Related papers: Product Formalisms for Measures on Spaces with Bin…

We propose a new method for representing data sets with a set of binary feature functions. We compute both the dyadic set structure determined by an order on the binary features together with the canonical product coefficient parameters for…

Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…

High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based…

Dimensionless learning is a data-driven framework for discovering dimensionless numbers and scaling laws from experimental measurements. This tutorial introduces the method, explaining how it transforms experimental data into compact…

We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent…

Measurement error is prevalent across all domains of scientific research where only imprecise observations, rather than the true underlying values, can be obtained. For example, estimates of human microbiome diversity are based on small…

Effect size measures and visualization techniques aimed at maximizing the interpretability and comparability of results from statistical models have long been of great importance and are recently again receiving increased attention in the…

This paper introduces \textit{measurement trees}, a novel class of metrics designed to combine various constructs into an interpretable multi-level representation of a measurand. Unlike conventional metrics that yield single values,…

We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…

Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

Throughout the life sciences we routinely seek to interpret measurements and observations using parameterised mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a…

Visual representations are defined in terms of minimal sufficient statistics of visual data, for a class of tasks, that are also invariant to nuisance variability. Minimal sufficiency guarantees that we can store a representation in lieu of…

With a plethora of available classification performance measures, choosing the right metric for the right task requires careful thought. To make this decision in an informed manner, one should study and compare general properties of…

This article discusses aeroacoustic imaging methods based on correlation measurements in the frequency domain. Standard methods in this field assume that the estimated correlation matrix is superimposed with additive white noise. In this…

Measurement bridges theory and empirics. Without measures that appropriately capture theoretical concepts, description will fail to represent reality and true causal inference will be impossible. Yet, the social sciences traffic in complex…

We introduce a uniform representation of general objects that captures the regularities with respect to their structure. It allows a representation of a general class of objects including geometric patterns and images in a sparse, modular,…

In addressing the challenge of interpretability and generalizability of artificial music intelligence, this paper introduces a novel symbolic representation that amalgamates both explicit and implicit musical information across diverse…

Measurement is an integral part of modern science, providing the fundamental means for evaluation, comparison, and prediction. In the context of visualization, several different types of measures have been proposed, ranging from approaches…

This paper considers the problem of low-dimensional visualisation of very high dimensional information sources for the purpose of situation awareness in the maritime environment. In response to the requirement for human decision support…