arXiv subjects

Róbert Rajkó

Publications and source records attributed to Róbert Rajkó.

6 recordsLinked to original sources

arXiv2026

Some surprising properties of essential data points visualization

Essential Data Points (EDPs) - the vertices of the convex hull of a bilinear data matrix $\mathbf{D}$ in its row space, column space, or both - are widely used in chemometrics to reduce the size of large data sets while nominally preserving their underlying geometric structure. Using simulated three- and two-component chromatographic/spectral data sets and a real source-apportionment data set ($\mathbf{D = C\, A^\mathsf{T}}$), together with Borgen-Rajkó plots, Procrustes analysis, and variance-covariance comparisons, we show that this preservation is only \emph{partial}: row-wise EDP reduction preserves the row-space geometry (inner and outer polygons) exactly while distorting the column-space geometry, and column-wise reduction shows the opposite behavior; joint row-and-column reduction distorts both. We then give a rigorous, general proof - based on the four fundamental subspaces of a matrix and its singular value decomposition $\mathbf{D = U\,S\,V^\mathsf{T}}$ - that the subspace which is \emph{not} being reduced is always preserved exactly, up to an orthogonal rotation, whereas the subspace whose ambient dimension shrinks is related to the original only through a general, non-orthogonal isomorphism. This distinction is confirmed numerically to machine precision ($\sim 10^{-14}$-$10^{-16}$) on the real data set, and a deliberate negative control confirms that the "ambient-shrinking" map is genuinely non-orthogonal (residual $\approx 1$). These results demonstrate that the apparent rotation of an EDP-reduced polygon relative to the original is not, in general, a rigid rotation, and that visual or numerical comparisons between an EDP-reduced data set and the original data require an explicit, mode-dependent change-of-basis correction before any geometric or statistical conclusion can be drawn. A MATLAB implementation of this correction is provided.

stat.CO↗

arXiv2026

Diffusion-Based Feature Denoising with NNMF for Robust handwritten digit multi-class classification

This work presents a robust multi-class classification framework for handwritten digits that combines diffusion-driven feature denoising with a hybrid feature representation. Inspired by our previous work on brain tumor classification, the proposed approach operates in a feature space to improve the robustness to noise and adversarial attacks. This manuscript is submitted as an extended abstract rather than a full-length press-ready paper. First, the input images are converted into tight, interpretable exemplification using Non-negative Matrix Factorization (NNMF). In parallel, special deep features are extracted using a computational neural network (CNN). These integral features are combined into a united hybrid representation. The main objective of this work is to extend our previously validated two-class framework to a multi-class handwritten digit classification scenario. To improve robustness, a step diffusion operation is used in the feature space by gradually adding Gaussian noise. A feature denoiser network is trained to reverse this operation and rebuild clean representations from tilted inputs. The courteous features are then applied for multi-class classification. The suggested method is evaluated in both baseline and adversarial settings using AutoAttack. The experimental outcome present that the diffusion-based hybrid model is both effective and robust, the CNN baseline models outperforming while maintain powerful classification performance. These results explain the activity of feature-level diffusion defense for reliable multi-class handwritten digit classification.

cs.CV↗

arXiv2026

Diffusion-Based Feature Denoising and Using NNMF for Robust Brain Tumor Classification

Brain tumor classification from magnetic resonance imaging, which is also known as MRI, plays a sensitive role in computer-assisted diagnosis systems. In recent years, deep learning models have achieved high classification accuracy. However, their sensitivity to adversarial perturbations has become an important reliability concern in medical applications. This study suggests a robust brain tumor classification framework that combines Non-Negative Matrix Factorization (NNMF or NMF), lightweight convolutional neural networks (CNNs), and diffusion-based feature purification. Initially, MRI images are preprocessed and converted into a non-negative data matrix, from which compact and interpretable NNMF feature representations are extracted. Statistical metrics, including AUC, Cohen's d, and p-values, are used to rank and choose the most discriminative components. Then, a lightweight CNN classifier is trained directly on the selected feature groups. To improve adversarial robustness, a diffusion-based feature-space purification module is introduced. A forward noise method followed by a learned denoiser network is used before classification. System performance is estimated using both clean accuracy and robust accuracy under powerful adversarial attacks created by AutoAttack. The experimental results show that the proposed framework achieves competitive classification performance while significantly enhancing robustness against adversarial perturbations.The findings presuppose that combining interpretable NNMF-based representations with a lightweight deep approach and diffusion-based defense technique supplies an effective and reliable solution for medical image classification under adversarial conditions.

cs.CV↗

arXiv2023

On problematic practice of using normalization in Self-modeling/Multivariate Curve Resolution (S/MCR)

The paper is briefly dealing with greater or lesser misused normalization in self-modeling/multivariate curve resolution (S/MCR) practice. The importance of the correct use of the ode solvers and apt kinetic illustrations are elucidated. The new terms, external and internal normalizations are defined and interpreted. The problem of reducibility of a matrix is touched. Improper generalization/development of normalization-based methods are cited as examples. The position of the extreme values of the signal contribution function is clarified. An Executable Notebook with Matlab Live Editor was created for algorithmic explanations and depictions.

stat.ME↗

arXiv2022

Partial Identifiability for Nonnegative Matrix Factorization

Given a nonnegative matrix factorization, $R$, and a factorization rank, $r$, Exact nonnegative matrix factorization (Exact NMF) decomposes $R$ as the product of two nonnegative matrices, $C$ and $S$ with $r$ columns, such as $R = CS^\top$. A central research topic in the literature is the conditions under which such a decomposition is unique/identifiable, up to trivial ambiguities. In this paper, we focus on partial identifiability, that is, the uniqueness of a subset of columns of $C$ and $S$. We start our investigations with the data-based uniqueness (DBU) theorem from the chemometrics literature. The DBU theorem analyzes all feasible solutions of Exact NMF, and relies on sparsity conditions on $C$ and $S$. We provide a mathematically rigorous theorem of a recently published restricted version of the DBU theorem, relying only on simple sparsity and algebraic conditions: it applies to a particular solution of Exact NMF (as opposed to all feasible solutions) and allows us to guarantee the partial uniqueness of a single column of $C$ or $S$. Second, based on a geometric interpretation of the restricted DBU theorem, we obtain a new partial identifiability result. This geometric interpretation also leads us to another partial identifiability result in the case $r=3$. Third, we show how partial identifiability results can be used sequentially to guarantee the identifiability of more columns of $C$ and $S$. We illustrate these results on several examples, including one from the chemometrics literature.

math.NA↗

arXiv2020

Employing Partial Least Squares Regression with Discriminant Analysis for Bug Prediction

Forecasting defect proneness of source code has long been a major research concern. Having an estimation of those parts of a software system that most likely contain bugs may help focus testing efforts, reduce costs, and improve product quality. Many prediction models and approaches have been introduced during the past decades that try to forecast bugged code elements based on static source code metrics, change and history metrics, or both. However, there is still no universal best solution to this problem, as most suitable features and models vary from dataset to dataset and depend on the context in which we use them. Therefore, novel approaches and further studies on this topic are highly necessary. In this paper, we employ a chemometric approach - Partial Least Squares with Discriminant Analysis (PLS-DA) - for predicting bug prone Classes in Java programs using static source code metrics. To our best knowledge, PLS-DA has never been used before as a statistical approach in the software maintenance domain for predicting software errors. In addition, we have used rigorous statistical treatments including bootstrap resampling and randomization (permutation) test, and evaluation for representing the software engineering results. We show that our PLS-DA based prediction model achieves superior performances compared to the state-of-the-art approaches (i.e. F-measure of 0.44-0.47 at 90% confidence level) when no data re-sampling applied and comparable to others when applying up-sampling on the largest open bug dataset, while training the model is significantly faster, thus finding optimal parameters is much easier. In terms of completeness, which measures the amount of bugs contained in the Java Classes predicted to be defective, PLS-DA outperforms every other algorithm: it found 69.3% and 79.4% of the total bugs with no re-sampling and up-sampling, respectively.

cs.SE↗