arXiv subjects

Narmina Baghirova

Publications and source records attributed to Narmina Baghirova.

6 recordsLinked to original sources

arXiv2026

Explainable Graph-theoretical Machine Learning with Application to Alzheimer's Disease Prediction

Dementia affects over 55 million people worldwide, projected to reach 139 million by 2050, with Alzheimer's disease (AD) accounting for 60-70% of cases. AD is associated with disruptions in metabolic brain connectivity. Detecting these disruptions early is crucial for AD management. FDG-PET is a useful tool for identifying such impairments. However, most studies rely on group-level analyses or thresholding, potentially masking individual differences and overlooking weaker yet biologically critical brain connections. Moreover, AD prediction largely focuses on univariate rather than multivariate outcomes. To address this, we introduce explainable graph-theoretical machine learning (XGML), a framework for constructing individual metabolic brain graphs and identifying subgraphs most predictive of multivariate disease-related outcomes. Using Alzheimer's Disease Neuroimaging Initiative (ADNI) FDG-PET data, we compared six graph representations against three non-graph baselines, each with six machine learning models using repeated stratified 3-fold cross-validation (10 repeats). The best configuration combined kernel density estimation with Hellinger distance and random forest. Across eight cognitive scores, it reached an overall Fisher-z-averaged Pearson correlation of r=0.595, with strongest performance for ADAS13 (r=0.67), ADAS11 (r=0.65), and ADASQ4 (r=0.62). We identified key edges that were jointly but differentially predictive across outcomes, suggesting their potential as network biomarkers of cognitive decline. Preliminary external feasibility validation on an OASIS3 cohort yielded weak predictive performance for CDRSB (r=0.26) and MMSE (r=0.18), likely reflecting cohort, protocol, and diagnostic differences. Overall, our results suggest the promise of graph-theoretical machine learning for biomarker discovery, disease prediction, and understanding the neural mechanisms underlying AD.

cs.LG↗

arXiv2026

Imputation-free transformer learning enables robust Alzheimer's disease prediction and calibrated uncertainty quantification across heterogeneous clinical cohorts

Accurate diagnostic classification and disease-severity prediction for Alzheimer's disease are hampered by the incompleteness and heterogeneity of real-world clinical data. Left unaddressed, these barriers prevent reliable disease modelling and hinder effective clinical evaluation. Conventional imputation strategies introduce systematic bias, distort inter-feature relationships, and yield overconfident predictions, limitations especially consequential in diagnostic settings. Here, we propose NITROGEN, an imputation-free transformer that jointly models within-patient feature dependencies and between-patient relational structure through masked and intersample attention, enabling robust multimodal learning directly from partially observed records. We trained NITROGEN on ADNI (N=7858 scans), and evaluated it on two independent cohorts: OASIS-3 (N=2675 scans) and AIBL (N=1286 scans). Across cohorts and diagnostic and cognitive score prediction tasks, NITROGEN showed robust calibration and uncertainty quantification advantages over tree-based ensemble methods, while maintaining competitive discriminative performance. Cross-cohort and cross-method analyses identified cortical thickness in the temporal pole, age, and APOE genotype as important, though not individually sufficient, features for AD classification. We further introduced a modality-aware uncertainty adjustment that augments predictive uncertainty proportionally to the importance of absent modalities, enabling calibrated confidence when diagnostic information is unavailable. Together, our results show that imputation-free attention learning preserved meaningful discrimination under cohort shift, revealing expected degradation on more distributionally different cohorts, and demonstrate that evaluating models along calibration, interpretability, and cross-cohort reliability, not accuracy alone, is essential for clinical deployment.

q-bio.NC↗

arXiv2025

Perfect phylogenies via the Minimum Uncovering Branching problem: efficiently solvable cases

In this paper, we present new efficiently solvable cases of the Minimum Uncovering Branching problem, an optimization problem with applications in cancer genomics introduced by Hujdurović, Husić, Milanič, Rizzi, and Tomescu in 2018. The problem involves a family of finite sets, and the goal is to map each non-maximal set to exactly one set that contains it, minimizing the sum of uncovered elements across all sets in the family. Hujdurović et al. formulated the problem in terms of branchings of the digraph formed by the proper set inclusion relation on the input sets and studied the problem complexity based on properties of the corresponding partially ordered set, in particular, with respect to its height and width, defined respectively as the maximum cardinality of a chain and an antichain. They showed that the problem is APX-complete for instances of bounded height and that a constant-factor approximation algorithm exists for instances of bounded width, but left the exact complexity for bounded-width instances open. In this paper, we answer this question by proving that the problem is solvable in polynomial time. We derive this result by examining the structural properties of optimal solutions and reducing the problem to computing maximum matchings in bipartite graphs and maximum weight antichains in partially ordered sets. We also introduce a new polynomially computable lower bound and identify another condition for polynomial-time solvability.

cs.DM↗

arXiv2024

Proportionally dense subgraphs of maximum size in degree-constrained graphs

A proportionally dense subgraph (PDS) of a graph is an induced subgraph of size at least two such that every vertex in the subgraph has proportionally as many neighbors inside as outside of the subgraph. Then, maxPDS is the problem of determining a PDS of maximum size in a given graph. If we further require that a PDS induces a connected subgraph, we refer to such problem as connected maxPDS. In this paper, we study the complexity of maxPDS with respect to parameters representing the density of a graph and its complement. We consider $Δ$, representing the maximum degree, $h$, representing the $h$-index, and degen, representing the degeneracy of a graph. We show that maxPDS is NP-hard parameterized by $Δ,h$ and degen. More specifically, we show that maxPDS is NP-hard on graphs with $Δ=4$, $h=4$ and degen=2. Then, we show that maxPDS is NP-hard when restricted to dense graphs, more specifically graphs $G$ such that $Δ(\overline{G})\leq 6$, and graphs $G$ such that $degen(\overline{G}) \leq 2$ and $\overline{G}$ is bipartite, where $\overline{G}$ represents the complement of $G$. On the other hand, we show that maxPDS is polynomial-time solvable on graphs with $h\le2$. Finally, we consider graphs $G$ such that $h(\overline{G})\le 2$ and show that there exists a polynomial-time algorithm for finding a PDS of maximum size in such graphs. This result implies polynomial-time complexity on graphs with $n$ vertices of minimum degree $n-3$, i.e. graphs $G$ such that $Δ(\overline{G})\le 2$. For each result presented in this paper, we consider connected maxPDS and explain how to extend it when we require connectivity.

cs.CC↗

arXiv2023

Finding $k$-community structures in special graph classes

For a fixed integer $k\ge 2$, a $k$-community structure in an undirected graph is a partition of its vertex set into $k$ sets called communities, each of size at least two, such that every vertex of the graph has proportionally at least as many neighbours in its own community as in any other community. In this paper, we give a necessary and sufficient condition for a forest on $n$ vertices to admit a $k$-community structure. Furthermore, we provide an $O(n^{2})$-time algorithm that computes such a $k$-community structure in a forest, if it exists. These results extend a result of [Bazgan et al., Structural and algorithmic properties of $2$-community structure, Algorithmica, 80(6):1890-1908, 2018]. We also show that if communities are allowed to have size one, then every forest with $n \geq k\geq 2$ vertices admits a $k$-community structure that can be found in time $O(n^{2})$. We then consider threshold graphs and show that every connected threshold graph admits a $2$-community structure if and only if it is not isomorphic to a star; also if such a $2$-community structure exists, we explain how to obtain it in linear time. We further describe two infinite families of disconnected threshold graphs, containing exactly one isolated vertex, that do not admit any $2$-community structure. Finally, we present a new infinite family of connected graphs that may contain an even or an odd number of vertices without $2$-community structures, even if communities are allowed to have size one.

math.CO↗

arXiv2022

Locally checkable problems parameterized by clique-width

We continue the study initiated by Bonomo-Braberman and Gonzalez in 2020 on $r$-locally checkable problems. We propose a dynamic programming algorithm that takes as input a graph with an associated clique-width expression and solves a $1$-locally checkable problem under certain restrictions. We show that it runs in polynomial time in graphs of bounded clique-width, when the number of colors of the locally checkable problem is fixed. Furthermore, we present a first extension of our framework to global properties by taking into account the sizes of the color classes, and consequently enlarge the set of problems solvable in polynomial time with our approach in graphs of bounded clique-width. As examples, we apply this setting to show that, when parameterized by clique-width, the $[k]-$Roman domination problem is FPT, and the $k$-community problem, Max PDS and other variants are XP.

cs.DM↗