Searcharxiv⌕ Search

arXiv subjects

Fatemeh Nassajian Mojarrad

Publications and source records attributed to Fatemeh Nassajian Mojarrad.

8 recordsLinked to original sources
arXiv2025

Learning a robust shape parameter for RBF approximation

Radial basis functions (RBFs) play an important role in function interpolation, in particular in an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a parameter called the shape parameter. There are many approaches in literature on how to appropriately choose it as to increase the accuracy of interpolation while avoiding instability issues. However, finding the optimal shape parameter value in general remains a challenge. In this work, we present a novel approach to determine the shape parameter in RBFs. First, we construct an optimisation problem to obtain a shape parameter that leads to an interpolation matrix with bounded condition number, then, we introduce a data-driven method that controls the condition of the interpolation matrix to avoid numerically unstable interpolations, while keeping a very good accuracy. In addition, a fall-back procedure is proposed to enforce a strict upper bound on the condition number, as well as a learning strategy to improve the performance of the data-driven method by learning from previously run simulations. We present numerical test cases to assess the performance of the proposed methods in interpolation tasks and in a RBF based finite difference (RBF-FD) method, in one and two-space dimensions.

math.NA↗
arXiv2024

Injecting Hierarchical Biological Priors into Graph Neural Networks for Flow Cytometry Prediction

In the complex landscape of hematologic samples such as peripheral blood or bone marrow derived from flow cytometry (FC) data, cell-level prediction presents profound challenges. This work explores injecting hierarchical prior knowledge into graph neural networks (GNNs) for single-cell multi-class classification of tabular cellular data. By representing the data as graphs and encoding hierarchical relationships between classes, we propose our hierarchical plug-in method to be applied to several GNN models, namely, FCHC-GNN, and effectively designed to capture neighborhood information crucial for single-cell FC domain. Extensive experiments on our cohort of 19 distinct patients, demonstrate that incorporating hierarchical biological constraints boosts performance significantly across multiple metrics compared to baseline GNNs without such priors. The proposed approach highlights the importance of structured inductive biases for gaining improved generalization in complex biological prediction tasks.

cs.LG↗
arXiv2024

A new variable shape parameter strategy for RBF approximation using neural networks

The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between ill-condition of the interpolation matrix and high accuracy. In this paper, we demonstrate how to use neural networks to determine the shape parameters in RBFs. In particular, we construct a multilayer perceptron trained using an unsupervised learning strategy, and use it to predict shape parameters for inverse multiquadric and Gaussian kernels. We test the neural network approach in RBF interpolation tasks and in a RBF-finite difference method in one and two-space dimensions, demonstrating promising results.

math.NA↗
arXiv2024

FlowCyt: A Comparative Study of Deep Learning Approaches for Multi-Class Classification in Flow Cytometry Benchmarking

This paper presents FlowCyt, the first comprehensive benchmark for multi-class single-cell classification in flow cytometry data. The dataset comprises bone marrow samples from 30 patients, with each cell characterized by twelve markers. Ground truth labels identify five hematological cell types: T lymphocytes, B lymphocytes, Monocytes, Mast cells, and Hematopoietic Stem/Progenitor Cells (HSPCs). Experiments utilize supervised inductive learning and semi-supervised transductive learning on up to 1 million cells per patient. Baseline methods include Gaussian Mixture Models, XGBoost, Random Forests, Deep Neural Networks, and Graph Neural Networks (GNNs). GNNs demonstrate superior performance by exploiting spatial relationships in graph-encoded data. The benchmark allows standardized evaluation of clinically relevant classification tasks, along with exploratory analyses to gain insights into hematological cell phenotypes. This represents the first public flow cytometry benchmark with a richly annotated, heterogeneous dataset. It will empower the development and rigorous assessment of novel methodologies for single-cell analysis.

cs.LG↗
arXiv2024

Why Attention Graphs Are All We Need: Pioneering Hierarchical Classification of Hematologic Cell Populations with LeukoGraph

In the complex landscape of hematologic samples such as peripheral blood or bone marrow, cell classification, delineating diverse populations into a hierarchical structure, presents profound challenges. This study presents LeukoGraph, a recently developed framework designed explicitly for this purpose employing graph attention networks (GATs) to navigate hierarchical classification (HC) complexities. Notably, LeukoGraph stands as a pioneering effort, marking the application of graph neural networks (GNNs) for hierarchical inference on graphs, accommodating up to one million nodes and millions of edges, all derived from flow cytometry data. LeukoGraph intricately addresses a classification paradigm where for example four different cell populations undergo flat categorization, while a fifth diverges into two distinct child branches, exemplifying the nuanced hierarchical structure inherent in complex datasets. The technique is more general than this example. A hallmark achievement of LeukoGraph is its F-score of 98%, significantly outclassing prevailing state-of-the-art methodologies. Crucially, LeukoGraph's prowess extends beyond theoretical innovation, showcasing remarkable precision in predicting both flat and hierarchical cell types across flow cytometry datasets from 30 distinct patients. This precision is further underscored by LeukoGraph's ability to maintain a correct label ratio, despite the inherent challenges posed by hierarchical classifications.

cs.LG↗
arXiv2024

HemaGraph: Breaking Barriers in Hematologic Single Cell Classification with Graph Attention

In the realm of hematologic cell populations classification, the intricate patterns within flow cytometry data necessitate advanced analytical tools. This paper presents 'HemaGraph', a novel framework based on Graph Attention Networks (GATs) for single-cell multi-class classification of hematological cells from flow cytometry data. Harnessing the power of GATs, our method captures subtle cell relationships, offering highly accurate patient profiling. Based on evaluation of data from 30 patients, HemaGraph demonstrates classification performance across five different cell classes, outperforming traditional methodologies and state-of-the-art methods. Moreover, the uniqueness of this framework lies in the training and testing phase of HemaGraph, where it has been applied for extremely large graphs, containing up to hundreds of thousands of nodes and two million edges, to detect low frequency cell populations (e.g. 0.01% for one population), with accuracies reaching 98%. Our findings underscore the potential of HemaGraph in improving hematoligic multi-class classification, paving the way for patient-personalized interventions. To the best of our knowledge, this is the first effort to use GATs, and Graph Neural Networks (GNNs) in general, to classify cell populations from single-cell flow cytometry data. We envision applying this method to single-cell data from larger cohort of patients and on other hematologic diseases.

q-bio.QM↗
arXiv2023

An arbitrarily high order and asymptotic preserving kinetic scheme in compressible fluid dynamic

We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics, both in time and space, which include the relaxation schemes by S. Jin and Z. Xin. These methods can use CFL number larger or equal to unity on regular Cartesian meshes for multi-dimensional case. These kinetic models depend on a small parameter that can be seen as a "Knudsen" number. The method is asymptotic preserving in this Knudsen number. Also, the computational costs of the method are of the same order of a fully explicit scheme. This work is the extension of Abgrall et al. (2022) \cite{Abgrall} to multi-dimensional systems. We have assessed our method on several problems for two dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions.

math.NA↗