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Machine-learning models, which are known to accurately predict patterns from large datasets, are crucial in decision making. Consequently, counterfactual explanations-methods explaining predictions by introducing input perturbations-have…

A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…

A new line of research uses compression methods to measure the similarity between signals. Two signals are considered similar if one can be compressed significantly when the information of the other is known. The existing compression-based…

For numerous reasons there raises a need for dimension reduction that preserves certain characteristics of data. In this work we focus on data coming from a mixture of Gaussian distributions and we propose a method that preserves…

Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…

While road obstacle detection techniques have become increasingly effective, they typically ignore the fact that, in practice, the apparent size of the obstacles decreases as their distance to the vehicle increases. In this paper, we…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

Large information sizes in samples and features can be encoded to speed up the learning of statistical models based on linear algebra and remove unwanted signals. Encoding information can reduce both sample and feature dimension to a…

With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…

Clustering is a common task in machine learning, but clusters of unlabelled data can be hard to quantify. The application of clustering algorithms in chemistry is often dependant on material representation. Ascertaining the effects of…

This paper studies high-dimensional canonical correlation analysis (CCA) with an emphasis on the vectors that define canonical variables. The paper shows that when two dimensions of data grow to infinity jointly and proportionally, the…

Face reconstruction and tracking is a building block of numerous applications in AR/VR, human-machine interaction, as well as medical applications. Most of these applications rely on a metrically correct prediction of the shape, especially,…

Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter…

At the crossway of machine learning and data analysis, anomaly detection aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

Pattern recognition based on a high-dimensional predictor is considered. A classifier is defined which is based on a Transformer encoder. The rate of convergence of the misclassification probability of the classifier towards the optimal…

In recent years, machine learning models have been increasingly applied to spectroscopic datasets for chemical and biomedical analysis. For their successful adoption, particularly in clinical and safety-critical settings, professionals and…

Computer model calibration is a crucial step in building a reliable computer model. In the face of massive physical observations, a fast estimation for the calibration parameters is urgently needed. To alleviate the computational burden, we…

The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, the similarity between two trajectories is quantified by means of heuristic…