Investigating paired comparisons after principal component analysis

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Evaluation of complementary numerical and visual approaches for investigating pairwise comparisons after principal component analysis

We propose and evaluate numerical and visual methods for investigating paired comparisons after principal component analysis (PCA). PCA results can be visualized to facilitate an understanding of the relationships between the products and the sensory attributes. But identifying and visualizing significant product differences in multiple PCs simultaneously is not straightforward. A benefit of the proposed methods is that they provide a screening tool for evaluating PCA results rapidly. We begin with a real data set which is analyzed and submitted to the truncated total bootstrap (TTB) procedure. This TTB procedure simulates and analyzes results from virtual panels. The TTB-derived results form clouds of uncertainty around each product and paired comparison. Although these clouds can be visualized directly or by plotting the smallest contours that enclose 95% of their kernel-estimated densities, we propose that plotting TTB-derived 95% confidence ellipsoids provide a less cumbersome approach. We show that it is also possible to calculate P values that evaluate whether pairs of products are discriminated in the PCA subspace. The interpretation of these P values coincides with the visual interpretation of the confidence ellipsoids. The volumes of these confidence ellipsoids, which quantify uncertainty, are calculated easily. The confidence ellipsoids, the P values, and the volumes provide a simple and consistent approach for investigating paired comparisons after PCA. We illustrate the methods with two real data sets, one a sensory quantitative-descriptive data set from a trained panel, the other a check-all-that-apply (CATA) data set from a consumer panel. We also conduct a simulation study based on each of these data sets. The results from these simulation studies show that under repetition, the 95% confidence ellipsoids often have coverage of approximately 95%, but in some cases, coverage can be substantially lower. This indicates that the proposed ellipsoids have an approximately frequentist interpretation, but coverage varies. The complementary numerical and visual approaches can be applied to a wide range of data sets from sensory evaluation and to data from other domains.submittedVersio

Discriminability and uncertainty in principal component analysis (PCA) of temporal check-all-that-apply (TCATA) data

Temporal check-all-that-apply (TCATA) data can be summarized and explored using principal component analysis (PCA). Here we analyze TCATA data on Syrah wines obtained from a trained sensory panel. We evaluate new and existing methods to explore the uncertainty in the PCA scores. To do so, we use the bootstrap procedure to obtain many virtual panels from the real panel’s data. Virtual-panel PCA scores are obtained using two methods. The first method, called the partial bootstrap (PB), obtains virtual-panel scores from regression. The second method, called the truncated total bootstrap (TTB), applies PCA to the virtual-panel results to obtain scores, which are truncated and superimposed on the real-panel scores by Procrustes rotation. We use the virtual scores from each method to investigate uncertainty in the real-panel PCA scores visually and numerically. To understand the uncertainty of the scores, we obtain confidence ellipses (CEs) and their areas, as well as confidence intervals (CIs) and their widths. Next, to determine whether PCA scores for different samples are well separated, we propose a procedure for approximating the standard errors of sample differences and correcting for multiple comparisons. We propose a discriminability index, and show that it can enhance the interpretability of PCA results. We incorporate graphical features into our PCA biplots to visualize discriminability. We did not find a large difference between the PB and TTB methods for understanding the uncertainty and discriminability in PCA scores. Although the TCATA data that we analyzed have a special structure, the methodological approaches presented here can be readily adapted to other applications of PCA.submittedVersio

Why use component-based methods in sensory science?

This paper discusses the advantages of using so-called component-based methods in sensory science. For instance, principal component analysis (PCA) and partial least squares (PLS) regression are used widely in the field; we will here discuss these and other methods for handling one block of data, as well as several blocks of data. Component-based methods all share a common feature: they define linear combinations of the variables to achieve data compression, interpretation, and prediction. The common properties of the component-based methods are listed and their advantages illustrated by examples. The paper equips practitioners with a list of solid and concrete arguments for using this methodology.publishedVersio

Designing a decision support system for tasting panels

Tasting Panels are used in Sensory Analysis in order to evaluate products according to the way they are perceived by human senses. In this context, the main job of a professional taster is to assess the sensorial characteristics of products, for example in the food industry. Evaluating the individual performance of the tasters is thus essential, so the results produced are as reliable as possible. The tasting process usually generates a large amount of data that is used in decisions about the products and can also be used to evaluate the tasters. The main objective of this work is to specify and conceptualize a Decision Support System (DSS) to help managing and handling the referred data. This is considered a valuable contribution, since there are no known technological decision tools to support the tasting process

Performance analysis and optimization of reduced complexity Low Density Parity Check decoding algorithms

grantor: University of TorontoReduced complexity decoding algorithms for Low Density Parity Check codes are presented. The performance of these algorithms is optimized using the concept of density evolution and they are shown to perform well in practical decoding situations. The codes are examined from a performance vs. complexity point of view. It is shown that there is an optimal complexity for practical decoders beyond which performance will suffer. The idea of practical decoding is used to develop the sum-transform-sum algorithm, which is very well suited for a fixed-point hardware implementation. The performance of this algorithm approaches that of the sum-product algorithm, but is much less complex.M.A.Sc

A context for Fascist art and culture : an examination of debates in Critica fascista (1923-1943

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Exploring the common and unique variability in TDS and TCATA data – A comparison using canonical correlation and orthogonalization.

Temporal Dominance of Sensations (TDS) and Temporal Check-all-that-Apply (TCATA) from three different case studies are compared by means of canonical correlation analysis, orthogonalization and principal component analysis of the vertically unfolded data (which means that the matrices compared have samples* timepoints in the rows and attributes in the columns). The multivariate analyses decompose the datasets into common and distinct components. The results showed that the major part of the variation is common between the two methods for the cases investigated, but that there were subtle differences showing better discrimination for TCATA than TDS. TDS showed a more complex data structure and more unique variation. The unique variation in TDS is, however, difficult to interpret. The methods are more different towards the end of the mastication, this can be explained both by the difficulty of assessors to agree on the dominant attributes at the bolus stage for TDS, and that assessors may forget to unclick attributes in TCATA. This work builds on recent methodological studies on temporal methods that aim to better understand differences among methodologies and ultimately to identify what methods could be better for answering different objectives.Exploring the common and unique variability in TDS and TCATA data – A comparison using canonical correlation and orthogonalization.acceptedVersio

Temporal Check-All-That-Apply characterization of Syrah wine finish

Trained panel evaluation of Syrah wine finish using the Temporal Check-All-That-Apply (TCATA) method. The panel (n=13) evaluated three wine treatments (H = high, A = adjusted, L = low) in a two-sip evaluation protocol using the TCATA method with 10 attributes (9 attributes plus “other”). The evaluation started when the sample was expectorated at 10 s, and continued for up to 180 s. For further details refer to Baker et al. (2016, doi:10.1111/1750-3841.13328).THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV