arXiv subjects

Miloš Savić

Publications and source records attributed to Miloš Savić.

9 recordsLinked to original sources

arXiv2026

Enhancing Distance-Based Graph Autoencoders with Structural Penalties for Dynamic Graph Embedding

Graph autoencoders (GAEs) are widely used for learning representations of dynamic graphs. However, their optimisation objectives typically do not take structural heterogeneity across nodes into account. We propose three distance-based GAE variants that incorporate structural penalties into the reconstruction loss. All variants share a two-layer Graph Convolutional Network encoder and a Euclidean-distance decoder trained with distance-based reconstruction objectives. We extend sparsity-corrected loss with two node-level regularization terms: (i) a hub penalty based on degree centrality, and (ii) a penalty based on Natural Community Local Intrinsic Dimensionality (NC-LID). The paper is motivated by prior evidence linking high NC-LID to reduced embedding quality. The proposed methods are designed to emphasize reconstruction errors for structurally ambiguous nodes. Experiments on multiple dynamic graph data sets show that incorporating NC-LID-based regularization consistently improves reconstruction performance over the baseline without structural regularization and the method using hub-aware regularization. These findings highlight NC-LID as a useful structural signal for enhancing distance-based graph autoencoders in dynamic settings.

cs.LG↗

arXiv2026

Federated Attention Autoencoders with a Stochastic Aggregation Scheme for Anomaly Detection

Outlier detection in decentralized data environments is a challenging task for many machine learning implementations, particularly in settings where data cannot be shared. Recently, there have been advances in federated outlier detection, some of which are based on the use of autoencoder networks. The introduction of attention mechanisms to autoencoders boosts their efficiency. However, the application of attention-based models in federated learning remains underdeveloped due to the absence of proper aggregation functions for these types of networks. In our work, we propose two novel aggregation functions tailored for attention-based autoencoders, which better preserve the learned information stored within the memory modules of these networks. We evaluated our approach on the KDDCUP10 dataset, and we showed that the proposed methods achieve up to 2.9\% and 5.1\% better results for F1 score and AUC ROC respectively when compared to traditional autoencoders.

cs.LG↗

arXiv2026

Attention, Anomalies! Handling Attention Layers in Unsupervised Federated Outlier Detection

Attention layers are the backbone of today's most powerful and impactful models. Models with multi-million and billion parameters rely on contextual knowledge provided by attention layers. However, their use goes well beyond just being the core component of large language models. One particularly interesting application is in Memory Augmented Autoencoders (MemAE), specifically for unsupervised representation learning in outlier detection tasks. It was shown that attention helps these models be more effective in centralized learning scenarios. Our work aims to address the lack of specialized aggregation techniques in Federated Learning (FL) when it comes to MemAE models. In this paper we analyze the intricacies of the architecture behind Memory Augmented Autoencoders, and propose novel, guided approaches to effectively aggregate these models in federated scenarios. We demonstrate our approach on non-IID datasets and show that these novel aggregation schemes are more robust when dealing with numerous edge nodes in environments with unbalanced datasets, specifically for unsupervised anomaly detection scenarios. This approach improves the performance of even very shallow autoencoders, allowing them to be used in resource constrained environments.

cs.LG↗

arXiv2025

Dynamic Graph Embedding Through Hub-aware Random Walks

The role of high-degree nodes, or hubs, in shaping graph dynamics and structure is well-recognized in network science, yet their influence remains underexplored in the context of dynamic graph embedding. Recent advances in representation learning for graphs have shown that random walk-based methods can capture both structural and temporal patterns, but often overlook the impact of hubs on walk trajectories and embedding stability. In this paper, we introduce DeepHub, a method for dynamic graph embedding that explicitly integrates hub sensitivity into random walk sampling strategies. Focusing on dynnode2vec as a representative dynamic embedding method, we systematically analyze the effect of hub-biased walks across nine real-world temporal networks. Our findings reveal that standard random walks tend to overrepresent hub nodes, leading to embeddings that underfit the evolving local context of less-connected nodes. By contrast, hub-aware walks can balance exploration, resulting in embeddings that better preserve temporal neighborhood structure and improve downstream task performance. These results suggest that hub-awareness is an important yet overlooked factor in dynamic graph embedding, and our work provides a foundation for more robust, structure-sensitive representation learning in evolving networks.

cs.SI↗

arXiv2025

CORTEX: A Cost-Sensitive Rule and Tree Extraction Method

Tree-based and rule-based machine learning models play pivotal roles in explainable artificial intelligence (XAI) due to their unique ability to provide explanations in the form of tree or rule sets that are easily understandable and interpretable, making them essential for applications in which trust in model decisions is necessary. These transparent models are typically used in surrogate modeling, a post-hoc XAI approach for explaining the logic of black-box models, enabling users to comprehend and trust complex predictive systems while maintaining competitive performance. This study proposes the Cost-Sensitive Rule and Tree Extraction (CORTEX) method, a novel rule-based XAI algorithm grounded in the multi-class cost-sensitive decision tree (CSDT) method. The original version of the CSDT is extended to classification problems with more than two classes by inducing the concept of an n-dimensional class-dependent cost matrix. The performance of CORTEX as a rule-extractor XAI method is compared to other post-hoc tree and rule extraction methods across several datasets with different numbers of classes. Several quantitative evaluation metrics are employed to assess the explainability of generated rule sets. Our findings demonstrate that CORTEX is competitive with other tree-based methods and can be superior to other rule-based methods across different datasets. The extracted rule sets suggest the advantages of using the CORTEX method over other methods by producing smaller rule sets with shorter rules on average across datasets with a diverse number of classes. Overall, the results underscore the potential of CORTEX as a powerful XAI tool for scenarios that require the generation of clear, human-understandable rules while maintaining good predictive performance.

cs.AI↗

arXiv2024

Local Intrinsic Dimensionality for Dynamic Graph Embeddings

The notion of local intrinsic dimensionality (LID) has important theoretical implications and practical applications in the fields of data mining and machine learning. Recent research efforts indicate that LID measures defined for graphs can improve graph representational learning methods based on random walks. In this paper, we discuss how NC-LID, a LID measure designed for static graphs, can be adapted for dynamic networks. Focusing on dynnode2vec as the most representative dynamic graph embedding method based on random walks, we examine correlations between NC-LID and the intrinsic quality of 10 real-world dynamic network embeddings. The obtained results show that NC-LID can be used as a good indicator of nodes whose embedding vectors do not tend to preserve temporal graph structure well. Thus, our empirical findings constitute the first step towards LID-aware dynamic graph embedding methods.

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arXiv2024

Hub-aware Random Walk Graph Embedding Methods for Classification

In the last two decades we are witnessing a huge increase of valuable big data structured in the form of graphs or networks. To apply traditional machine learning and data analytic techniques to such data it is necessary to transform graphs into vector-based representations that preserve the most essential structural properties of graphs. For this purpose, a large number of graph embedding methods have been proposed in the literature. Most of them produce general-purpose embeddings suitable for a variety of applications such as node clustering, node classification, graph visualisation and link prediction. In this paper, we propose two novel graph embedding algorithms based on random walks that are specifically designed for the node classification problem. Random walk sampling strategies of the proposed algorithms have been designed to pay special attention to hubs -- high-degree nodes that have the most critical role for the overall connectedness in large-scale graphs. The proposed methods are experimentally evaluated by analyzing the classification performance of three classification algorithms trained on embeddings of real-world networks. The obtained results indicate that our methods considerably improve the predictive power of examined classifiers compared to currently the most popular random walk method for generating general-purpose graph embeddings (node2vec).

cs.LG↗

arXiv2023

Local Intrinsic Dimensionality Measures for Graphs, with Applications to Graph Embeddings

The notion of local intrinsic dimensionality (LID) is an important advancement in data dimensionality analysis, with applications in data mining, machine learning and similarity search problems. Existing distance-based LID estimators were designed for tabular datasets encompassing data points represented as vectors in a Euclidean space. After discussing their limitations for graph-structured data considering graph embeddings and graph distances, we propose NC-LID, a novel LID-related measure for quantifying the discriminatory power of the shortest-path distance with respect to natural communities of nodes as their intrinsic localities. It is shown how this measure can be used to design LID-aware graph embedding algorithms by formulating two LID-elastic variants of node2vec with personalized hyperparameters that are adjusted according to NC-LID values. Our empirical analysis of NC-LID on a large number of real-world graphs shows that this measure is able to point to nodes with high link reconstruction errors in node2vec embeddings better than node centrality metrics. The experimental evaluation also shows that the proposed LID-elastic node2vec extensions improve node2vec by better preserving graph structure in generated embeddings.

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arXiv2021

Tax Evasion Risk Management Using a Hybrid Unsupervised Outlier Detection Method

Big data methods are becoming an important tool for tax fraud detection around the world. Unsupervised learning approach is the dominant framework due to the lack of label and ground truth in corresponding data sets although these methods suffer from low interpretability. HUNOD, a novel hybrid unsupervised outlier detection method for tax evasion risk management, is presented in this paper. In contrast to previous methods proposed in the literature, the HUNOD method combines two outlier detection approaches based on two different machine learning designs (i.e, clustering and representational learning) to detect and internally validate outliers in a given tax dataset. The HUNOD method allows its users to incorporate relevant domain knowledge into both constituent outlier detection approaches in order to detect outliers relevant for a given economic context. The interpretability of obtained outliers is achieved by training explainable-by-design surrogate models over results of unsupervised outlier detection methods. The experimental evaluation of the HUNOD method is conducted on two datasets derived from the database on individual personal income tax declarations collected by the Tax Administration of Serbia. The obtained results show that the method indicates between 90% and 98% internally validated outliers depending on the clustering configuration and employed regularization mechanisms for representational learning.

cs.LG↗