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The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…

Predictive models are increasingly deployed for the purpose of determining access to services such as credit, insurance, and employment. Despite potential gains in productivity and efficiency, several potential problems have yet to be…

Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…

We propose a new method for modelling simple longitudinal data. We aim to do this in a flexible manner (without restrictive assumptions about the shapes of individual trajectories), while exploiting structural similarities between the…

Variable selection is a procedure to attain the truly important predictors from inputs. Complex nonlinear dependencies and strong coupling pose great challenges for variable selection in high-dimensional data. In addition, real-world…

Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS…

Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence…

Clustering ensemble has emerged as an important research topic in the field of machine learning. Although numerous methods have been proposed to improve clustering quality, most existing approaches overlook the need for interpretability in…

We survey work on the paradigm called "computing by observing." Its central feature is that one considers the behavior of an evolving system as the result of a computation. To this end an observer records this behavior. It has turned out…

We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few…

One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical…

The aim of this paper is to present a new method of approximation of planar data set using only arcs or segments. The first problem we are trying to solve is the following: the CNC machines can work only with simple curves (arcs or…

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…

Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the…

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…

An interpretable model or method has several appealing features, such as reliability to adversarial examples, transparency of decision-making, and communication facilitator. However, interpretability is a subjective concept, and even its…

This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-represent a functional subspace in terms of directions of decreasing smoothness as represented by a generalized…

Astronomy is in an era where all-sky surveys are mapping the Galaxy. The plethora of photometric, spectroscopic, asteroseismic and astrometric data allows us to characterise the comprising stars in detail. Here we quantify to what extent…

Today, as increasingly complex predictive models are developed, simple rule sets remain a crucial tool to obtain interpretable predictions and drive high-stakes decision making. However, a single rule set provides a partial representation…

To reduce human error and prejudice, many high-stakes decisions have been turned over to machine algorithms. However, recent research suggests that this does not remove discrimination, and can perpetuate harmful stereotypes. While…