S. Džeroski
Famous AuthorPublications
Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration
We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data. SORT estimates expansion coefficients directly from observations using L1-regularized regression, avoiding explicit quadrature or analytic inner-product evaluation. The central application is data-driven discovery of ordinary differential equations: vector fields are represented in chosen orthogonal bases and learned as sparse coefficient expansions. This provides a complementary route to symbolic regression, grammar-based discovery, and SINDy-style sparse identification by first recovering a compact spectral representation, which can later guide searches for simpler analytic forms. Across the dynamical-system experiments, SORT matches or improves upon library-based sparse-regression baselines when the basis is well adapted to the problem, and shows more stable degradation under sparse sampling, noisy derivative estimates, and representation mismatch. Specific examples illustrate why this representation is useful: if a finite library misses the problem-specific nonlinearity, the resulting model can fail. SORT is not immune to mismatch, but it shifts the problem away from brittle selection among generic terms to basis design adapted to the problem domain. The experiments also show that dominant low-order coefficients persist as model order increases, supporting order-consistent model growth. Beyond equation discovery, the same learned expansion supports nonlinear approximation and estimation of complex, high-dimensional integrals by coefficient readout. Overall, SORT provides a reusable intermediate representation for system identification, approximation, and integration, while making basis design an explicit part of the scientific modeling problem.
Design Choices That Matter: A Functional ANOVA Analysis for Remote Sensing Multi-Label Classification
Benchmarking deep learning (DL) models for multi-label classification (MLC) of remote sensing images (RSI) typically yields rankings that do not generalize beyond the evaluated datasets. In this work, we move beyond rankings by employing functional analysis of variance (fANOVA) to systematically quantify the contributions of individual design choices and their interactions to performance variability. We conduct two empirical analyses covering 48 and 20 DL models, respectively, spanning design choices such as network architecture, fine-tuning strategy, learning strategy, and initialization. By applying fANOVA across seven MLC RSI datasets, we construct dataset meta-representations that capture design-choice sensitivity profiles. Hierarchical clustering of these meta-representations reveals that datasets naturally group according to how they respond to design decisions, with patterns strongly linked to intrinsic dataset properties such as scale, spatial resolution, and label space complexity. Our findings show that for large-scale datasets, fine-tuning strategy and architecture are dominant factors, while in data-limited regimes, initialization becomes decisive. For intermediate regimes, the interaction between architecture and learning strategy governs performance.
On Solving the Multiple Variable Gapped Longest Common Subsequence Problem
This paper addresses the Variable Gapped Longest Common Subsequence (VGLCS) problem, a generalization of the classical LCS problem involving flexible gap constraints between consecutive solutions' characters. The problem arises in molecular sequence comparison, where structural distance constraints between residues must be respected, and in time-series analysis where events are required to occur within specified temporal delays. We propose a search framework based on the root-based state graph representation, in which the state space comprises a generally large number of rooted state subgraphs. To cope with the resulting combinatorial explosion, an iterative beam search strategy is employed, dynamically maintaining a global pool of promising candidate root nodes, enabling effective control of diversification across iterations. To exploit the search for high-quality solutions, several known heuristics from the LCS literature are utilized into the standalone beam search procedure. To the best of our knowledge, this is the first comprehensive computational study on the VGLCS problem comprising 320 synthetic instances with up to 10 input sequences and up to 500 characters. Experimental results show robustness of the designed approach over the baseline beam search in comparable runtimes.
HELM: Hierarchical and Explicit Label Modeling with Graph Learning for Multi-Label Image Classification
Hierarchical multi-label classification (HMLC) is essential for modeling complex label dependencies in remote sensing. Existing methods, however, struggle with multi-path hierarchies where instances belong to multiple branches, and they rarely exploit unlabeled data. We introduce HELM (\textit{Hierarchical and Explicit Label Modeling}), a novel framework that overcomes these limitations. HELM: (i) uses hierarchy-specific class tokens within a Vision Transformer to capture nuanced label interactions; (ii) employs graph convolutional networks to explicitly encode the hierarchical structure and generate hierarchy-aware embeddings; and (iii) integrates a self-supervised branch to effectively leverage unlabeled imagery. We perform a comprehensive evaluation on four remote sensing image (RSI) datasets (UCM, AID, DFC-15, MLRSNet). HELM achieves state-of-the-art performance, consistently outperforming strong baselines in both supervised and semi-supervised settings, demonstrating particular strength in low-label scenarios.
Quantifying the Impact of Modules and Their Interactions in the PSO-X Framework
The PSO-X framework incorporates dozens of modules that have been proposed for solving single-objective continuous optimization problems using particle swarm optimization. While modular frameworks enable users to automatically generate and configure algorithms tailored to specific optimization problems, the complexity of this process increases with the number of modules in the framework and the degrees of freedom defined for their interaction. Understanding how modules affect the performance of algorithms for different problems is critical to making the process of finding effective implementations more efficient and identifying promising areas for further investigation. Despite their practical applications and scientific relevance, there is a lack of empirical studies investigating which modules matter most in modular optimization frameworks and how they interact. In this paper, we analyze the performance of 1424 particle swarm optimization algorithms instantiated from the PSO-X framework on the 25 functions in the CEC'05 benchmark suite with 10 and 30 dimensions. We use functional ANOVA to quantify the impact of modules and their combinations on performance in different problem classes. In practice, this allows us to identify which modules have greater influence on PSO-X performance depending on problem features such as multimodality, mathematical transformations and varying dimensionality. We then perform a cluster analysis to identify groups of problem classes that share similar module effect patterns. Our results show low variability in the importance of modules in all problem classes, suggesting that particle swarm optimization performance is driven by a few influential modules.