We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions to classify sets of points, and can be computed using existing binary SVM algorithms in higher-dimensional spaces, including soft-margin SVM algorithms. We describe how the theoretical guarantees of standard support vector machines transfer to these new classes of multi-class support vector machines. We give a new simple proof of a geometric characterization of support vectors for largest margin SVMs by Veelaert.

Ordinal regression is a specialized supervised problem where the labels show an inherent order. The order distinguishes it from normal multi-class problem. Support Vector Ordinal Regression, as an outstanding ordinal regression model, is widely used in many ordinal regression tasks. However, like most supervised learning algorithms, the design of SVOR is based on the assumption that the training data are real and reliable, which is difficult to satisfy in real-world data. In many practical applications, outliers are frequently present in the training set, potentially leading to misguide the learning process, such that the performance is non-optimal. In this paper, we propose a novel capped $\ell_{p}$-norm loss function that is theoretically robust to both light and heavy outliers. The capped $\ell_{p}$-norm loss can help the model detect and eliminate outliers during training process. Adhering to this concept, we introduce a new model, Capped $\ell_{p}$-Norm Support Vector Ordinal Regression(CSVOR), that is robust to outliers. CSVOR uses a weight matrix to detect and eliminate outliers during the training process to improve the robustness to outliers. Moreover, a Re-Weighted algorithm algorithm which is illustrated convergence by our theoretical results is proposed to effectively minimize the corresponding problem. Extensive experimental results demonstrate that our model outperforms state-of-the-art(SOTA) methods, particularly in the presence of outliers.

Column generation (CG) is a powerful technique for solving optimization problems that involve a large number of variables or columns. This technique begins by solving a smaller problem with a subset of columns and gradually generates additional columns as needed. However, the generation of columns often requires solving difficult subproblems repeatedly, which can be a bottleneck for CG. To address this challenge, we propose a novel method called machine learning enhanced ant colony optimization (MLACO), to efficiently generate multiple high-quality columns from a subproblem. Specifically, we train a ML model to predict the optimal solution of a subproblem, and then integrate this ML prediction into the probabilistic model of ACO to sample multiple high-quality columns. Our experimental results on the bin packing problem with conflicts show that the MLACO method significantly improves the performance of CG compared to several state-of-the-art methods. Furthermore, when our method is incorporated into a Branch-and-Price method, it leads to a significant reduction in solution time.

In this paper, we explore the optimization of metal recycling with a focus on real-time differentiation between alloys of copper and aluminium. Spectral data, obtained through Prompt Gamma Neutron Activation Analysis (PGNAA), is utilized for classification. The study compares data from two detectors, cerium bromide (CeBr$_{3}$) and high purity germanium (HPGe), considering their energy resolution and sensitivity. We test various data generation, preprocessing, and classification methods, with Maximum Likelihood Classifier (MLC) and Conditional Variational Autoencoder (CVAE) yielding the best results. The study also highlights the impact of different detector types on classification accuracy, with CeBr$_{3}$ excelling in short measurement times and HPGe performing better in longer durations. The findings suggest the importance of selecting the appropriate detector and methodology based on specific application requirements.

Bone non-union is among the most severe complications associated with trauma surgery, occurring in 10-30% of cases after long bone fractures. Treating non-unions requires a high level of surgical expertise and often involves multiple revision surgeries, sometimes even leading to amputation. Thus, more accurate prognosis is crucial for patient well-being. Recent advances in machine learning (ML) hold promise for developing models to predict non-union healing, even when working with smaller datasets, a commonly encountered challenge in clinical domains. To demonstrate the effectiveness of ML in identifying candidates at risk of failed non-union healing, we applied three ML models (logistic regression, support vector machine, and XGBoost) to the clinical dataset TRUFFLE, which includes 797 patients with long bone non-union. The models provided prediction results with 70% sensitivity, and the specificities of 66% (XGBoost), 49% (support vector machine), and 43% (logistic regression). These findings offer valuable clinical insights because they enable early identification of patients at risk of failed non-union healing after the initial surgical revision treatment protocol.

Unmanned boats, while navigating at sea, utilize active compensation systems to mitigate wave disturbances experienced by onboard instruments and equipment. However, there exists a lag in the measurement of unmanned boat attitudes, thus introducing unmanned boat motion attitude prediction to compensate for the lag in the signal acquisition process. This paper, based on the basic principles of waves, derives the disturbance patterns of waves on unmanned boats from the wave energy spectrum. Through simulation analysis of unmanned boat motion attitudes, motion attitude data is obtained, providing experimental data for subsequent work. A combined prediction model based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Particle Swarm Optimization (PSO), and Support Vector Machine (SVM) is designed to predict the motion attitude of unmanned boats. Simulation results validate its superior prediction accuracy compared to traditional prediction models. For example, in terms of mean absolute error, it improves by 17% compared to the EMD-PSO-SVM model.

This calls into question the reasonableness of expecting users to make informed decisions given that they do not comprehend the terms. A technology that can automate the simplification and categorization of popular ToS documents would be immensely beneficial, enhancing user understanding of accepted policies and facilitating the identification of concerning changes. We envision an automated system that begins with the text of a ToS document for a new product or service. The prospective user copies and pastes the text into an automated tool, which extracts key concepts and then presents some information in a format that is shorter and easier to read, such as a numeric/letter score alongside a bullet list of the most important concepts. Our work focuses on extracting key concepts from a data corpus we scraped from Terms of Service; Didn't Read (ToS;DR) [38].

Alzheimer's disease is a severe neurological brain disorder. It is not curable, but earlier detection can help improve symptoms in a great deal. The machine learning-based approaches are popular and well-motivated models for many medical image processing tasks such as computer-aided diagnosis. These techniques can vastly improve the process for accurate diagnosis of Alzheimer's disease. In this paper, we investigate the performance of these techniques for Alzheimer's disease detection and classification using brain MRI and PET images from the OASIS database. The proposed system takes advantage of the powerful artificial neural network and support vector machines as classifiers, as well as principal component analysis as a feature extraction technique. The results indicate that the combined scheme achieves good accuracy and offers a significant advantage over the other approaches.

Deep Neural Networks are prone to learning and relying on spurious correlations in the training data, which, for high-risk applications, can have fatal consequences. Various approaches to suppress model reliance on harmful features have been proposed that can be applied post-hoc without additional training. Whereas those methods can be applied with efficiency, they also tend to harm model performance by globally shifting the distribution of latent features. To mitigate unintended overcorrection of model behavior, we propose a reactive approach conditioned on model-derived knowledge and eXplainable Artificial Intelligence (XAI) insights. While the reactive approach can be applied to many post-hoc methods, we demonstrate the incorporation of reactivity in particular for P-ClArC (Projective Class Artifact Compensation), introducing a new method called R-ClArC (Reactive Class Artifact Compensation). Through rigorous experiments in controlled settings (FunnyBirds) and with a real-world dataset (ISIC2019), we show that introducing reactivity can minimize the detrimental effect of the applied correction while simultaneously ensuring low reliance on spurious features.

The rapid developments of various machine learning models and their deployments in several applications has led to discussions around the importance of looking beyond the accuracies of these models. Fairness of such models is one such aspect that is deservedly gaining more attention. In this work, we analyse the natural language representations of documents and sentences (i.e., encodings) for any embedding-level bias that could potentially also affect the fairness of the downstream tasks that rely on them. We identify bias in these encodings either towards or against different sub-groups based on the difference in their reconstruction errors along various subsets of principal components. We explore and recommend ways to mitigate such bias in the encodings while also maintaining a decent accuracy in classification models that use them.