A data-driven functional projection approach for the selection of feature ranges in spectra with ICA or cluster analysis

Prediction problems from spectra are largely encountered in chemometry. In addition to accurate predictions, it is often needed to extract information about which wavelengths in the spectra contribute in an effective way to the quality of the prediction. This implies to select wavelengths (or wavelength intervals), a problem associated to variable selection. In this paper, it is shown how this problem may be tackled in the specific case of smooth (for example infrared) spectra. The functional character of the spectra (their smoothness) is taken into account through a functional variable projection procedure. Contrarily to standard approaches, the projection is performed on a basis that is driven by the spectra themselves, in order to best fit their characteristics. The methodology is illustrated by two examples of functional projection, using Independent Component Analysis and functional variable clustering, respectively. The performances on two standard infrared spectra benchmarks are illustrated.Comment: A paraitr

Constrained variable clustering and the best basis problem in functional data analysis

International audienceFunctional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained from a fine grid sampling of functional data, all methods benefit from a prior simplification of the functions that reduces the redundancy induced by the regularity. In this paper we propose to use a clustering approach that targets variables rather than individual to design a piecewise constant representation of a set of functions. The contiguity constraint induced by the functional nature of the variables allows a polynomial complexity algorithm to give the optimal solution

Exploratory Analysis of Functional Data via Clustering and Optimal Segmentation

We propose in this paper an exploratory analysis algorithm for functional data. The method partitions a set of functions into $K$ clusters and represents each cluster by a simple prototype (e.g., piecewise constant). The total number of segments in the prototypes, $P$, is chosen by the user and optimally distributed among the clusters via two dynamic programming algorithms. The practical relevance of the method is shown on two real world datasets

On-line quality control in polymer processing using hyperspectral imaging

L’industrie du plastique se tourne de plus en plus vers les matériaux composites afin d’économiser de la matière et/ou d’utiliser des matières premières à moindres coûts, tout en conservant de bonnes propriétés. L’impressionnante adaptabilité des matériaux composites provient du fait que le manufacturier peut modifier le choix des matériaux utilisés, la proportion selon laquelle ils sont mélangés, ainsi que la méthode de mise en œuvre utilisée. La principale difficulté associée au développement de ces matériaux est l’hétérogénéité de composition ou de structure, qui entraîne généralement des défaillances mécaniques. La qualité des prototypes est normalement mesurée en laboratoire, à partir de tests destructifs et de méthodes nécessitant la préparation des échantillons. La mesure en-ligne de la qualité permettrait une rétroaction quasi-immédiate sur les conditions d’opération des équipements, en plus d’être directement utilisable pour le contrôle de la qualité dans une situation de production industrielle. L’objectif de la recherche proposée consiste à développer un outil de contrôle de qualité pour la qualité des matériaux plastiques de tout genre. Quelques sondes de type proche infrarouge ou ultrasons existent présentement pour la mesure de la composition en-ligne, mais celles-ci ne fournissent qu’une valeur ponctuelle à chaque acquisition. Ce type de méthode est donc mal adapté pour identifier la distribution des caractéristiques de surface de la pièce (i.e. homogénéité, orientation, dispersion). Afin d’atteindre cet objectif, un système d’imagerie hyperspectrale est proposé. À l’aide de cet appareil, il est possible de balayer la surface de la pièce et d’obtenir une image hyperspectrale, c’est-à-dire une image formée de l’intensité lumineuse à des centaines de longueurs d’onde et ce, pour chaque pixel de l’image. L’application de méthodes chimiométriques permettent ensuite d’extraire les caractéristiques spatiales et spectrales de l’échantillon présentes dans ces images. Finalement, les méthodes de régression multivariée permettent d’établir un modèle liant les caractéristiques identifiées aux propriétés de la pièce. La construction d’un modèle mathématique forme donc l’outil d’analyse en-ligne de la qualité des pièces qui peut également prédire et optimiser les conditions de fabrication.The use of plastic composite materials has been increasing in recent years in order to reduce the amount of material used and/or use more economic materials, all of which without compromising the properties. The impressive adaptability of these composite materials comes from the fact that the manufacturer can choose the raw materials, the proportion in which they are blended as well as the processing conditions. However, these materials tend to suffer from heterogeneous compositions and structures, which lead to mechanical weaknesses. Product quality is generally measured in the laboratory, using destructive tests often requiring extensive sample preparation. On-line quality control would allow near-immediate feedback on the operating conditions and may be transferrable to an industrial production context. The proposed research consists of developing an on-line quality control tool adaptable to plastic materials of all types. A number of infrared and ultrasound probes presently exist for on-line composition estimation, but only provide single-point values at each acquisition. These methods are therefore less adapted for identifying the spatial distribution of a sample’s surface characteristics (e.g. homogeneity, orientation, dispersion). In order to achieve this objective, a hyperspectral imaging system is proposed. Using this tool, it is possible to scan the surface of a sample and obtain a hyperspectral image, that is to say an image in which each pixel captures the light intensity at hundreds of wavelengths. Chemometrics methods can then be applied to this image in order to extract the relevant spatial and spectral features. Finally, multivariate regression methods are used to build a model between these features and the properties of the sample. This mathematical model forms the backbone of an on-line quality assessment tool used to predict and optimize the operating conditions under which the samples are processed