detection using Deep Learning (DL) techniques.
Identifying top-performing channels associated with high classification accuracy for PD detection using the novel GSP-based feature set.
Validating the superiority of the GSP-based methodology by benchmarking the performance of classical signal processing (Time-frequency spectrograms) and network-based approaches (Adjacency matrix heatmaps) on these top-performing channels.
The processes and approaches used for developing the invention have been explained below:

Graph Signal Processing
Graph Signal Processing defines the signals on vertices of a graph. It offer a precise representation of both structural connectivity and signal amplitude variations. GSP is considered an extension of classical signal processing (CSP) to a non-euclidean domain, such that we can adopt various classical signal processing concepts with minor modifications in graph signal scenario. A weighted graph with M vertices is modeled as G(V,E,W) where V = {1,2,3,...,M} is the set of vertices, E is the edge set connecting pair of vertices, and W represents the weights associated with each edge. W is an MXM matrix and each element〖 W〗_( ij) has a value if the node i and j are connected, 〖 W〗_( ij) = 0 if they are not connected. All the non-zero 〖 W〗_( ij) values are unity in the case of an unweighted graph. The non-negative real-valued elements of this matrix represent the nature of vertex connectivity of the graph and are called adjacency matrix or weighted adjacency matrix. In an undirected graph model without self-loops, the weighted adjacency matrix is symmetric with zero diagonal elements. The degree matrix D is a diagonal matrix where each diagonal element D_(j j) indicates the summation of all edge weights connected to j^th vertex. Degree of a vertex j, D_(j j) =∑_i▒〖 W〗_( ij) also helps reveal each vertex’s significance. Another meaningful representation of graph connectivity is given by the Laplacian matrix L, which combines the weighted adjacency matrix and degree matrix, L = D - W. Laplacian matrix constitutes non-negative real-valued diagonal elements, and its off-diagonal positions are occupied by negative real-valued entries. The normalized form of the graph Laplacian matrix is given by:
L_norm=D^((-1)/2) LD^((-1)/2)

Graphs Fourier Transform (GFT)
Graph Laplacian matrix bridges the gap between GSP and CSP by extending basic CSP operations to vertex domains. In GSP, the notion of frequency is conveyed by the variation of eigenvalues 〖{λ_i}〗_(i=1,2,3,...,N) corresponding to the eigenvectors 〖{u_i}〗_(i=1,2,3,...,N) . The GFT, X(λ_i) of a graph signal x[n]ϵR^N defined on the nodes of a graph G indexed by vertices 〖{v_n }〗_(n=1,2,3,...,N ) is given by:
X(λ_i) = ⟨ 𝑥, u_i ⟩ =∑_(n=1)^N▒〖x[n] u_i [n]〗

Similarly, the Inverse GFT (IGFT) is given by
x = IGFT {X} = UX

x[n]=∑_(i=1)^N▒〖X(λ_i) u_i [n]〗
Therefore, GFT can be interpreted as an expansion of graph signal in terms of eigenvectors of its graph Laplacian matrix [28, 27].
Windowed Graph Fourier Transforms (WGFT)
The localized windowed signal spectrum is obtained by multiplying the graph signal x[n] with a localization window . WGFT of a graph signal x[n] is defined as,
S(m,i) =∑_(n=1)^N▒x[n] h_m [n]u_i [n]
Selecting a suitable localization window function is crucial in WGFT-based vertex domain analysis. As in the case of STFT, WGFT also requires an optimum window for providing a vertex-frequency representation with considerable resolution in both the vertex and the spectral domains. The window must include the current and its neighborhood vertices and is also required to confine the signal content around the given vertex m. S(m,i) are the elements of WGFT matrix S and each column of S is given by,

S_m=GFT{x[n] h_m [n]}=U^T 〖x_h〗_m

where 〖x_h〗_m is the windowed graph signal, which is the product of signal samples with localization widow centered around vertex m. Localization windows can be defined in vertex and spectral domains. In the present invention, graph signals derived from single-channel EEG signals using the novel graph signal modeling algorithm are further subjected to the Windowed Graph Fourier Transform (WGFT) to generate the appropriate vertex-frequency representation.

Visibility Graph (VG)
Visibility graph algorithms enable us to use different graph theory concepts in analyzing time series data. This algorithm maps each amplitude of the time series data into graph vertices. A connection is established among two such nodes if visibility exists between them. Visibility graphs preserve the structural properties of the time series by mapping periodic series into regular graphs, random time series to random graphs, and fractal time series to scale-free graphs.

Natural Visibility Graph (NVG)
For NVG, the following criteria ensure visibility between two arbitrary amplitudes of the time series, (t_i,〖 x〗_i) and (t_j,〖 x〗_j) with an intermediate data sample (t_k,〖 x〗_k):
〖 x〗_k<〖 x〗_j+(〖 x〗_i-〖 x〗_j)(t_j-t_k)/(t_j-t_i )
Where t_i x_k for all k,such that i < k < j
The present invention aims to advance the traditional EEG analysis by integrating advanced GSP-based approaches, thereby improving classification performance. Instead of performing traditional EEG analysis, EEG graph signals are generated, and GSP-based techniques are applied to them to derive enhanced features. The approach on Parkinson’s Disease EEG datasets is evaluated and DL techniques are applied for PD detection.

The method involves preprocessing of the single-channel EEG signal data comprising average re-referencing, bandpass filtering, down sampling, and Independent Component Analysis for eye movement artifact removal. The system of the present invention comprises of a series of modules working interconnectedly to derive vertex frequency plots from single-channel EEG signals for classifying PD.

Fig.1 illustrates the block diagram representing the system of the present invention. The Conversion module (CM) is configured to convert single-channel Electroencephalogram (EEG) signals from PD and Healthy Control (HC) subjects into networks using visibility graph programs (VGPs). The Graph Signal Generation Module (GSGM) is configured to generate graph signals by defining pooled EEG amplitudes on the vertices of these networks. EEG epochs are subdivided into smaller segments to which three different dimensionality reduction techniques are applied namely, Maximum pooling (Max-pooling), Minimum pooling (Min-pooling), and Average-pooling (Avg-pooling). This results in three sets of EEG amplitudes corresponding to the applied pooling operation. Further, three different visibility graph algorithms are applied namely, Natural, Horizontal, and Weighted Natural to these pooled sets of EEG amplitudes, resulting in nine different visibility graphs from each epoch. Subsequently, meaningful representations of the connectivity-functional information are generated in the form of graph signals by defining pooled EEG amplitudes on the vertices of these networks. This comprehensive procedure is executed for all epochs of a specific channel across all subjects within the PD and Healthy Control (HC) groups. The Vertex-Frequency Plot Generation Module (VFPGM) which is configured to generate vertex-frequency plots from the graph signals using windowed graph Fourier transforms (WGFT), generates the vertex-frequency plots (VFP) from graph signals derived from each epoch of a single-channel EEG signal. Thereafter, the Performance Assessment Module (PAM) which is configured to assess the performance of the vertex-frequency plots in PD detection using DL models, assesses the performance of each of these nine vertex-frequency plots (VFP) in PD detection using two DL models, viz. Vision Transformer (ViT) and Transfer Learning with pre-trained network ResNet-50. The same analysis is repeated for all the channels to identify the best sensitive channel and DL model suitable for PD detection. The graph signal with an optimized combination of the visibility graph algorithm (VGA) and pooling technique (PT) that maximizes the classification accuracy are identified. This is followed by a comparative evaluation of PD detection using non-GSP classical features derived from the top-performing channels to validate the efficiency of the novel GSP-based approach.

Dataset
Datasets were obtained from publicly available repositories of the University of New Mexico (UNM) and the University of Iowa (UI) for developing the invention and assessing its performance. The UNM dataset included 27 EEG recordings each (17 male and 10 female subjects) in PD and healthy control (HC), whereas the UI dataset had 14 (6 male and 8 female) subjects each across the PD and healthy categories (HC). In both these datasets, the EEG signals were recorded using a Brain Vision system with 64 Ag/AgCl electrodes at a sampling rate of 500 Hz. CPz is the reference channel for the UNM dataset, while Pz is the reference channel for the UI dataset. As both repositories contain EEG recordings with different reference channels, the remaining 62 channels common to both datasets were selected. The two repositories contain resting-state EEG recordings with eyes open. Effectively, the EEG recordings of 41 PD patients and 41 healthy controls were analyzed. To ensure demographic matching between diseased and healthy populations, the selection of healthy controls was based on characteristics such as age, gender, education, and premorbid intelligence comparable to those of the PD population.

Preprocessing
The experiments were conducted primarily in MATLAB and Python programming environments. While MATLAB R2021a was used to define graph signals and generate Vertex-frequency plots, Python was used to realize the transfer learning and ViT approaches for PD classification. Average re-referencing to the raw EEG signals was initially applied to mitigate the effect of artifacts on the signal of interest. Subsequently, the EEG recordings were subjected to a band-pass filter with a pass band frequency range of 0.5 to 45 Hz, which preserves the low-frequency region, since the information crucial for differentiating PD from HC primarily resides in the low-frequency bands of the EEG spectrum. Additionally, modeling these EEG signals with a sampling frequency of 500 Hz as a graph signal increases computational complexity, given the substantial number of vertices and edges generated. Hence, the data was down-sampled to a frequency of 128 Hz to ensure that the low-frequency content of the signal remains distortion-free. Furthermore, independent component analysis (ICA) was utilized to remove the ICA components corresponding to eye movement artifacts. Additionally, EEG signals were segmented into 10-second epochs with a 5-second overlap, assuming the similarity of demographics across all segments.

Graph Signal Modeling: A novel generic algorithm
After preprocessing, the down-sampled 128 Hz EEG signals contained 1280 samples per epoch. Considering the overheads of converting each epoch to a graph with 1280 nodes, each epoch was subdivided into 64 groups of 20 samples each. Three different pooling techniques were evaluated, viz. min-pooling, max-pooling, and avg-pooling, for dimensionality reduction in each sub-group. As a result, each epoch was downscaled to 64 EEG data samples that can now be easily represented as a graph with 64 nodes. Each epoch was transferred with 64 pooled amplitudes into three different visibility graphs using Natural, Weighted Natural, and Horizontal visibility graph algorithms. Further, graph signals were modelled by defining the corresponding pooled amplitudes over the vertices of the derived graph. This process resulted in nine different graph signals by combining three sets of pooled amplitudes with three visibility graph algorithms.

Algorithm (program) 1 presents a generalized sequence of steps involved in modeling graph signals G_z from raw EEG X∈R^MXN with M channels and N samples in each channel. Fig. 2 and Fig. 3 illustrate the graph signals derived using WNVG, NVG, and HVG with max, min, and average-pooled amplitudes from HC and PD EEGs, respectively.
PD detection using Deep Learning models
In recent years, AI-assisted diagnostic systems have significantly impacted the diagnosis of neurodegenerative diseases. The present invention includes two different DL approaches to PD detection: ResNet-50 pre-trained model and Vision Transformers (ViT). ResNet-50 is one of the most powerful pre-trained networks that has residual connections. This enables them to learn residual functions without vanishing gradient problems. ViT helps capture global context information from images without introducing image-specific inductive biases into the architecture. In ViT, linearly embedded fixed-size patches of vertex-frequency plots are fed into a transformer encoder after adding positional embeddings. Fig.4 demonstrates the basic ViT architecture with vertex-frequency plots as the input. Table 1 below lists the hyperparameters used for the DL architectures. Both the DL models follow a 60:20:20 ratio for the train-validation-test split respectively with a non-overlapping test set.

Table 1: Hyperparameters used in Deep Learning (DL) architecture
Hyperparameters ViT ResNet-50
Learning rate 2𝑒−6 0.0001
Batch size 16 64
Dropout 0.1 0.5
Number of heads 12 -
Gamma 0.96 -
Image size 224 224
Patch size 16 -
classes 2 2
Optimizer Adam sgd
Loss Cross Entropy Cross Entropy

Experimental Evaluation
PD and HC EEG signals were analyzed using novel GSP-based vertex-frequency features derived from nine different graph signals. Two DL models were applied for this analysis: ResNet-50 and ViT to demonstrate the potential and consistency of the newly derived GSP-based vertex-frequency features in capturing PD-related neurological changes with basic and advanced DL architectures respectively. Finally, to highlight the superiority of the vertex-frequency features, the findings were validated by applying the same DL models on the time-frequency plots and heat maps of the graph adjacency matrices generated from top-performing channels.

Analysis using Vertex-frequency plots
Analogous to the time-frequency representations of non-stationary signals in Classical Signal Processing (CSP), the vertex-frequency representations in GSP effectively portray graph signals with vertex-varying spectral components. Weighted Graph Fourier Transform (WGFT), the vertex domain counterpart of Short-Graph Fourier Transform (STFT) was used in this work to derive vertex-frequency plots (VFP) from the graph signals. Translation and modulation are two underlying operations of WGFT. Translation of window function in vertex domain is equivalent to taking Inverse Graph Fourier Transform (IGFT) of the product of GFT of window function and GFT of delta function centered at that particular node. Modulation in the vertex domain can be done by multiplying the window function with an eigenvector of the graph Laplacian.

The nine graph signals obtained from the three visibility graph algorithms and three pooling techniques were converted to their corresponding vertex-frequency plots and classified using the DL models. The performance of each graph signal was compared in detecting PD from HC. Fig. 5 (a) and (b) illustrate vertex-frequency plots of HC and PD subjects defined using WNVG-Max algorithm. Table 2 shows the accuracy and F1 score of ViT in classifying vertex-frequency plots of graph signals derived from UNM and UI datasets. They also capture the corresponding visibility graph algorithms and pooling techniques used for defining the graph signals. Additionally, we report the best channel that forms the basis for these graph signals.

Table 2: Performance of ViT in PD detection of UNM and UI dataset using vertex-frequency plots.
UNM UI
Graph Signals F1 Score Accuracy Channel F1 Score Accuracy Channel
WNVG-Max 0.9931 0.9937 TP8 0.9950 0.9950 TP8
WNVG-Min 0.9832 0.9826 TP8 0.9595 0.9596 TP8
WNVG-Avg 0.9699 0.9699 TP8 0.9872 0.9876 TP8
NVG-Max 0.8573 0.8576 TP9 0.6434 0.6500 P4
NVG-Min 0.9273 0.9272 TP8 0.9576 0.9577 TP8
NVG-Avg 0.8581 0.8594 TP8 0.9651 0.9652 TP8
HVG-Max 0.7668 0.7674 P6 0.6340 0.6342 P6
HVG-Min 0.6343 0.6326 P6 0.6718 0.6720 P6
HVG-Avg 0.6213 0.6204 TP9 0.6760 0.6755 P6

The performance of the GSP-based PD detection system is evaluated using accuracy.

where, TRP, TRN, FLP, and FLN are the count of true positive, true negative, false positive, and false negative subjects, respectively. Graph signal is derived from that particular EEG channel.

Similarly, table 3 illustrates the effectiveness of yet another pre-trained DL model, ResNet-50, in PD detection over UNM and UI datasets. The vertex-frequency analysis identifies WNVG with max pooled amplitudes as the best-performing graph signal modeling algorithm -WNVG-Max algorithm.

Thereafter, the top channels exhibiting superior performance in PD detection were identified using the WNVG-Max algorithm. Figure 8 (a) depicts the classification accuracies of these optimal channels rank ordered across UNM and UI datasets and figure 8 (b) demonstrates the optimal channel position highlighted on a topoplot.

Table 3: Performance of ResNet-50 in PD detection of UNM and UI dataset using vertex-frequency plots
UNM UI
Graph Signals F1 Score Accuracy Channel F1 Score Accuracy Channel
WNVG-Max 0.9411 0.9417 TP8 0.9890 0.9891 TP8
WNVG-Min 0.9726 0.9708 TP8 0.9845 0.9847 TP8
WNVG-Avg 0.9587 0.9584 TP8 0.9767 0.9765 TP8
NVG-Max 0.9706 0.9707 TP8 0.7756 0.7915 P6
NVG-Min 0.9709 0.9701 TP8 0.9562 0.9561 TP8
NVG-Avg 0.8098 0.8155 TP8 0.9560 0.9563 TP8
HVG-Max 0.7755 0.7850 P8 0.9787 0.9790 TP8
HVG-Min 0.7183 0.7193 P6 0.9681 0.9674 TP8
HVG-Avg 0.6871 0.6882 P6 0.8347 0.8504 PO8

The top-performing channels of the UNM dataset are TP8, PO8, P6, TP9, and P8, while those of UI are TP8, PO8, P6, CP5, and P4. Three channels viz. TP8, PO8, and P6 are common across both datasets. Fig. 6 shows training and validation accuracies of ViT and ResNet-50 using WNVG graph signals for UI and UNM datasets. The confusion matrix of ViT trained using vertex-frequency plots derived from WNVG-Max graph signals of UI and UNM dataset are given in Fig.7 (a) and (b). Fig.7 (c) and (d) present the confusion matrix of ResNet-50 when trained using vertex-frequency plots derived from WNVG-Min graph signal of UNM and WNVG-Max graph signal of UI datasets respectively.

As PD exhibits specific temporal and spectral characteristics, time-frequency analysis helps to capture such distinct variations, therefore standard analysis in the time-frequency domain was used to validate the novel vertex-frequency analysis approach of the present invention in PD detection. The time-frequency spectrograms derived from the top-performing channels of UNM and UI datasets were classified using the aforementioned DL models. Fig. 9 illustrates the time-frequency spectrograms of HC and PD subjects. Tables 4 and 5 list the classification performances of ViT and ResNet-50 in PD detection using time-frequency spectrograms derived from the top five channels of UNM and UI, respectively.

Table 4: Performance of ViT in PD detection of UNM and UI datasets using time-frequency spectrograms
UNM UI
Channel F1 Score Accuracy Channel F1 Score Accuracy
TP8 0.8055 0.8066 TP8 0.7203 0.7209
TP9 0.8012 0.8015 P6 0.7512 0.7513
PO8 0.7810 0.7815 P4 0.8011 0.8010
P6 0.8077 0.8077 CP5 0.8077 0.8077
P8 0.7848 0.7895 PO8 0.8664 0.8739

Table 5: Performance of ResNet-50 in PD detection of UNM and UI datasets using time-frequency spectrograms
UNM UI
Channel F1 Score Accuracy Channel F1 Score Accuracy
TP8 0.7266 0.7261 TP8 0.8813 0.8809
PO8 0.7770 0.7759 PO8 0.9123 0.9147
TP9 0.7221 0.7344 P6 0.8144 0.8148
P8 0.7604 0.7593 P4 0.7728 0.7735
P6 0.4254 0.5145 CP5 0.8099 0.8085

Finally, the UNM and UI datasets were analyzed using the vertex interconnections. Adjacency matrices of WNVG-max pooled networks were generated from top-performing channels of UNM and UI datasets. These adjacency matrices were then transformed into heatmaps and classified using the same DL models. Adjacency matrix heatmaps provide an interpretable visual representation of connectivity patterns of the network and help to identify structural anomalies associated with PD. Fig. 10 illustrates the adjacency heatmaps obtained from EEG of HC and PD, respectively. Tables 6 and 7 describe the performances of ViT and ResNet-50 for detecting PD using Adjacency matrix heatmaps derived from the top five channels of UNM and UI, respectively.

Table 6: Performance of ViT in PD detection of UNM and UI datasets using Adjacency matrix heatmaps
UNM UI
Channel F1 Score Accuracy Channel F1 Score Accuracy
TP8 0.8353 0.8361 TP8 0.9533 0.9531
P6 0.8320 0.8321 P6 0.8196 0.8261
PO8 0.5566 0.5605 PO8 0.6062 0.6070
TP9 0.6889 0.6899 CP5 0.6491 0.6468

P8 0.6714 0.6729 P4 0.6622 0.6617

Table 7: Performance of ResNet-50 in PD detection of UNM and UI datasets using Adjacency matrix heatmaps
UNM UI
Channel F1 Score Accuracy Channel F1 Score Accuracy
TP8 0.8448 0.8513 TP8 0.9372 0.9369
P6 0.8153 0.8162 P6 0.8131 0.8638
PO8 0.6682 0.7391 PO8 0.6571 0.6584
TP9 0.6447 0.6449 CP5 0.6418 0.6422
P8 0.6111 0.6137 P4 0.5464 0.5466

It was observed that the vertex-frequency plots of graph signals obtained from weighted natural visibility graphs with max-pooled amplitude of UI dataset, when passed through the Vision Transformer, yielded the highest classification accuracies of 99.50%. Additionally, the WNVG-Max algorithm applied to UNM dataset demonstrated a comparable accuracy of 99.37%. The WNVG graph signals generally exhibit more than 95% classification accuracy across all three pooling techniques on both datasets. ViT achieves classification accuracies of more than 85% and 95% for most Natural Visibility Graph (NVG) graph signals derived from UNM and UI datasets, respectively. However, Horizontal Visibility Graph (HVG) graph signals from both datasets demonstrate the lowest performance in PD detection. Similar trends were observed in the classification results using ResNet-50, where classification accuracies higher than 90% are obtained from all WNVG and most NVG graph signals. HVG graph signals obtained from the UNM dataset exhibit lower classification accuracies than similar categories of graph signals derived from UI.

Thus, the Weighted Natural Visibility Graph with Max-Pooling (WNVG-Max) algorithm emerged as the ideal combination of visibility graph algorithms and pooling techniques for modeling graph signals. Vertex-frequency analysis was repeated across all the remaining channels to identify the optimized set of EEG channels for PD detection across both datasets. It was observed that the DL models used in the present invention offer high performance throughout the analysis when trained with Vertex-frequency plots generated from TP8, PO8, P6, TP9, and P8 and channels of UNM and TP8, PO8, P6, CP5, and P4 channels of UI datasets. The optimized channels were also analyzed using GSP-based vertex-frequency plots, CSP-based time-frequency spectrograms, and Network-based adjacency matrix heatmap. Time-frequency spectrogram conveys only functional information and adjacency matrix heatmap can capture structural details alone. However, the GSP-based vertex-frequency plots generated by the system of the present invention combines structural and functional information, effectively outperforming the other techniques.

Fig. 11 highlights the superior performance of the novel GSP-based vertex-frequency features of the present invention in PD detection using ViT and ResNet-50 compared to time-frequency spectrograms and adjacency matrix heatmaps. The conventional CSP-based and network-based approaches generate promising results, however, their performance was found to be inferior as compared to the approach involving vertex-frequency plots obtained from the WNVG-max algorithm. The superior performance exhibited by classic models such as ResNet-50 could be attributed to the efficacy of the feature set generated by the novel graph modeling technique of the present invention. The optimized channels demonstrating the highest performance were observed to be from the parietal region, highlighting the significance of EEG from the parietal region in PD detection. This comparative analysis using GSP and non-GSP features clearly demonstrates the impact of our novel GSP-based approach in PD detection. Fig. 12 shows the flow chart depicting the method used in the invention for detecting Parkinson’s disease.

The present invention involves a novel approach for defining graph signals from EEG data. The novelty of the invention is the WNVG-Max algorithm, a cogent representation of single-channel EEG as graph signals, combining visibility graph algorithms and pooling techniques. Adopting vertex-frequency plots of the graph signal as a feature set for DL-based detection models of neurological conditions such as PD represents another key novelty of the invention, to the extent that even classic models such as ResNet-50 exhibit superior performance. The performance of graph signals in detecting PD using vertex-frequency plots has been evaluated and results validated based on standard approaches such as time-frequency spectrograms and adjacency matrix heatmaps. The GSP-based method of the present invention not only suggests a set of optimized top-performing channels for PD detection from EEG data but also works better than other classical feature extraction approaches for PD detection, as it effectively combines structural and functional information in the form of graph signals. This work can be further expanded to detect neurological disorders such as Alzheimer’s disease, epilepsy, schizophrenia, etc.
, Claims:1. A System (S) for detecting and classifying Parkinson’s disease (PD) using integrated Graph Signal Processing (GSP) and Deep Learning (DL), the System (S) comprising:
- A conversion module (CM) configured to convert single-channel Electroencephalogram (EEG) signals into networks using visibility graph programs and pooling techniques,
- a graph signal generation module (GSGM) configured to generate graph signals from pooled EEG amplitudes on the vertices of the networks generated;
- a vertex-frequency plot generation module (VFPGM) configured to generate vertex-frequency plots (VFP) from graph signals;
wherein, Vertex-frequency plots derived from graph signals act as optimal feature sets for detecting neurological changes in the brain to accurately classify Parkinson’s disease (PD).
2. The system (S) as claimed in claim 1, wherein the conversion module (CM) is configured to use at least one visibility graph program (VGP) selected from a group consisting of: Natural, Weighted Natural, and Horizontal visibility graph programs.
3. The system (S) as claimed in claim 1, wherein the graph signal generation module (GSGM) is configured to generate a set of pooled EEG amplitudes from each EEG epoch using at least one of minimum, maximum, and average pooling techniques.
4. The system (S) as claimed in claim 1, wherein the vertex-frequency plots (VFP) are generated from graph signals using windowed graph Fourier transforms (WGFT).
5. The system (S) as claimed in claim 1, comprising a performance assessment module (PAM) configured to assess the performance of the vertex-frequency plots in PD detection using DL models.
6. The system (S) as claimed in claim 1, wherein the performance assessment module (PAM) is configured to use at least one DL model selected from a group consisting of: Vision Transformer (ViT) and Transfer Learning with pretrained network ResNet-50.
7. The system (S) as claimed in claim 1, comprising an optimal channel identification module (OCIM) configured to identify optimal channels associated with high classification accuracy for PD detection.
8. The system (S) as claimed in claim 7, wherein the optimal channel identification module is configured to identify the optimal channels based on the performance of the vertex-frequency plots in PD detection.
9. The System (S) as claimed in claim 1, wherein the integrated visibility graph algorithms (VGP) and pooling techniques (PT) used, the optimal combination of the aforementioned VGP and PTis the Weighted Natural Visibility Graph with Maximum-Pooling (WNVG-Max).
10. The system (S) as claimed in claim 1, wherein single-channel EEG epochs are subdivided into smaller segments to which three different dimensionality reduction techniques are applied namely, Maximum pooling (Max-pooling), Minimum pooling (Min-pooling), and Average-pooling (Avg-pooling), resulting in three sets of EEG amplitudes corresponding to the applied pooling operation.
11. The system (S) as claimed in claim 10, wherein three different visibility graph programs (VGP) namely, Natural, Horizontal, and Weighted Natural are applied to the pooled sets of EEG amplitudes, resulting in nine different visibility graphs from each epoch.
12. A method for detecting Parkinson's Disease (PD) using the system as claimed in claim 1, the method comprising:
- preprocessing the EEG signals by average re-referencing, bandpass filtering, down sampling, and Independent Component Analysis (ICA) for eye movement artifact removal;
- processing epochs of single-channel signals into smaller segments by applying dimensionality reduction techniques namely Maximum pooling (Max-pooling), Minimum pooling (Min-pooling), and Average-pooling (Avg-pooling), resulting in three sets of EEG amplitudes corresponding to the applied pooling operation;
- applying visibility graph algorithms namely Natural, Horizontal, and Weighted Natural to these pooled sets of EEG amplitudes, resulting in nine different visibility graphs from each epoch;
- generating graph signals by defining pooled EEG amplitudes on the vertices of networks through visibility graph programs (VGP);
- generating vertex-frequency plots from graph signals derived from each epoch by windowed graph Fourier transforms (WGFT);
- assessing the performance of each of the nine vertex-frequency plots in PD detection using two DL models, namely Vision Transformer and Transfer Learning with pre-trained network ResNet-50;
- repeating the same analysis for all the channels to identify the best sensitive channel and DL model suitable for PD detection;
- identifying the graph signal with an optimized combination of the visibility graph programs and pooling technique that maximizes the classification accuracy.