Blog

Tensor Decomposition: PARAFAC and Tucker

Traditional data analysis methods often rely on matrices, but when applied to complex, multimodal datasets they can struggle to uncover meaningful latent structures. High-order (multiway) data analysis extends beyond the two-dimensional matrix framework, providing more powerful tools for identifying patterns and relationships in multi-dimensional data. In this post, I review two cornerstone techniques (PARAFAC and Tucker) which generalize familiar methods like singular value decomposition (SVD) and bilinear principal component analysis (PCA) to higher-order tensors.

Aug 23, 2025
Christian L. Goueguel
62 min

Beyond Standard Boxplot: The Adjusted and Generalized Boxplots

Boxplots, also known as box-and-whisker plots, have been a cornerstone of data visualization since their introduction by John Tukey in the late 1970s. Despite their enduring utility, boxplot assumes a symmetrical mesokurtic distribution and might misrepresent datasets with skewness or heavy tails. Alternative approaches have been proposed to address these limitations.

Dec 10, 2024
Christian L. Goueguel
16 min

Robust Measures of Tail Weight in Distributions

Traditional measures like kurtosis have long been used to capture the weight of the tails of a distribution. However, kurtosis comes with limitations, particularly its sensitivity to outliers and lack of robustness. In this blog post, we will explore two robust measures for tail weight.

Oct 20, 2023
Christian L. Goueguel
12 min

Exploring Three Orthogonal Signal Correction (OSC) Algorithms

Orthogonal signal correction (OSC) is a powerful preprocessing technique frequently used to remove variation in spectral data that is orthogonal to the property of interest. Over the years, several implementations of OSC have emerged, with the most notable being those by Wold et al., Sjöblom et al., and Fearn. This post compares these three methods, exploring their algorithmic approaches and practical implications.

May 25, 2023
Christian L. Goueguel
19 min

Optical Breakdown Threshold in Water

Cascade (or avalanche) ionization and multiphoton ionization are the two primary mechanisms responsible for laser-induced plasma (LIP) formation in water. These absorption processes are influenced by the intensity of the laser pulse and the physical and chemical properties of the water itself. This post focuses on providing a concise overview of these key mechanisms.

Sep 7, 2022
Christian L. Goueguel
8 min

Chemometric Modeling with Tidymodels: A Tutorial for Spectroscopic Data

In this post, we demonstrate how to build robust chemometric models for spectroscopic data using the Tidymodels framework in R. This workflow is designed to cater to beginners and advanced practitioners alike, offering an end-to-end guide from data preprocessing to model evaluation and interpretation.

Apr 17, 2022
Christian L. Goueguel
11 min

Covariance vs Correlation in PCA: What’s the Difference?

Principal Component Analysis can use either correlation or covariance matrices, but when should you use which? This post walks through the fundamental differences between these two approaches.

Mar 15, 2021
Christian L. Goueguel
4 min

Multivariate Outlier Detection in High-Dimensional Spectral Data

High-dimensional data are particularly challenging for outlier detection. Robust PCA methods have been developed to build models that are unaffected by outliers in high dimensions. These outliers are generally characterized by their deviation from the PCA subspace.

Jan 7, 2020
Christian L. Goueguel
9 min

An Overview of Orthogonal Partial Least Squares

Have you ever heard of Orthogonal Partial Least-Squares (OPLS)? This article aims to give you a clear and concise overview of OPLS and its advantages in the development of more efficient predictive models.

Dec 20, 2019
Christian L. Goueguel
6 min

Should We Use Standard Error or Standard Deviation?

One of the most common questions in statistics is whether to report standard error (SE) or standard deviation (SD) when presenting data. While these two measures are related, they serve fundamentally different purposes and choosing the wrong one can mislead your audience. Let’s break down when to use each.

Nov 28, 2019
Christian L. Goueguel
5 min

The Pseudo-Voigt Function

In spectroscopy, especially laser spectroscopy, accurate modeling of spectral line shapes is essential for analyzing the physical and chemical properties of matter. A commonly used approximation is the pseudo-Voigt function, which serves as a simplified representation of the Voigt profile. The Voigt profile, defined as the convolution of a Gaussian function and a Lorentzian function, accurately describes the line shapes, but its calculation is often time consuming.

Apr 5, 2019
Christian L. Goueguel
14 min
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