arXiv subjects

Michel van de Velden

Publications and source records attributed to Michel van de Velden.

8 recordsLinked to original sources

arXiv2026

Visualizing Class Specific Heterogeneous Tendencies using R

In this paper we introduce the R package mccca, which implements multiple-class cluster correspondence analysis (MCCCA) proposed in M.Takagishi et al., (2022). MCCCA is a statistical method that identifies and visualizes heterogeneous tendencies specific to ``classes'' (e.g., gender and nationality) in a low dimensional space. In MCCCA, two kinds of variables, external and active variables, are distinguished. External variables directly define classes whereas the active variables are used to derive class-specific clusters of observations (individuals). In this paper, we show how to apply MCCCA and how to visualize its results using mccca. We illustrate the procedure for performing MCCCA by applying it to two data sets.

stat.ME↗

arXiv2025

Generating Random Vectors satisfying Linear and Nonlinear Constraints

We consider the problem of generating n-dimensional vectors with a fixed sum, with the goal of generating a uniform distribution of vectors over a valid region. This means that each possible vector has an equal probability of being generated. The Dirichlet-Rescale (DRS) algorithm, introduced by Griffin et al. (2020), aims to generate a uniform distribution of vectors with fixed sum that satisfies lower and upper bounds on the individual entries. However, we demonstrate that the uniform distribution property of the DRS algorithm does not hold in general. Using an analytical procedure and a statistical test, we show that the vectors generated by the DRS algorithm do not appear to be drawn from a uniform distribution. To resolve this issue, we propose the Dirichlet-Rescale-Constraints (DRSC) algorithm, which handles more general constraints, including both linear and nonlinear constraints, while ensuring that the vectors are drawn from a uniform distribution. In our computational experiments we demonstrate the effectiveness of the DRSC algorithm.

math.OC↗

arXiv2024

Classifier Chain Networks for Multi-Label Classification

The classifier chain is a widely used method for analyzing multi-labeled data sets. In this study, we introduce a generalization of the classifier chain: the classifier chain network. The classifier chain network enables joint estimation of model parameters, and allows to account for the influence of earlier label predictions on subsequent classifiers in the chain. Through simulations, we evaluate the classifier chain network's performance against multiple benchmark methods, demonstrating competitive results even in scenarios that deviate from its modeling assumptions. Furthermore, we propose a new measure for detecting conditional dependencies between labels and illustrate the classifier chain network's effectiveness using an empirical data set.

stat.ML↗

arXiv2024

Unbiased mixed variables distance

Defining a distance in a mixed setting requires the quantification of observed differences of variables of different types and of variables that are measured on different scales. There exist several proposals for mixed variable distances, however, such distances tend to be biased towards specific variable types and measurement units. That is, the variable types and scales influence the contribution of individual variables to the overall distance. In this paper, we define unbiased mixed variable distances for which the contributions of individual variables to the overall distance are not influenced by measurement types or scales. We define the relevant concepts to quantify such biases and we provide a general formulation that can be used to construct unbiased mixed variable distances.

stat.ME↗

arXiv2023

Dual scaling of rating data

When applied to contingency tables, dual scaling and correspondence are mathematically equivalent methods. For the analysis of rating data, however, the methods differ. To a large extent this is due to differences in preprocessing of the data. In particular, in dual scaling, ratings are either transformed to rank order, or to successive category data before applying a customised dual scaling approach. In correspondence analysis, on the other hand, a so-called doubling of the original ratings is applied before applying the usual correspondence analysis formulas. In this paper, we consider these differences in detail. We propose a dual scaling variant that can be applied directly to the ratings and we compare theoretical as well as practical properties of the different approaches.

stat.ME↗

arXiv2023

A general framework for implementing distances for categorical variables

The degree to which subjects differ from each other with respect to certain properties measured by a set of variables, plays an important role in many statistical methods. For example, classification, clustering, and data visualization methods all require a quantification of differences in the observed values. We can refer to the quantification of such differences, as distance. An appropriate definition of a distance depends on the nature of the data and the problem at hand. For distances between numerical variables, there exist many definitions that depend on the size of the observed differences. For categorical data, the definition of a distance is more complex, as there is no straightforward quantification of the size of the observed differences. Consequently, many proposals exist that can be used to measure differences based on categorical variables. In this paper, we introduce a general framework that allows for an efficient and transparent implementation of distances between observations on categorical variables. We show that several existing distances can be incorporated into the framework. Moreover, our framework quite naturally leads to the introduction of new distance formulations and allows for the implementation of flexible, case and data specific distance definitions. Furthermore, in a supervised classification setting, the framework can be used to construct distances that incorporate the association between the response and predictor variables and hence improve the performance of distance-based classifiers.

stat.ML↗

arXiv2022

Effects of Visual Priming on Rating Scale Usage

Rating scales are much used in survey research. Often, it is assumed that the scores obtained through rating scales can be compared within and between respondents when studies are in one country. In addition, it is assumed that they can be treated as a numerical scale. In this paper, we study the anchoring effect of a visual stimulus on rating scale usage. To do so, we set up a randomized experiment where the experimental group was primed by asking to rate the filling of a cylinder that was presented visually. For a five point rating scale, we find the effect that primed respondents use Category 1 less and Categories 3 and 4 more, and no effect on Categories 2 and 5.

stat.AP↗

arXiv2019

Visualizing class specific heterogeneous tendencies in categorical data

In multiple correspondence analysis, both individuals (observations) and categories can be represented in a biplot that jointly depicts the relationships across categories or individuals, as well as the associations between them. Additional information about the individuals can enhance interpretation capacities, such as by including categorical variables for which the interdependencies are not of immediate concern, but that facilitate the interpretation of the plot with respect to relationships between individuals and categories. This article proposes a new method for adding such information, according to a multiple-set cluster correspondence analysis approach that identifies clusters specific to classes, or subsets of the data that correspond to the categories of the additional variables. The proposed method can construct a biplot that depicts heterogeneous tendencies of individual members, as well as their relationships with the original categorical variables. A simulation study to investigate the performance of this proposed method and an application to data regarding road accidents in the United Kingdom confirms the viability of this approach.

stat.ME↗