arXiv subjects

Mudassir Shabbir

Publications and source records attributed to Mudassir Shabbir.

At least 19 recordsLinked to original sources

arXiv2026

An upper bound on generalized cospectral mates of oriented hraphs using skew-walk matrices

Let $D$ be an oriented graph with skew-adjacency matrix $S(D)$. Two oriented graphs $D$ and $C$ are said to share the same generalized skew spectrum if $S(D)$ and $S(C)$ have the same eigenvalues, and $J-S(D)$ and $J-S(C)$ also have the same eigenvalues, where $J$ is the all-ones matrix. Such graphs that are not isomorphic are generalized cospectral mates. We derive tight upper bounds on the number of generalized cospectral mates that an oriented graph can admit, based on arithmetic criteria involving the determinant of its skew-walk matrix. As a special case, we also provide a criterion for an oriented graph to be weakly determined by its generalized skew spectrum (WDGSS), that is, its only generalized cospectral mate is its transpose. These criteria relate directly to the controllability of graphs, a fundamental concept in the control of networked systems, thereby connecting spectral characterization of graphs to graph controllability.

math.CO↗

arXiv2026

On the number of generalized cospectral mates of graphs

This paper establishes an upper bound on the number of generalized cospectral mates of simple graphs, where the generalized spectrum consists of the spectrum of a graph and its complement. Moving beyond the classical problem of identifying graphs determined by their generalized spectrum, we address the more quantitative question of how many non-isomorphic graphs can share the same generalized spectrum. Our approach is based on arithmetic constraints derived from the Smith Normal Form (SNF) of the walk matrix, which leads to a tight upper bound on the number of generalized cospectral mates of a graph. Our upper bound applies to a much broader class of graphs than those previously shown to have no generalized cospectral mates (graphs determined by generalized spectrum). Consequently, this work extends the family of graphs for which strong and informative spectral uniqueness results are available

math.CO↗

arXiv2025

A Survey of Graph Unlearning

Graph unlearning emerges as a crucial advancement in the pursuit of responsible AI, providing the means to remove sensitive data traces from trained models, thereby upholding the \textit{right to be forgotten}. It is evident that graph machine learning exhibits sensitivity to data privacy and adversarial attacks, necessitating the application of graph unlearning techniques to address these concerns effectively. In this comprehensive survey paper, we present the first systematic review of graph unlearning approaches, encompassing a diverse array of methodologies and offering a detailed taxonomy and up-to-date literature overview to facilitate the understanding of researchers new to this field. To ensure clarity, we provide lucid explanations of the fundamental concepts and evaluation measures used in graph unlearning, catering to a broader audience with varying levels of expertise. Delving into potential applications, we explore the versatility of graph unlearning across various domains, including but not limited to social networks, adversarial settings, recommender systems, and resource-constrained environments like the Internet of Things, illustrating its potential impact in safeguarding data privacy and enhancing AI systems' robustness. Finally, we shed light on promising research directions, encouraging further progress and innovation within the domain of graph unlearning. By laying a solid foundation and fostering continued progress, this survey seeks to inspire researchers to further advance the field of graph unlearning, thereby instilling confidence in the ethical growth of AI systems and reinforcing the responsible application of machine learning techniques in various domains.

cs.LG↗

arXiv2025

Feature Construction Using Network Control Theory and Rank Encoding for Graph Machine Learning

In this article, we utilize the concept of average controllability in graphs, along with a novel rank encoding method, to enhance the performance of Graph Neural Networks (GNNs) in social network classification tasks. GNNs have proven highly effective in various network-based learning applications and require some form of node features to function. However, their performance is heavily influenced by the expressiveness of these features. In social networks, node features are often unavailable due to privacy constraints or the absence of inherent attributes, making it challenging for GNNs to achieve optimal performance. To address this limitation, we propose two strategies for constructing expressive node features. First, we introduce average controllability along with other centrality metrics (denoted as NCT-EFA) as node-level metrics that capture critical aspects of network topology. Building on this, we develop a rank encoding method that transforms average controllability or any other graph-theoretic metric into a fixed-dimensional feature space, thereby improving feature representation. We conduct extensive numerical evaluations using six benchmark GNN models across four social network datasets to compare different node feature construction methods. Our results demonstrate that incorporating average controllability into the feature space significantly improves GNN performance. Moreover, the proposed rank encoding method outperforms traditional one-hot degree encoding, improving the ROC AUC from 68.7% to 73.9% using GraphSAGE on the GitHub Stargazers dataset, underscoring its effectiveness in generating expressive and efficient node representations.

cs.LG↗

arXiv2025

Walk Matrix-Based Upper Bounds on Generalized Cospectral Mates

The problem of characterizing graphs determined by their spectrum (DS) or generalized spectrum (DGS) has been a longstanding topic of interest in spectral graph theory, originating from questions in chemistry and mathematical physics. While previous studies primarily focus on identifying whether a graph is DGS, we address a related yet distinct question: how many non-isomorphic generalized cospectral mates a graph can have? Building upon recent advances that connect this question to the properties of the walk matrix, we introduce a broad family of graphs and establish an explicit upper bound on the number of non-isomorphic generalized cospectral mates they can have. This bound is determined by the arithmetic structure of the determinant of the walk matrix, offering a refined criterion for quantifying the multiplicity of generalized cospectral graphs. This result sheds new light on the structure of generalized cospectral graphs and provides a refined arithmetic criterion for bounding their multiplicity.

math.CO↗

arXiv2025

Learning Backbones: Sparsifying Graphs through Zero Forcing for Effective Graph-Based Learning

This paper introduces a novel framework for graph sparsification that preserves the essential learning attributes of original graphs, improving computational efficiency and reducing complexity in learning algorithms. We refer to these sparse graphs as "learning backbones". Our approach leverages the zero-forcing (ZF) phenomenon, a dynamic process on graphs with applications in network control. The key idea is to generate a tree from the original graph that retains critical dynamical properties. By correlating these properties with learning attributes, we construct effective learning backbones. We evaluate the performance of our ZF-based backbones in graph classification tasks across eight datasets and six baseline models. The results demonstrate that our method outperforms existing techniques. Additionally, we explore extensions using node distance metrics to further enhance the framework's utility.

cs.LG↗

arXiv2024

NeuroGraph: Benchmarks for Graph Machine Learning in Brain Connectomics

Machine learning provides a valuable tool for analyzing high-dimensional functional neuroimaging data, and is proving effective in predicting various neurological conditions, psychiatric disorders, and cognitive patterns. In functional magnetic resonance imaging (MRI) research, interactions between brain regions are commonly modeled using graph-based representations. The potency of graph machine learning methods has been established across myriad domains, marking a transformative step in data interpretation and predictive modeling. Yet, despite their promise, the transposition of these techniques to the neuroimaging domain has been challenging due to the expansive number of potential preprocessing pipelines and the large parameter search space for graph-based dataset construction. In this paper, we introduce NeuroGraph, a collection of graph-based neuroimaging datasets, and demonstrated its utility for predicting multiple categories of behavioral and cognitive traits. We delve deeply into the dataset generation search space by crafting 35 datasets that encompass static and dynamic brain connectivity, running in excess of 15 baseline methods for benchmarking. Additionally, we provide generic frameworks for learning on both static and dynamic graphs. Our extensive experiments lead to several key observations. Notably, using correlation vectors as node features, incorporating larger number of regions of interest, and employing sparser graphs lead to improved performance. To foster further advancements in graph-based data driven neuroimaging analysis, we offer a comprehensive open-source Python package that includes the benchmark datasets, baseline implementations, model training, and standard evaluation.

cs.LG↗

arXiv2024

Improving Graph Machine Learning Performance Through Feature Augmentation Based on Network Control Theory

Network control theory (NCT) offers a robust analytical framework for understanding the influence of network topology on dynamic behaviors, enabling researchers to decipher how certain patterns of external control measures can steer system dynamics towards desired states. Distinguished from other structure-function methodologies, NCT's predictive capabilities can be coupled with deploying Graph Neural Networks (GNNs), which have demonstrated exceptional utility in various network-based learning tasks. However, the performance of GNNs heavily relies on the expressiveness of node features, and the lack of node features can greatly degrade their performance. Furthermore, many real-world systems may lack node-level information, posing a challenge for GNNs.To tackle this challenge, we introduce a novel approach, NCT-based Enhanced Feature Augmentation (NCT-EFA), that assimilates average controllability, along with other centrality indices, into the feature augmentation pipeline to enhance GNNs performance. Our evaluation of NCT-EFA, on six benchmark GNN models across two experimental setting. solely employing average controllability and in combination with additional centrality metrics. showcases an improved performance reaching as high as 11%. Our results demonstrate that incorporating NCT into feature enrichment can substantively extend the applicability and heighten the performance of GNNs in scenarios where node-level information is unavailable.

cs.LG↗

arXiv2024

Control-based Graph Embeddings with Data Augmentation for Contrastive Learning

In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of 'augmented' graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph's structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning.

cs.LG↗

arXiv2023

Enhanced Graph Neural Networks with Ego-Centric Spectral Subgraph Embeddings Augmentation

Graph Neural Networks (GNNs) have shown remarkable merit in performing various learning-based tasks in complex networks. The superior performance of GNNs often correlates with the availability and quality of node-level features in the input networks. However, for many network applications, such node-level information may be missing or unreliable, thereby limiting the applicability and efficacy of GNNs. To address this limitation, we present a novel approach denoted as Ego-centric Spectral subGraph Embedding Augmentation (ESGEA), which aims to enhance and design node features, particularly in scenarios where information is lacking. Our method leverages the topological structure of the local subgraph to create topology-aware node features. The subgraph features are generated using an efficient spectral graph embedding technique, and they serve as node features that capture the local topological organization of the network. The explicit node features, if present, are then enhanced with the subgraph embeddings in order to improve the overall performance. ESGEA is compatible with any GNN-based architecture and is effective even in the absence of node features. We evaluate the proposed method in a social network graph classification task where node attributes are unavailable, as well as in a node classification task where node features are corrupted or even absent. The evaluation results on seven datasets and eight baseline models indicate up to a 10% improvement in AUC and a 7% improvement in accuracy for graph and node classification tasks, respectively.

cs.SI↗

arXiv2023

Controllability Backbone in Networks

This paper studies the controllability backbone problem in dynamical networks defined over graphs. The main idea of the controllability backbone is to identify a small subset of edges in a given network such that any subnetwork containing those edges/links has at least the same network controllability as the original network while assuming the same set of input/leader vertices. We consider the strong structural controllability (SSC) in our work, which is useful but computationally challenging. Thus, we utilize two lower bounds on the network's SSC based on the zero forcing notion and graph distances. We provide algorithms to compute controllability backbones while preserving these lower bounds. We thoroughly analyze the proposed algorithms and compute the number of edges in the controllability backbones. Finally, we compare and numerically evaluate our methods on random graphs.

eess.SY↗

arXiv2023

Learning-Based Heuristic for Combinatorial Optimization of the Minimum Dominating Set Problem using Graph Convolutional Networks

A dominating set of a graph $\mathcal{G=(V, E)}$ is a subset of vertices $S\subseteq\mathcal{V}$ such that every vertex $v\in \mathcal{V} \setminus S$ outside the dominating set is adjacent to a vertex $u\in S$ within the set. The minimum dominating set problem seeks to find a dominating set of minimum cardinality and is a well-established NP-hard combinatorial optimization problem. We propose a novel learning-based heuristic approach to compute solutions for the minimum dominating set problem using graph convolutional networks. We conduct an extensive experimental evaluation of the proposed method on a combination of randomly generated graphs and real-world graph datasets. Our results indicate that the proposed learning-based approach can outperform a classical greedy approximation algorithm. Furthermore, we demonstrate the generalization capability of the graph convolutional network across datasets and its ability to scale to graphs of higher order than those on which it was trained. Finally, we utilize the proposed learning-based heuristic in an iterative greedy algorithm, achieving state-of-the-art performance in the computation of dominating sets.

cs.LG↗

arXiv2023

Sequential Graph Neural Networks for Source Code Vulnerability Identification

Vulnerability identification constitutes a task of high importance for cyber security. It is quite helpful for locating and fixing vulnerable functions in large applications. However, this task is rather challenging owing to the absence of reliable and adequately managed datasets and learning models. Existing solutions typically rely on human expertise to annotate datasets or specify features, which is prone to error. In addition, the learning models have a high rate of false positives. To bridge this gap, in this paper, we present a properly curated C/C++ source code vulnerability dataset, denoted as CVEFunctionGraphEmbeddings (CVEFGE), to aid in developing models. CVEFGE is automatically crawled from the CVE database, which contains authentic and publicly disclosed source code vulnerabilities. We also propose a learning framework based on graph neural networks, denoted SEquential Graph Neural Network (SEGNN) for learning a large number of code semantic representations. SEGNN consists of a sequential learning module, graph convolution, pooling, and fully connected layers. Our evaluations on two datasets and four baseline methods in a graph classification setting demonstrate state-of-the-art results.

cs.CR↗

arXiv2023

Computing Graph Descriptors on Edge Streams

Feature extraction is an essential task in graph analytics. These feature vectors, called graph descriptors, are used in downstream vector-space-based graph analysis models. This idea has proved fruitful in the past, with spectral-based graph descriptors providing state-of-the-art classification accuracy. However, known algorithms to compute meaningful descriptors do not scale to large graphs since: (1) they require storing the entire graph in memory, and (2) the end-user has no control over the algorithm's runtime. In this paper, we present streaming algorithms to approximately compute three different graph descriptors capturing the essential structure of graphs. Operating on edge streams allows us to avoid storing the entire graph in memory, and controlling the sample size enables us to keep the runtime of our algorithms within desired bounds. We demonstrate the efficacy of the proposed descriptors by analyzing the approximation error and classification accuracy. Our scalable algorithms compute descriptors of graphs with millions of edges within minutes. Moreover, these descriptors yield predictive accuracy comparable to the state-of-the-art methods but can be computed using only 25% as much memory.

cs.LG↗

arXiv2021

Resilient Distributed Vector Consensus Using Centerpoints

In this paper, we study the resilient vector consensus problem in networks with adversarial agents and improve resilience guarantees of existing algorithms. A common approach to achieving resilient vector consensus is that every non-adversarial (or normal) agent in the network updates its state by moving towards a point in the convex hull of its \emph{normal} neighbors' states. Since an agent cannot distinguish between its normal and adversarial neighbors, computing such a point, often called as \emph{safe point}, is a challenging task. To compute a safe point, we propose to use the notion of \emph{centerpoint}, which is an extension of the median in higher dimensions, instead of Tverberg partition of points, which is often used for this purpose. We discuss that the notion of centerpoint provides a complete characterization of safe points in $\mathbb{R}^d$. In particular, we show that a safe point is essentially an interior centerpoint if the number of adversaries in the neighborhood of a normal agent $i$ is less than $\frac{N_i}{d+1} $, where $d$ is the dimension of the state vector and $N_i$ is the total number of agents in the neighborhood of $i$. Consequently, we obtain necessary and sufficient conditions on the number of adversarial agents to guarantee resilient vector consensus. Further, by considering the complexity of computing centerpoints, we discuss improvements in the resilience guarantees of vector consensus algorithms and compare with the other existing approaches. Finally, we numerically evaluate the performance of our approach through experiments.

eess.SY↗

arXiv2021

Computation of the Distance-based Bound on Strong Structural Controllability in Networks

In this paper, we study the problem of computing a tight lower bound on the dimension of the strong structurally controllable subspace (SSCS) in networks with Laplacian dynamics. The bound is based on a sequence of vectors containing the distances between leaders (nodes with external inputs) and followers (remaining nodes) in the underlying network graph. Such vectors are referred to as the distance-to-leaders vectors. {We give exact and approximate algorithms to compute the longest sequences of distance-to-leaders vectors, which directly provide distance-based bounds on the dimension of SSCS. The distance-based bound is known to outperform the other known bounds (for instance, based on zero-forcing sets), especially when the network is partially strong structurally controllable. Using these results, we discuss an application of the distance-based bound in solving the leader selection problem for strong structural controllability. Further, we characterize strong structural controllability in path and cycle graphs with a given set of leader nodes using sequences of distance-to-leaders vectors. Finally, we numerically evaluate our results on various graphs.

eess.SY↗

arXiv2021

SEMOUR: A Scripted Emotional Speech Repository for Urdu

Designing reliable Speech Emotion Recognition systems is a complex task that inevitably requires sufficient data for training purposes. Such extensive datasets are currently available in only a few languages, including English, German, and Italian. In this paper, we present SEMOUR, the first scripted database of emotion-tagged speech in the Urdu language, to design an Urdu Speech Recognition System. Our gender-balanced dataset contains 15,040 unique instances recorded by eight professional actors eliciting a syntactically complex script. The dataset is phonetically balanced, and reliably exhibits a varied set of emotions as marked by the high agreement scores among human raters in experiments. We also provide various baseline speech emotion prediction scores on the database, which could be used for various applications like personalized robot assistants, diagnosis of psychological disorders, and getting feedback from a low-tech-enabled population, etc. On a random test sample, our model correctly predicts an emotion with a state-of-the-art 92% accuracy.

cs.SD↗

arXiv2021

Edge Augmentation with Controllability Constraints in Directed Laplacian Networks

In this paper, we study the maximum edge augmentation problem in directed Laplacian networks to improve their robustness while preserving lower bounds on their strong structural controllability (SSC). Since adding edges could adversely impact network controllability, the main objective is to maximally densify a given network by selectively adding missing edges while ensuring that SSC of the network does not deteriorate beyond certain levels specified by the SSC bounds. We consider two widely used bounds: first is based on the notion of zero forcing (ZF), and the second relies on the distances between nodes in a graph. We provide an edge augmentation algorithm that adds the maximum number of edges in a graph while preserving the ZF-based SSC bound, and also derive a closed-form expression for the exact number of edges added to the graph. Then, we examine the edge augmentation problem while preserving the distance-based bound and present a randomized algorithm that guarantees an approximate solution with high probability. Finally, we numerically evaluate and compare these edge augmentation solutions.

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