Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified exact low-dimensional embeddings, the limits of the required embedding dimensions remain unclear. We presently prove that lower dimensional embeddings are possible when using Euclidean metric embeddings as opposed to vector-based Logistic PCA (LPCA) embeddings. In particular, we provide an efficient logarithmic search procedure for identifying the exact embedding dimension and demonstrate how metric embeddings enable inference of the exact embedding dimensions of large-scale networks by exploiting that the metric properties can be used to provide linearithmic scaling. Empirically, we show that our approach extracts substantially lower dimensional representations of networks than previously reported for small-sized networks. For the first time, we demonstrate that even large-scale networks can be effectively embedded in very low-dimensional spaces, and provide examples of scalable, exact reconstruction for graphs with up to a million nodes. Our approach highlights that the intrinsic dimensionality of networks is substantially lower than previously reported and provides a computationally efficient assessment of the exact embedding dimension also of large-scale networks. The surprisingly low dimensional representations achieved demonstrate that networks in general can be losslessly represented using very low dimensional feature spaces, which can be used to guide existing network analysis tasks from community detection and node classification to structure revealing exact network visualizations.

The aim of this paper is to investigate an attempt to build a binary classification algorithm using principles of geometry such as vectors, planes, and vector algebra. The basic idea behind the proposed algorithm is that a hyperplane can be used to completely separate a given set of data points mapped to n dimensional space, if the given data points are linearly separable in the n dimensions. Since points are the foundational elements of any geometrical construct, by manipulating the position of points used for the construction of a given hyperplane, the position of the hyperplane itself can be manipulated. The paper includes testing data against other classifiers on a variety of standard machine learning datasets. With a focus on support vector machines, since they and our proposed classifier use the same geometrical construct of hyperplane, and the versatility of SVMs make them a good bench mark for comparison. Since the algorithm focuses on moving the points through the hyperspace to which the dataset has been mapped, it has been dubbed as moving points algorithm.

In continual time series analysis using neural networks, catastrophic forgetting (CF) of previously learned models when training on new data domains has always been a significant challenge. This problem is especially challenging in vehicle estimation and control, where new information is sequentially introduced to the model. Unfortunately, existing work on continual learning has not sufficiently addressed the adverse effects of catastrophic forgetting in time series analysis, particularly in multivariate output environments. In this paper, we present EM-ReSeleCT (Efficient Multivariate Representative Selection for Continual Learning in Time Series Tasks), an enhanced approach designed to handle continual learning in multivariate environments. Our approach strategically selects representative subsets from old and historical data and incorporates memory-based continual learning techniques with an improved optimization algorithm to adapt the pre-trained model on new information while preserving previously acquired information. Additionally, we develop a sequence-to-sequence transformer model (autoregressive model) specifically designed for vehicle state estimation. Moreover, we propose an uncertainty quantification framework using conformal prediction to assess the sensitivity of the memory size and to showcase the robustness of the proposed method. Experimental results from tests on an electric Equinox vehicle highlight the superiority of our method in continually learning new information while retaining prior knowledge, outperforming state-of-the-art continual learning methods. Furthermore, EM-ReSeleCT significantly reduces training time, a critical advantage in continual learning applications.

Stochastic gradient descent (SGD) optimization methods are the method of choice to train deep artificial neural networks (ANNs) in data-driven learning problems (see, for instance, [1, 7, 33, 36, 38, 41] and the references therein) as well as scientific computing problems (see, for example, [3, 13, 19, 22, 26, 40] and the references therein). However, often not the plain vanilla standard SGD optimization method is the employed optimizer but instead more sophisticated accelerated and adaptive variants of the standard SGD method such as the adaptive moment estimation SGD (Adam) optimizer (see [32]) are used in practically relevant deep ANN training problems. We also refer, for instance, to [2, 20, 23, 29, 35, 39] for monographs and surveys treating SGD optimization methods for the training of ANNs. The considered SGD optimization method is used with the aim to minimize the true risk function (the objective function) of the considered ANN learning problem so that, roughly speaking, the realization function of the deep ANN minimizing the true risk function approximates as best as possible the output data given the input data. Despite the omnipresent use of SGD optimization methods in the training of ANNs, it remains, in basically all practically relevant scenarios, a fundamental open problem to provide a rigorous theoretical description and explanation for the convergence (and non-convergence) properties of SGD optimization methods in deep learning. In particular, it remains an open question to prove or disprove convergence of the true risk of SGD optimization methods to the optimal/infimal true risk value in the training of deep ANNs (cf., for example, [11, 18, 31, 34] and the literature review in Subsection 1.4 below). In this work we contribute to this open problem of research in two aspects.

Hypertensive retinopathy (HR) is a severe eye disease that may cause permanent vision loss if not diagnosed early. Traditional diagnostic methods are time-consuming and subjective, highlighting the need for an automated, reliable system. Existing studies often use a single Deep Learning (DL) model, struggling to distinguish HR stages. This study introduces a three-stage approach to enhance HR diagnosis accuracy. Initially, 14 CNN models were tested, identifying DenseNet169, MobileNet, and ResNet152 as the most effective. DenseNet169 achieved 87.73% accuracy, 87.75% precision, 87.73% recall, 87.67% F1-score, and 0.8359 Cohen's Kappa. MobileNet followed with 86.40% accuracy, 86.60% precision, 86.40% recall, 86.31% F1-score, and 0.8180 Cohen's Kappa. ResNet152 ranked third with 85.87% accuracy, 86.01% precision, 85.87% recall, 85.83% F1-score, and 0.8188 Cohen's Kappa. In the second stage, deep features from these models were fused and classified using Machine Learning (ML) algorithms (SVM, RF, XGBoost). SVM (sigmoid kernel) performed best with 92.00% accuracy, 91.93% precision, 92.00% recall, 91.91% F1-score, and 0.8930 Cohen's Kappa. The third stage applied meta-heuristic optimization (GA, ABC, PSO, HHO) for feature selection. HHO yielded 94.66% accuracy, precision, and recall, 94.64% F1-score, and 0.9286 Cohen's Kappa. The proposed approach surpassed single CNN models and previous studies in HR diagnosis accuracy and generalization.

Node classification is a key task in temporal graph learning (TGL). Real-life temporal graphs often introduce new node classes over time, but existing TGL methods assume a fixed set of classes. This assumption brings limitations, as updating models with full data is costly, while focusing only on new classes results in forgetting old ones. Graph continual learning (GCL) methods mitigate forgetting using old-class subsets but fail to account for their evolution. We define this novel problem as temporal graph continual learning (TGCL), which focuses on efficiently maintaining up-to-date knowledge of old classes. To tackle TGCL, we propose a selective learning framework that substitutes the old-class data with its subsets, Learning Towards the Future (LTF). We derive an upper bound on the error caused by such replacement and transform it into objectives for selecting and learning subsets that minimize classification error while preserving the distribution of the full old-class data. Experiments on three real-world datasets validate the effectiveness of LTF on TGCL.

Credit card fraud imposes significant costs on both cardholders and issuing banks. Fraudsters often disguise their crimes, such as using legitimate transactions through several benign users to bypass anti-fraud detection. Existing graph neural network (GNN) models struggle with learning features of camouflaged, indirect multi-hop transactions due to their inherent over-smoothing issues in deep multi-layer aggregation, presenting a major challenge in detecting disguised relationships. Therefore, in this paper, we propose a novel High-order Graph Representation Learning model (HOGRL) to avoid incorporating excessive noise during the multi-layer aggregation process. In particular, HOGRL learns different orders of \emph{pure} representations directly from high-order transaction graphs. We realize this goal by effectively constructing high-order transaction graphs first and then learning the \emph{pure} representations of each order so that the model could identify fraudsters' multi-hop indirect transactions via multi-layer \emph{pure} feature learning. In addition, we introduce a mixture-of-expert attention mechanism to automatically determine the importance of different orders for jointly optimizing fraud detection performance. We conduct extensive experiments in both the open source and real-world datasets, the result demonstrates the significant improvements of our proposed HOGRL compared with state-of-the-art fraud detection baselines. HOGRL's superior performance also proves its effectiveness in addressing high-order fraud camouflage criminals.

Pairwise learning includes various machine learning tasks, with ranking and metric learning serving as the primary representatives. While randomized coordinate descent (RCD) is popular in various learning problems, there is much less theoretical analysis on the generalization behavior of models trained by RCD, especially under the pairwise learning framework. In this paper, we consider the generalization of RCD for pairwise learning. We measure the on-average argument stability for both convex and strongly convex objective functions, based on which we develop generalization bounds in expectation. The early-stopping strategy is adopted to quantify the balance between estimation and optimization. Our analysis further incorporates the low-noise setting into the excess risk bound to achieve the optimistic bound as $O(1/n)$, where $n$ is the sample size.

Over recent decades, extensive research has aimed to overcome the restrictive underlying assumptions required for a Generalized Linear Model to generate accurate and meaningful predictions. These efforts include regularizing coefficients, selecting features, and clustering ordinal categories, among other approaches. Despite these advances, efficiently clustering nominal categories in GLMs without incurring high computational costs remains a challenge. This paper introduces Ranking to Variable Fusion (R2VF), a two-step method designed to efficiently fuse nominal and ordinal categories in GLMs. By first transforming nominal features into an ordinal framework via regularized regression and then applying variable fusion, R2VF strikes a balance between model complexity and interpretability. We demonstrate the effectiveness of R2VF through comparisons with other methods, highlighting its performance in addressing overfitting and finding a proper set of covariates.

Existing pretraining data mixing methods for large language models (LLMs) typically follow a domain-wise methodology, a top-down process that first determines domain weights and then performs uniform data sampling across each domain. However, these approaches neglect significant inter-domain overlaps and commonalities, failing to control the global diversity of the constructed training dataset. Further, uniform sampling within domains ignores fine-grained sample-specific features, potentially leading to suboptimal data distribution. To address these shortcomings, we propose a novel sample-wise data mixture approach based on a bottom-up paradigm. This method performs global cross-domain sampling by systematically evaluating the quality and diversity of each sample, thereby dynamically determining the optimal domain distribution. Comprehensive experiments across multiple downstream tasks and perplexity assessments demonstrate that SampleMix surpasses existing domain-based methods. Meanwhile, SampleMix requires 1.4x to 2.1x training steps to achieves the baselines' performance, highlighting the substantial potential of SampleMix to optimize pre-training data.