Graph theory offers a versatile language for modeling relationships by representing entities as vertices interconnected by edges [1]. While undirected graphs assume symmetric connections, directed, bidirected, and multidirected variants capture richer orientation and multiplicity semantics. Graph Neural Networks (GNNs) have rapidly advanced the field of learning on graphs, with recent extensions addressing directed edges [2–4]. In this paper, we introduce two novel GNN architectures—Bidirected GNNs and Multidirected GNNs—which inherently respect endpoint-specific directions and parallel-edge counts [5–8]. We demonstrate how these models naturally encode complex orientation patterns and provide illustrative examples to highlight their expressiveness. We anticipate that our contributions will spur further advances in graph representation learning for complex network structures.

Anesthesia plays a pivotal role in modern surgery by facilitating controlled states of unconsciousness. Precise control is crucial for safe and pain-free surgeries. Monitoring anesthesia depth accurately is essential to guide anesthesiologists, optimize drug usage, and mitigate postoperative complications. This study focuses on enhancing the classification performance of anesthesia-induced transitions between wakefulness and deep sleep into eight classes by leveraging advanced graph neural network (GNN). The research combines seven datasets into a single dataset comprising 290 samples and investigates key brain regions, to develop a robust classification framework. Initially, the dataset is augmented using the Synthetic Minority Over-sampling Technique (SMOTE) to expand the sample size to 1197. A graph-based approach is employed to get the intricate relationships between features, constructing a graph dataset with 1197 nodes and 714,610 edges, where nodes represent data samples and edges are the connections between the nodes. The connection (edge weight) is calculated using Spearman correlation coefficient matrix. An optimized GNN model is developed through an ablation study of eight hyperparameters, achieving an accuracy of 92.8%. The model’s performance is further evaluated against one-dimensional (1D) CNN, and six machine learning models, demonstrating superior classification capabilities for small and imbalanced datasets. Additionally, we evaluated the proposed model on six different anesthesia datasets, observing no decline in performance. This work advances the understanding and classification of anesthesia states, providing a valuable tool for improved anesthesia management.

Proceeding of: 6th International Work-Conference on Artificial and Natural Neural Networks, IWANN 2001 Granada, Spain, June 13–15, 2001In the recent years, the interest to develop automatic methods to determine appropriate architectures of feed-forward neural networks has increased. Most of the methods are based on evolutionary computation paradigms. Some of the designed methods are based on direct representations of the parameters of the network. These representations do not allow scalability, so to represent large architectures, very large structures are required. An alternative more interesting are the indirect schemes. They codify a compact representation of the neural network. In this work, an indirect constructive encoding scheme is presented. This scheme is based on cellular automata representations in order to increase the scalability of the method

While large margin classifiers are originally an outcome of an optimization framework, support vectors (SVs) can be obtained from geometric approaches. This article presents advances in the use of Gabriel graphs (GGs) in binary and multiclass classification problems. For Chipclass, a hyperparameter-less and optimization-less GG-based binary classifier, we discuss how activation functions and support edge (SE)-centered neurons affect the classification, proposing smoother functions and structural SV (SSV)-centered neurons to achieve margins with low probabilities and smoother classification contours. We extend the neural network architecture, which can be trained with backpropagation with a softmax function and a cross-entropy loss, or by solving a system of linear equations. A new subgraph-/distance-based membership function for graph regularization is also proposed, along with a new GG recomputation algorithm that is less computationally expensive than the standard approach. Experimental results with the Friedman test show that our method was better than previous GG-based classifiers and statistically equivalent to tree-based models.

This research aims to enhance lung cancer prediction using advanced machine learning techniques. The major finding is that integrating graph convolutional networks (GCNs) with graph attention networks (GATs) significantly improves predictive accuracy. The problem addressed is the need for early and accurate detection of lung cancer, leveraging a dataset from Kaggle's "Lung Cancer Prediction Dataset," which includes 309 instances and 16 attributes. The proposed A-GCN with GAT model is meticulously engineered with multiple layers and hidden units, optimized through hyperparameter adjustments, early stopping mechanisms, and Adam optimization techniques. Experimental results demonstrate the model's superior performance, achieving an accuracy of 0.9454, precision of 0.9213, recall of 0.9743, and an F1 score of 0.9482. These findings highlight the model's efficacy in capturing intricate patterns within patient data, facilitating early interventions and personalized treatment plans. This research underscores the potential of graph-based methodologies in medical research, particularly for lung cancer prediction, ultimately aiming to improve patient outcomes and survival rates through proactive healthcare interventions.

Eickhoff R, Sitte J, Rückert U. Robust Local Cluster Neural Networks (ESANN). In: Proceedings of the 14th European Symposium on Artificial Neural Networks (ESANN). Bruges, Belgium; 2006: 119-124.Artificial neural networks are intended to be used in future nanoelectronics since their biological examples seem to be robust to noise. In this paper, we analyze the robustness of Local Cluster Neural Networks and determine upper bounds on the mean square error for noise contaminated weights and inputs

Many interesting datasets ubiquitous in machine learning and deep learning can be described via graphs. As the scale and complexity of graph-structured datasets increase, such as in expansive social networks, protein folding, chemical interaction networks, and material phase transitions, improving the efficiency of the machine learning techniques applied to these is crucial. In this study, we focus on Graph Neural Networks (GNN) that have found great success in tasks such as node or edge classification and link prediction. However, standard GNN models have scaling limits due to necessary recursive calculations performed through dense graph relationships that lead to memory and runtime bottlenecks. While new approaches for processing larger networks are needed to advance graph techniques, and several have been proposed, we study how GNNs could be parallelized using existing tools and frameworks that are known to be successful in the deep learning community. In particular, we investigate applying pipeline parallelism to GNN models with GPipe, introduced by Google in 2018.

Multi-omics data is increasingly being utilized to advance computational methods for cancer classification. However, multi-omics data integration poses significant challenges due to the high dimensionality, data complexity, and distinct characteristics of various omics types. This study addresses these challenges and evaluates three graph neural network architectures for multi-omics (MO) integration based on graph-convolutional networks (GCN), graph-attention networks (GAT), and graph-transformer networks (GTN) for classifying 31 cancer types and normal tissues. To address the high-dimensionality of multi-omics data, we employed LASSO (Least Absolute Shrinkage and Selection Operator) regression for feature selection, leading to the creation of LASSO-MOGCN, LASSO-MOGAT, and LASSO-MOTGN models. Graph structures for the networks were constructed using gene correlation matrices and protein-protein interaction networks for multi-omics integration of messenger-RNA, micro-RNA, and DNA methylation data. Such data integration enables the networks to dynamically focus on important relationships between biological entities, improving both model performance and interpretability. Among the models, LASSO-MOGAT with a correlation-based graph structure achieved state-of-the-art accuracy (95.9%) and outperformed the LASSO-MOGCN and LASSO-MOTGN models in terms of precision, recall, and F1-score. Our findings demonstrate that integrating multi-omics data in graph-based architectures enhances cancer classification performance by uncovering distinct molecular patterns that contribute to a better understanding of cancer biology and potential biomarkers for disease progression.

Graph Neural Networks (GNN) show good results in classification and regression on graphs, notwithstanding most GNN models use a limited depth. In fact, they are composed of only a few stacked graph convolutional layers. One reason for this is the number of parameters growing with the number of GNN layers. In this paper, we show how using a recurrent graph convolution layer can help in building deeper GNNs, without increasing the complexity of the training phase, while improving on the predictive performances. We also analyze how the depth of the model influences the final result

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world data, particularly for datasets exhibiting a highly non-Euclidean latent anatomy or power-law distributions. Hyperbolic geometry, with its constant negative curvature and exponential growth property, naturally accommodates such structures, offering a promising alternative for learning rich graph representations. This survey paper provides a comprehensive review of the rapidly evolving field of Hyperbolic Graph Learning (HGL). We systematically categorize and analyze existing methods broadly dividing them into (1) hyperbolic graph embedding-based techniques, (2) graph neural network-based hyperbolic models, and (3) emerging paradigms. Beyond methodologies, we extensively discuss diverse applications of HGL across multiple domains, including recommender systems, knowledge graphs, bioinformatics, and other relevant scenarios, demonstrating the broad applicability and effectiveness of hyperbolic geometry in real-world graph learning tasks. Most importantly, we identify several key challenges that serve as directions for advancing HGL, including handling complex data structures, developing geometry-aware learning objectives, ensuring trustworthy and scalable implementations, and integrating with foundation models, e.g., large language models. We highlight promising research opportunities in this exciting interdisciplinary area. A comprehensive repository can be found at https://github.com/digailab/awesome-hyperbolic-graph-learning.

Colorectal liver metastases (CRLM) are a significant challenge in oncology, as recurrence after liver resection is frequently observed. Accurate prediction of CRLM recurrence is important to guide specific treatment strategies and improve clinical outcomes. To address this issue, this study proposes a novel framework. To the best of current knowledge, this is the first approach to integrate graph neural networks (GNNs) and causal inference to predict postresection CRLM recurrence using clinical and pathological characteristics. In addition, a GNNExplainer framework is also utilized for the interpretability of the models beyond predictive accuracy. The proposed framework identifies the factors of recurrence and their impact on patient outcomes, not only providing predictions to clinicians but also explaining the underlying reasons. Furthermore, causal inference strengthens the model by confirming factors. The relevance of these variables is also shown through counterfactual and interventional analyses, allowing for more evidence‐based choices. The GCN model of theframework exhibits high performance with a test accuracy of 99.40%, an aF1‐score of 99.21%, and a receiver operating characteristic area under the curve (ROC AUC) of 99.97%. An extensive evaluation shows the clinical applicability of the proposed framework.

Proceeding of: IEEE International Joint Conference on Neural Networks, IJCNN 2004, Budapest, 25-29 July 2004Many methods to codify artificial neural networks have been developed to avoid the disadvantages of direct encoding schema, improving the search into the solution's space. A method to analyse how the search space is covered and how are the movements along search process applying genetic operators is needed in order to evaluate the different encoding strategies for multilayer perceptrons (MLP). In this paper, the generative capacity, this is how the search space is covered for a indirect scheme based on cellular systems, is studied. The capacity of the methods to cover the search space (topologies of MLP space) is compared with the direct encoding scheme.Publicad

Graph Neural Network (GNN) research is rapidly growing thanks to the capacity of GNNs in learning distributed representations from graph-structured data. However, centralizing a massive amount of real-world graph data for GNN training is prohibitive due to privacy concerns, regulation restrictions, and commercial competitions. Federated learning (FL), a trending distributed learning paradigm, provides possibilities to solve this challenge while preserving data privacy. Despite recent advances in vision and language domains, there is no suitable platform for the FL of GNNs. To this end, we introduce FedGraphNN, an open FL benchmark system that can facilitate research on federated GNNs. FedGraphNN is built on a unified formulation of graph FL and contains a wide range of datasets from different domains, popular GNN models, and FL algorithms, with secure and efficient system support. Particularly for the datasets, we collect, preprocess, and partition 36 datasets from 7 domains, including both publicly available ones and specifically obtained ones such as hERG and Tencent. Our empirical analysis showcases the utility of our benchmark system, while exposing significant challenges in graph FL: federated GNNs perform worse in most datasets with a non-IID split than centralized GNNs; the GNN model that attains the best result in the centralized setting may not maintain its advantage in the FL setting. These results imply that more research efforts are needed to unravel the mystery behind federated GNNs. Moreover, our system performance analysis demonstrates that the FedGraphNN system is computationally efficient and secure to large-scale graphs datasets. We maintain the source code at https://github.com/FedML-AI/FedGraphNN.

Recursive neural networks (RNNs) and graph neural networks (GNNs) are two connectionist models that can directly process graphs. RNNs and GNNs exploit a similar processing framework, but they can be applied to different input domains. RNNs require the input graphs to be directed and acyclic, whereas GNNs can process any kind of graphs. The aim of this paper consists in understanding whether such a difference affects the behaviour of the models on a real application. An experimental comparison on an image classification problem is presented, showing that GNNs outperforms RNNs. Moreover the main differences between the models are also discussed w.r.t. their input domains, their approximation capabilities and their learning algorithms

Graph Neural Networks (GNNs) have been widely used for the representation learning of various structured graph data. While promising, most existing GNNs oversimplified the complexity and diversity of the edges in the graph, and thus inefficient to cope with ubiquitous heterogeneous graphs, which are typically in the form of multi-relational graph representations. In this paper, we propose RioGNN, a novel Reinforced, recursive and flexible neighborhood selection guided multi-relational Graph Neural Network architecture, to navigate complexity of neural network structures whilst maintaining relation-dependent representations. We first construct a multi-relational graph, according to the practical task, to reflect the heterogeneity of nodes, edges, attributes and labels. To avoid the embedding over-assimilation among different types of nodes, we employ a label-aware neural similarity measure to ascertain the most similar neighbors based on node attributes. A reinforced relation-aware neighbor selection mechanism is developed to choose the most similar neighbors of a targeting node within a relation before aggregating all neighborhood information from different relations to obtain the eventual node embedding. Particularly, to improve the efficiency of neighbor selecting, we propose a new recursive and scalable reinforcement learning framework with estimable depth and width for different scales of multi-relational graphs. RioGNN can learn more discriminative node embedding with enhanced explainability due to the recognition of individual importance of each relation via the filtering threshold mechanism. Comprehensive experiments on real-world graph data and practical tasks demonstrate the advancements of effectiveness, efficiency and the model explainability, as opposed to other comparative GNN models.

This research investigates the integration of neutrosophic logic with Graph Neural Networks (GNNs) for disease transmission risk prediction. Neutrosophic Graph Neural Networks (NGNNs) extend the capabilities of Fuzzy Graph Neural Networks (F-GNNs) as utilized in this paper to process structured information. By merging neutrosophic logic with GNNs, the technique significantly improved the handling of uncertainty while monitoring contagious diseases. The standard GNN model fails to process unreliable and unspecific information commonly found in epidemiological data collections. The neutrosophic triplets (T,I,F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathcal {T, I, F})$$\end{document} within NGNNs represent uncertain components found in disease outbreak conditions. Improved message passage through the NGNN works best while processing complex and extended datasets that programmers structure with Python. The risk evaluation and transmission uncertainty of diseases appear in visual heat maps to assist in the analysis of network dynamics. Through visual output, the health sector receives essential information related to outbreak development for making better decisions. By uniting state-of-the-art computing solutions with health-related implementation, this approach establishes superior standards for medical risk evaluation and produces foundational capabilities for future research. The authors established a firm foundation for advanced epidemic simulation and risk assessment through their work, which integrates theoretical graph theory advances into practical public health scenarios.

A collaborative work between Northumbria University and University of Peradeniya (Sri Lanka). It presents a novel technique based on Artificial Neural Networks for fast extraction of individual harmonic components. The technique was tested on a real-time hardware platform and results obtained showed that it is significantly faster and less computationally complex than other techniques. The paper complements other publications by the author (see paper 1) on the important area of “Power Quality” of electric power networks. It involves the application of advanced techniques in artificial intelligence to solve power systems problems

The assessment of highly-risky situations at road intersections have been recently revealed as an important research topic within the context of the automotive industry. In this paper we shall introduce a novel approach to compute risk functions by using a combination of a highly non-linear processing model in conjunction with a powerful information encoding procedure. Specifically, the elements of information either static or dynamic that appear in a road intersection scene are encoded by using directed positional acyclic labeled graphs. The risk assessment problem is then reformulated in terms of an inductive learning task carried out by a recursive neural network. Recursive neural networks are connectionist models capable of solving supervised and non-supervised learning problems represented by directed ordered acyclic graphs. The potential of this novel approach is demonstrated through well predefined scenarios. The major difference of our approach compared to others is expressed by the fact of learning the structure of the risk. Furthermore, the combination of a rich information encoding procedure with a generalized model of dynamical recurrent networks permit us, as we shall demonstrate, a sophisticated processing of information that we believe as being a first step for building future advanced intersection safety systems

In this paper, we will consider the universal approximation properties of a recently introduced neural network model called graph neural network (GNN) which can be used to process structured data inputs, e.g. acyclic graph, cyclic graph, directed or un-directed graphs. This class of neural networks implements a function (G, n) 2 IRm that maps a graph Gand one of its nodes n onto an m-dimensional Euclidean space. We characterize the functions that can be approximated by GNNs, in probability, up to any prescribed degree of precision. This set contains the maps that satisfy a property, called preservation of the unfolding equivalence, and includes most of the practically useful functions on graphs; the only known exception is when the input graph contains particular patterns of symmetries when unfolding equivalence may not be preserved. The result can be considered an extension of the universal approximation property established for the classic feedforward neural networks. Some experimental examples are used to show the computational capabilities of the proposed model

Graph Neural Networks (GNNs) have experienced rapid advancements in recent years due to their ability to learn meaningful representations from graph data structures. However, in most real-world settings, such as financial transaction networks and healthcare networks, this data is localized to different data owners and cannot be aggregated due to privacy concerns. Federated Learning (FL) has emerged as a viable machine learning approach for training a shared model that iteratively aggregates local models trained on decentralized data. This addresses privacy concerns while leveraging parallelism. State-of-the-art methods enhance the privacy-respecting convergence accuracy of federated GNN training by sharing remote embeddings of boundary vertices through a server (EmbC). However, they are limited by diminished performance due to large communication costs. In this article, we propose OptimES, an optimized federated GNN training framework that employs remote neighbourhood pruning, overlapping the push of embeddings to the server with local training, and dynamic pulling of embeddings to reduce network costs and training time. We perform a rigorous evaluation of these strategies for four common graph datasets with up to $111M$ vertices and $1.8B$ edges. We see that a modest drop in per-round accuracy due to the preemptive push of embeddings is out-stripped by the reduction in per-round training time for large and dense graphs like Reddit and Products, converging up to $\approx 3.5\times$ faster than EmbC and giving up to $\approx16\%$ better accuracy than the default federated GNN learning. While accuracy improvements over default federated GNNs are modest for sparser graphs like Arxiv and Papers, they achieve the target accuracy about $\approx11\times$ faster than EmbC.

The complex and nonlinear relationships between assets, firms, and economic indicators are not thoroughly captured by conventional risk modeling methods in the constantly changing landscape of volatile financial markets. This research introduces a new model based on Graph Neural Network (GNN) that utilizes the graph-based structure of financial systems to offer improvements in financial risk modelling using graph-based constructs. Graph Neural Networks (GNNs) [5] are leveraged to represent market entities as nodes and their complex interrelations as edges across both temporal and relational dimensions to allow deep representation learning. This work uses a combined estimate of systemic risk and probability of contagion pathways through historical market data, macroeconomic signals, and sector dependence. Experimental results on real-world financial datasets show that the proposed model achieves superior performance in volatility forecasting, stress testing and anomaly detection tasks compared to conventional machine learning methods. The GNN-driven framework provides such a forward-looking, adaptive tool set for robust financial decision making under high uncertainty.

Graph neural networks have proved to be a key tool for dealing with many problems and domains such as chemistry, natural language processing and social networks. While the structure of the layers is simple, it is difficult to identify the patterns learned by the graph neural network. Several works propose post-hoc methods to explain graph predictions, but few of them try to generate interpretable models. Conversely, the topic of the interpretable models is highly investigated in image recognition. Given the similarity between image and graph domains, we analyze the adaptability of prototype-based neural networks for graph and node classification. In particular, we investigate the use of two interpretable networks, ProtoPNet and TesNet, in the graph domain. We show that the adapted networks manage to reach better or higher accuracy scores than their respective black-box models and comparable performances with state-of-the-art self-explainable models. Showing how to extract ProtoPNet and TesNet explanations on graph neural networks, we further study how to obtain global and local explanations for the trained models. We then evaluate the explanations of the interpretable models by comparing them with post-hoc approaches and self-explainable models. Our findings show that the application of TesNet and ProtoPNet to the graph domain produces qualitative predictions while improving their reliability and transparency

Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to enable effective representation learning that inherently incorporates a weight-sharing mechanism, we develop graph neural networks that leverage the properties of hypercomplex feature transformation. In particular, in our proposed class of models, the multiplication rule specifying the algebra itself is inferred from the data during training. Given a fixed model architecture, we present empirical evidence that our proposed model incorporates a regularization effect, alleviating the risk of overfitting. We also show that for fixed model capacity, our proposed method outperforms its corresponding real-formulated GNN, providing additional confirmation for the enhanced expressivity of HC embeddings. Finally, we test our proposed hypercomplex GNN on several open graph benchmark datasets and show that our models reach state-of-the-art performance while consuming a much lower memory footprint with 70& fewer parameters. Our implementations are available at https://github.com/bayer-science-for-a-better-life/phc-gnn.

Medical treatment costs are rising for many reasons. These include an increasing world population, an aging population, greater healthcare needs, more diseases, and inflation. With AI's emergence in navigation, voice recognition, image lesion segmentation, ride-sharing, and smartphone personal assistants, the healthcare industry has quickly adopted it. Initial preprocessing includes standardization, missing values, and discarding anomalies. Next, the model is trained using the obtained features. Spearman correlation, a rank-based nonparametric statistic, can quantify monotonic correlation strength and direction. Even with missing values, the Graph Convolutional Network (GCN) performs well in model training. The suggested model outperformed state-of-the-art alternatives with 93.48% accuracy. It outperformed TransLSTM and GraphSAGE on complex datasets. This research stresses the system's ability to improve healthcare forecast accuracy through preprocessing, feature extraction, and GCN model training. Results show that AI can improve healthcare analytics despite lacking data.

Graph Neural Networks (Scarselli et al., 2009) exploit an iterative diffusion procedure to compute the node states as the fixed point of the trainable state transition function. In this paper, we show how to cast this scheme as a constrained optimization problem, thus avoiding the unfolding procedure required for the computation of the fixed point. This is done by searching for saddle points of the Lagrangian function in the space of the weights, state variables and Lagrange multipliers. The proposed approach shows state-of-the-art performance in multiple standard benchmarks in graph domains

Recent advances in molecular representation learning have produced highly effective encodings of molecules for numerous cheminformatics and bioinformatics tasks. However, extracting general chemical insight while balancing predictive accuracy, interpretability, and computational efficiency remains a major challenge. In this work, we introduce a novel Graph Neural Network (GNN) architecture that combines compressed higher-order topological signals with standard molecular features. Our approach captures global geometric information while preserving computational tractability and human-interpretable structure. We evaluate our model across a range of benchmarks, from small-molecule datasets to complex material datasets, and demonstrate superior performance using a parameter-efficient architecture. We achieve the best performing results in both accuracy and robustness across almost all benchmarks. We open source all code \footnote{All code and results can be found on Github https://github.com/rahulkhorana/TFC-PACT-Net}.

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications, where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on the existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this article, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art GNNs into four categories, namely, recurrent GNNs, convolutional GNNs, graph autoencoders, and spatial-temporal GNNs. We further discuss the applications of GNNs across various domains and summarize the open-source codes, benchmark data sets, and model evaluation of GNNs. Finally, we propose potential research directions in this rapidly growing field

Navigation and mobility are some of the major problems faced by visually impaired people in their daily lives. Advances in computer vision led to the proposal of some navigation systems. However, most of them require expensive and/or heavy hardware. In this paper we propose the use of convolutional neural networks (CNN), transfer learning, and semi-supervised learning (SSL) to build a framework aimed at the visually impaired aid. It has low computational costs and, therefore, may be implemented on current smartphones, without relying on any additional equipment. The smartphone camera can be used to automatically take pictures of the path ahead. Then, they will be immediately classified, providing almost instantaneous feedback to the user. We also propose a dataset to train the classifiers, including indoor and outdoor situations with different types of light, floor, and obstacles. Many different CNN architectures are evaluated as feature extractors and classifiers, by fine-tuning weights pre-trained on a much larger dataset. The graph-based SSL method, known as particle competition and cooperation, is also used for classification, allowing feedback from the user to be incorporated without retraining the underlying network. 92\% and 80\% classification accuracy is achieved in the proposed dataset in the best supervised and SSL scenarios, respectively.