In the context of the growing proliferation of user devices and the concurrent surge in data volumes, the complexities arising from the substantial increase in data have posed formidable challenges to conventional machine learning model training. Particularly, this is evident within resource-constrained and security-sensitive environments such as those encountered in networks associated with the Internet of Things (IoT). Federated Learning has emerged as a promising remedy to these challenges by decentralizing model training to edge devices or parties, effectively addressing privacy concerns and resource limitations. Nevertheless, the presence of statistical heterogeneity in non-Independently and Identically Distributed (non-IID) data across different parties poses a significant hurdle to the effectiveness of FL. Many FL approaches have been proposed to enhance learning effectiveness under statistical heterogeneity. However, prior studies have uncovered a gap in the existing research landscape, particularly in the absence of a comprehensive comparison between federated methods addressing statistical heterogeneity in detecting IoT attacks. In this research endeavor, we delve into the exploration of FL algorithms, specifically FedAvg, FedProx, and Scaffold, under different data distributions. Our focus is on achieving a comprehensive understanding of and addressing the challenges posed by statistical heterogeneity. In this study, We classify large-scale IoT attacks by utilizing the CICIoT2023 dataset. Through meticulous analysis and experimentation, our objective is to illuminate the performance nuances of these FL methods, providing valuable insights for researchers and practitioners in the domain.

Tensor decomposition faces fundamental challenges in analyzing high-dimensional data, where traditional methods based on reconstruction and fixed-rank constraints often fail to capture semantically meaningful structures. This paper introduces a no-rank tensor decomposition framework grounded in metric learning, which replaces reconstruction objectives with a discriminative, similarity-based optimization. The proposed approach learns data-driven embeddings by optimizing a triplet loss with diversity and uniformity regularization, creating a feature space where distance directly reflects semantic similarity. We provide theoretical guarantees for the framework's convergence and establish bounds on its metric properties. Evaluations across diverse domains -- including face recognition (LFW, Olivetti), brain connectivity analysis (ABIDE), and simulated data (galaxy morphology, crystal structures) -- demonstrate that our method outperforms baseline techniques, including PCA, t-SNE, UMAP, and tensor decomposition baselines (CP and Tucker). Results show substantial improvements in clustering metrics (Silhouette Score, Davies-Bouldin Index, Calinski-Harabasz Index, Separation Ratio, Adjusted Rand Index, Normalized Mutual Information) and reveal a fundamental trade-off: while metric learning optimizes global class separation, it deliberately transforms local geometry to align with semantic relationships. Crucially, our approach achieves superior performance with smaller training datasets compared to transformer-based methods, offering an efficient alternative for domains with limited labeled data. This work establishes metric learning as a paradigm for tensor-based analysis, prioritizing semantic relevance over pixel-level fidelity while providing computational advantages in data-scarce scenarios.

Deep learning has shown high performance on spectroscopic inverse problems when sufficient data is available. However, it is often the case that data in spectroscopy is scarce, and this usually causes severe overfitting problems with deep learning methods. Traditional machine learning methods are viable when datasets are smaller, but the accuracy and applicability of these methods is generally more limited. We introduce a deep learning method for classification of molecular spectra based on learning integral operators via integral equations of the first kind, which results in an algorithm that is less affected by overfitting issues on small datasets, compared to other deep learning models. The problem formulation of the deep learning approach is based on inverse problems, which have traditionally found important applications in spectroscopy. We perform experiments on real world data to showcase our algorithm. It is seen that the model outperforms traditional machine learning approaches such as decision tree and support vector machine, and for small datasets it outperforms other deep learning models. Therefore, our methodology leverages the power of deep learning, still maintaining the performance when the available data is very limited, which is one of the main issues that deep learning faces in spectroscopy, where datasets are often times of small size.

We present an algorithm for learning operators between Banach spaces, based on the use of Leray-Schauder mappings to learn a finite-dimensional approximation of compact subspaces. We show that the resulting method is a universal approximator of (possibly nonlinear) operators. We demonstrate the efficiency of the approach on two benchmark datasets showing it achieves results comparable to state of the art models.

We obtain a new universal approximation theorem for continuous operators on arbitrary Banach spaces using the Leray-Schauder mapping. Moreover, we introduce and study a method for operator learning in Banach spaces $L^p$ of functions with multiple variables, based on orthogonal projections on polynomial bases. We derive a universal approximation result for operators where we learn a linear projection and a finite dimensional mapping under some additional assumptions. For the case of $p=2$, we give some sufficient conditions for the approximation results to hold. This article serves as the theoretical framework for a deep learning methodology whose implementation will be provided in subsequent work.

Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization procedure. This approach allows to leverage the nonlocal properties of integral operators in machine learning, but it is computationally expensive. In this article, we introduce a framework for neural integral equations based on spectral methods that allows us to learn an operator in the spectral domain, resulting in a cheaper computational cost, as well as in high interpolation accuracy. We study the properties of our methods and show various theoretical guarantees regarding the approximation capabilities of the model, and convergence to solutions of the numerical methods. We provide numerical experiments to demonstrate the practical effectiveness of the resulting model.

Battery performance datasets are typically non-normal and multicollinear. Extrapolating such datasets for model predictions needs attention to such characteristics. This study explores the impact of data normality in building machine learning models. In this work, tree-based regression models and multiple linear regressions models are each built from a highly skewed non-normal dataset with multicollinearity and compared. Several techniques are necessary, such as data transformation, to achieve a good multiple linear regression model with this dataset; the most useful techniques are discussed. With these techniques, the best multiple linear regression model achieved an R^2 = 81.23% and exhibited no multicollinearity effect for the dataset used in this study. Tree-based models perform better on this dataset, as they are non-parametric, capable of handling complex relationships among variables and not affected by multicollinearity. We show that bagging, in the use of Random Forests, reduces overfitting. Our best tree-based model achieved accuracy of R^2 = 97.73%. This study explains why tree-based regressions promise as a machine learning model for non-normally distributed, multicollinear data.

Americans prefer a space program that focuses on potential asteroid impacts, scientific research and using robots to explore the cosmos over sending humans back to the moon or on to Mars, a poll shows. The poll by The Associated Press and the NORC Center for Public Affairs Research, released Thursday, one month before the 50th anniversary of the Apollo 11 moon landing, lists asteroid and comet monitoring as the No. 1 desired objective for the United States space program. About two-thirds of Americans call that very or extremely important, and about a combined 9 in 10 say it's at least moderately important. The poll comes as the White House pushes to get astronauts back on the moon, but only about a quarter of Americans said moon or Mars exploration by astronauts should be among the space program's highest priorities. About another third called each of those moderately important.

CAPE CANAVERAL, FLORIDA - Americans prefer a space program that focuses on potential asteroid impacts, scientific research and using robots to explore the cosmos over sending humans back to the moon or on to Mars, a poll shows. The poll by The Associated Press-NORC Center for Public Affairs Research, released Thursday, one month before the 50th anniversary of the Apollo 11 moon landing, lists asteroid and comet monitoring as the No. 1 desired objective for the U.S. space program. About two-thirds of Americans call that very or extremely important, and about a combined 9 in 10 say it's at least moderately important. The poll comes as the White House pushes to get astronauts back on the moon, but only about a quarter of Americans said moon or Mars exploration by astronauts should be among the space program's highest priorities. About another third called each of those moderately important.

CAPE CANAVERAL, Fla. -- Americans prefer a space program that focuses on potential asteroid impacts, scientific research and using robots to explore the cosmos over sending humans back to the moon or on to Mars, a poll shows. The poll by The Associated Press and the NORC Center for Public Affairs Research, released Thursday, one month before the 50th anniversary of the Apollo 11 moon landing, lists asteroid and comet monitoring as the No. 1 desired objective for the U.S. space program. About two-thirds of Americans call that very or extremely important, and about a combined 9 in 10 call it at least moderately important. The poll comes as the White House pushes to get astronauts back on the moon, but only about a quarter of Americans said moon or Mars exploration by astronauts should be among the space program's highest priorities. About another third called each of those moderately important.