Kernel-based retrieval models for hyperspectral image data optimized with Kernel Flows

Kernel-based statistical methods are efficient, but their performance depends heavily on the selection of kernel parameters. In literature, the optimization studies on kernel-based chemometric methods is limited and often reduced to grid searching. Previously, the authors introduced Kernel Flows (KF) to learn kernel parameters for Kernel Partial Least-Squares (K-PLS) regression. KF is easy to implement and helps minimize overfitting. In cases of high collinearity between spectra and biogeophysical quantities in spectroscopy, simpler methods like Principal Component Regression (PCR) may be more suitable. In this study, we propose a new KF-type approach to optimize Kernel Principal Component Regression (K-PCR) and test it alongside KF-PLS. Both methods are benchmarked against non-linear regression techniques using two hyperspectral remote sensing datasets.

Statistical Batch-Based Bearing Fault Detection

In the domain of rotating machinery, bearings are vulnerable to different mechanical faults, including ball, inner, and outer race faults. Various techniques can be used in condition-based monitoring, from classical signal analysis to deep learning methods. Based on the complex working conditions of rotary machines, multivariate statistical process control charts such as Hotelling's $T^2$ and Squared Prediction Error are useful for providing early warnings. However, these methods are rarely applied to condition monitoring of rotating machinery due to the univariate nature of the datasets. In the present paper, we propose a multivariate statistical process control-based fault detection method that utilizes multivariate data composed of Fourier transform features extracted for fixed-time batches. Our approach makes use of the multidimensional nature of Fourier transform characteristics, which record more detailed information about the machine's status, in an effort to enhance early defect detection and diagnosis. Experiments with varying vibration measurement locations (Fan End, Drive End), fault types (ball, inner, and outer race faults), and motor loads (0-3 horsepower) are used to validate the suggested approach. The outcomes illustrate our method's effectiveness in fault detection and point to possible broader uses in industrial maintenance.

Varroa destructor detection on honey bees using hyperspectral imagery

Hyperspectral (HS) imagery in agriculture is becoming increasingly common. These images have the advantage of higher spectral resolution. Advanced spectral processing techniques are required to unlock the information potential in these HS images. The present paper introduces a method rooted in multivariate statistics designed to detect parasitic Varroa destructor mites on the body of western honey bee Apis mellifera, enabling easier and continuous monitoring of the bee hives. The methodology explores unsupervised (K-means++) and recently developed supervised (Kernel Flows - Partial Least-Squares, KF-PLS) methods for parasitic identification. Additionally, in light of the emergence of custom-band multispectral cameras, the present research outlines a strategy for identifying the specific wavelengths necessary for effective bee-mite separation, suitable for implementation in a custom-band camera. Illustrated with a real-case dataset, our findings demonstrate that as few as four spectral bands are sufficient for accurate parasite identification.

KF-PLS: Optimizing Kernel Partial Least-Squares (K-PLS) with Kernel Flows

Partial Least-Squares (PLS) Regression is a widely used tool in chemometrics for performing multivariate regression. PLS is a bi-linear method that has a limited capacity of modelling non-linear relations between the predictor variables and the response. Kernel PLS (K-PLS) has been introduced for modelling non-linear predictor-response relations. In K-PLS, the input data is mapped via a kernel function to a Reproducing Kernel Hilbert space (RKH), where the dependencies between the response and the input matrix are assumed to be linear. K-PLS is performed in the RKH space between the kernel matrix and the dependent variable. Most available studies use fixed kernel parameters. Only a few studies have been conducted on optimizing the kernel parameters for K-PLS. In this article, we propose a methodology for the kernel function optimization based on Kernel Flows (KF), a technique developed for Gaussian process regression (GPR). The results are illustrated with four case studies. The case studies represent both numerical examples and real data used in classification and regression tasks. K-PLS optimized with KF, called KF-PLS in this study, is shown to yield good results in all illustrated scenarios. The paper presents cross-validation studies and hyperparameter analysis of the KF methodology when applied to K-PLS.