Application of PLS‐DA in multivariate image analysis

Some special topics in multivariate image analysis

Multivariate image analysis (MIA) aims to extract useful information from multivariate image structures such as hypercubes. Multivariate image regression is particularly useful for the development of calibration models for quantitative analysis of hypercubes. The key step in multivariate calibration is model selection; this includes the selection of method (e.g. partial least squares or ridge regression) and setting of parameters within the selected method (e.g. number of latent variables or ridge parameter). Sub-optimal selection of method and or parameters generally leads to poor predictive performance on future samples. While conventional methods such as cross-validation are indispensible in this task, the inherent nature of hyperspectral images may also be exploited. Application of a given calibration model to each pixel in a hypercube results in a prediction map whose features may be used to evaluate the model itself. This paper explores the application of various image statistics extracted from prediction images as model performance metrics for MIA.

2D-Discrete Fourier Transform: Generalization of the MIA-QSAR strategy in molecular modeling

Variations in the quality of wheat kernels can be an important problem in the cereal industry. In particular, desiccation conditions play an essential role in both the technological characteristics of the kernel and its ability to sprout. In planta desiccation constitutes a key stage in the determinism of the functional properties of seeds. The impact of desiccation on the endosperm texture of seed is presented in this work. A simple imaging system had previously been developed to acquire multivariate images to characterize the heterogeneity of food materials. A special algorithm for the use under principal component analysis (PCA) was developed to process the acquired multivariate images. Wheat grains were collected at physiological maturity, and were subjected to two types of drying conditions that induced different kinetics of water loss. A data set containing 24 images (dimensioned 702×524 pixels) corresponding to the different desiccation stages of wheat kernels was acquired at different wavelengths and then analyzed. A comparison of the images of kernel sections highlighted changes in kernel texture as a function of their drying conditions. Slow drying led to a floury texture, whereas fast drying caused a glassy texture. The automated imaging system thus developed is sufficiently rapid and economical to enable the characterization in large collections of grain texture as a function of time and water content.

Application of partial least squares and radial basis function neural networks in multivariate imaging analysis-quantitative structure activity relationship: Study of cyclin dependent kinase 4 inhibitors

One hundred and sixty-eight genotypes of cotton from the same growing region were used as a germplasm group to study the validity of different genetic distances in constructing cotton core subset. Mixed linear model approach was employed to unbiasedly predict genotypic values of 20 traits for eliminating the environmental effect. Six commonly used genetic distances (Euclidean, standardized Euclidean, Mahalanobis, city block, cosine and correlation distances) combining four commonly used hierarchical cluster methods (single distance, complete distance, unweighted pair-group average and Ward's methods) were used in the least distance stepwise sampling (LDSS) method for constructing different core subsets. The analyses of variance (ANOVA) of different evaluating parameters showed that the validities of cosine and correlation distances were inferior to those of Euclidean, standardized Euclidean, Mahalanobis and city block distances. Standardized Euclidean distance was slightly more effective than Euclidean, Mahalanobis and city block distances. The principal analysis validated standardized Euclidean distance in the course of constructing practical core subsets. The covariance matrix of accessions might be ill-conditioned when Mahalanobis distance was used to calculate genetic distance at low sampling percentages, which led to bias in small-sized core subset construction. The standardized Euclidean distance is recommended in core subset construction with LDSS method.

In this paper, we investigate the possibilities offered by the extension of the connected component trees (cc-trees) to multivariate images. We propose a general framework for image processing using the cc-tree based on the lattice theory and we discuss the possible applications depending on the properties of the underlying ordered set. This theoretical reflexion is illustrated by two applications in multispectral astronomical imaging: source separation and object detection.

Cereals are a major source of food security, income, livelihood, and employment in Nepal. However, there is a lack of time-series data for cereals to have a full understanding of the level of production, productivity, and self-reliance in food production in the country. The objectives of this chapter are to assess patterns and dynamics of cereal production, productivity, and import growth, and analyze food demand and self-sufficiency in Nepal. The major data sources for the chapter came from the national statistics, published and unpublished research papers, and policy documents. We used a compound growth rate estimation, coefficient of variation, and instability index techniques for analyzing dynamics and variability of the growth of food production and productivity over time. In addition, production and demand growth of cereals and self-sufficiency ratios were estimated for the next three decades until 2050 using different scenarios of production, population, demand growth, and the effect of climate change. Autoregressive regression model was used to analyze the relation between domestic production and income growth with import. The findings revealed that present production and productivity of cereals are low to meet current and future food demands of increasing population. Moreover, limited marketable surplus available at household level is the fundamental reason for steady increase in food imports. As a result, the country will continue to import a large quantity of cereals, particularly rice and maize in the future too. The country cannot achieve cereal self-sufficiency until 2030 under current growth rate of production, population, and negative effects of climate change. We suggest that government increase investment in agricultural research and development (R&D) to generate new and higher-level technologies and production practices for sustainable intensification of cereals with adequate policy support and services for ensuring national and household-level food and nutrition security to meet SDGs 1 and 2 by 2030.KeywordsCereal productionFood securityFood importProductivity growthSelf-sufficiency

Hellwig’s method is a multi-criteria decision-making technique designed to facilitate the ranking of alternatives based on their proximity to the ideal solution. Typically, this approach calculates distances using the Euclidean norm, assuming implicitly that the considered criteria are independent. However, in real-world situations, the assumption of criteria independence is rarely met. The paper aims to propose an extension of Hellwig’s method by incorporating the Mahalanobis distance. Substituting the Euclidean distance with the Mahalanobis distance has proven to be effective in handling correlations among criteria, especially in the context of asymmetrical relationships between criteria. Subsequently, we investigate the impact of the Euclidean and Mahalanobis distance measures on the several variants of Hellwig procedures, analyzing examples based on various illustrative data with 10 alternatives and 4 criteria. Additionally, we examine the influence of three normalization formulas in Hellwig’s aggregation procedures. The investigation results indicate that both the distance measure and normalization formulas have some impact on the final rankings. The evaluation and ranking of alternatives using the Euclidean distance measure are influenced by the normalization formula, albeit to a limited extent. In contrast, the Mahalanobis distance-based Hellwig’s method remains unaffected by the choice of normalization formulas. The study concludes that the ranking of alternatives is strongly dependent on the distance measure employed, whether it is Euclidean or Mahalanobis. The Mahalanobis distance-based Hellwig method is deemed a valuable tool for decision-makers in real-life situations. It enables the evaluation of alternatives by considering interactions between criteria, providing a more comprehensive perspective for decision-making.

We propose a novel method to improve the performance of existing three dimensional (3D) human face recognition algorithms that employ Euclidean distances between facial fiducial points as features. We further investigate a novel 3D face recognition algorithm that employs geodesic and Euclidean distances between facial fiducial points. We demonstrate that this algorithm is robust to changes in facial expression. Geodesic and Euclidean distances were calculated between pairs of 25 facial fiducial points. For the proposed algorithm, geodesic distances and 'global curvature' characteristics, defined as the ratio of geodesic to Euclidean distance between a pairs of points, were employed as features. The most discriminatory features were selected using stepwise linear discriminant analysis (LDA). These were projected onto 11 LDA directions, and face models were matched using the Euclidean distance metric. With a gallery set containing one image each of 105 subjects and a probe set containing 663 images of the same subjects, the algorithm produced EER=1.4% and a rank 1 RR=98.64%. It performed significantly better than existing algorithms based on principal component analysis and LDA applied to face range images. Its verification performance for expressive faces was also significantly better than an algorithm that employed Euclidean distances between facial fiducial points as features.

The distance-based regression model has many applications in analysis of multivariate response regression in various fields, such as ecology, genomics, genetics, human microbiomics, and neuroimaging. It yields a pseudo F test statistic that assesses the relation between the distance (dissimilarity) of the subjects and the predictors of interest. Despite its popularity in recent decades, the statistical properties of the pseudo F test statistic have not been revealed to our knowledge. This study derives the asymptotic properties of the pseudo F test statistic using spectral decomposition under the matrix normal assumption, when the utilized dissimilarity measure is the Euclidean or Mahalanobis distance. The pseudo F test statistic with the Euclidean distance has the same distribution as the quotient of two Chi-squared-type mixtures. The denominator and numerator of the quotient are approximated using a random variable of the form \(\xi\chi_d^2+\eta\) and the approximate error bound is given. The pseudo F test statistic with the Mahalanobis distance follows an F distribution. In simulation studies, the approximated distribution well matched the “exact” distribution obtained by the permutation procedure. The obtained distribution was further validated on H1N1 influenza data, aging human brain data, and embryonic imprint data.

This study reports the application of an electronic nose for the identification and classification of red wines aged three different methods. The signals of the different wines detected by the 10 sensors present in the E-nose are significantly different from each other. The response to the signal generates a typical chemical fingerprint of the volatile compounds present in the wines. Principal Component Analysis can be applied for the dimensionality reduction of the collected signal. Since the total contribution rate of the first three principal components is up to 97.27%, different wines can be distinguished from each other by the three principal components. Euclidean distance, correlation analysis, Mahalanobis distance and linear discrimination analysis can offer 100% accuracy for known samples, and the accuracy rate can reach 88.9% for the 18 test samples. In addition, numerous advantages exist compared with sensory analysis in both authentication and quality control of wines.

The principle component analysis(PCA) is a common feature extraction method in machine learning and pattern recognition approaches. PCA has been used in many applications, and face recognition in which specific faces are recognizing in an images database is one of the popular applications. The default distance metric which has been used with PCA based-face recognition is Euclidean distance. In this study, we have tested the Mahalanobis distance instead of Euclidean, and PCA based on Mahalanobis distance suggested a better performance on our students images database with highest recognition rate. However, we proposed weighted and normalized Mahalanobis distance based PCA-face recognition(PCA_WNMD). The proposed algorithm (PCA_WNMD) showed an improvement in faces recognition rate when tested on our students images database compared to PCA based on Mahalanobis and default Euclidean distances.

Analytical capabilities of chemiresistive microsensor arrays in a simulated Martian atmosphere

Multivariate Image and Texture Analysis in Solid Oral Dosage Form Development