arXiv subjects

Jan de Leeuw

Publications and source records attributed to Jan de Leeuw.

8 recordsLinked to original sources

arXiv2025

Yet Another Smacof -- Square Symmetric Case

We rewrite the metric/nonmetric and weighted/unweighted versions of the smacof program for square symmetric data as one monolithic C program. R is used for taking care of the data and parameter setup, the I/O, and of issuing a single call to .C() to start the computations. This makes this new smacofSS() program five to fifty times as fast (for our examples) as the smacofSym() function from the R smacof package. Utilities for various initial configurations and plots are included in the package. Examples are included to compare output and time for the R and C versions and to illustrate the various plots.

stat.CO↗

arXiv2025

Metric/Nonmetric Elastic MDS

We present R and C implementations for metric (ratio) and non-metric (ordinal) versions of Elastic MDS, the multidimensional scaling technique proposed by McGee (1966). The R and C versions are compared for speed, with the C version anywhere from 15 to 100 times as fast as the R version.

stat.CO↗

arXiv2025

Differentiating Generalized Eigenvalues and Eigenvectors

We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of a vector of parameters. In addition we provide functions in R to compute these derivatives, both in the general case and in various special cases. Formulae are checked against Jacobians and Hessians computed by numerical differentiation. Some applications to multivariate data analysis are discussed.

stat.CO↗

arXiv2024

Majorizing Stress Formula Two

Modifications of the smacof algorithm for multidimensional scaling are proposed that provide a convergent majorization algorithm for Kruskal's stress formula two.

math.NA↗

arXiv2024

Higher Partials of fStress

We define *fDistances*, which generalize Euclidean distances, squared distances, and log distances. The least squares loss function to fit fDistances to dissimilarity data is *fStress*. We give formulas and R/C code to compute partial derivatives of orders one to four of fStress, relying heavily on the use of Faà di Bruno's chain rule formula for higher derivatives.

stat.CO↗

arXiv2024

Global Minima by Penalized Full-dimensional Scaling

The full-dimensional (metric, Euclidean, least squares) multidimensional scaling stress loss function is combined with a quadratic external penalty function term. The trajectory of minimizers of stress for increasing values of the penalty parameter is then used to find (tentative) global minima for low-dimensional multidimensional scaling. This is illustrated with several one-dimensional and two-dimensional examples.

stat.CO↗

arXiv2023

Parcel loss prediction in last-mile delivery: deep and non-deep approaches with insights from Explainable AI

Within the domain of e-commerce retail, an important objective is the reduction of parcel loss during the last-mile delivery phase. The ever-increasing availability of data, including product, customer, and order information, has made it possible for the application of machine learning in parcel loss prediction. However, a significant challenge arises from the inherent imbalance in the data, i.e., only a very low percentage of parcels are lost. In this paper, we propose two machine learning approaches, namely, Data Balance with Supervised Learning (DBSL) and Deep Hybrid Ensemble Learning (DHEL), to accurately predict parcel loss. The practical implication of such predictions is their value in aiding e-commerce retailers in optimizing insurance-related decision-making policies. We conduct a comprehensive evaluation of the proposed machine learning models using one year data from Belgian shipments. The findings show that the DHEL model, which combines a feed-forward autoencoder with a random forest, achieves the highest classification performance. Furthermore, we use the techniques from Explainable AI (XAI) to illustrate how prediction models can be used in enhancing business processes and augmenting the overall value proposition for e-commerce retailers in the last mile delivery.

cs.LG↗

arXiv2022

Improved approximation and visualization of the correlation matrix

The graphical representation of the correlation matrix by means of different multivariate statistical methods is reviewed, a comparison of the different procedures is presented with the use of an example data set, and an improved representation with better fit is proposed. Principal component analysis is widely used for making pictures of correlation structure, though as shown a weighted alternating least squares approach that avoids the fitting of the diagonal of the correlation matrix outperforms both principal component analysis and principal factor analysis in approximating a correlation matrix. Weighted alternating least squares is a very strong competitor for principal component analysis, in particular if the correlation matrix is the focus of the study, because it improves the representation of the correlation matrix, often at the expense of only a minor percentage of explained variance for the original data matrix, if the latter is mapped onto the correlation biplot by regression. In this article, we propose to combine weighted alternating least squares with an additive adjustment of the correlation matrix, and this is seen to lead to further improved approximation of the correlation matrix.

stat.CO↗