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Abstract Background Multiple co-inertia analysis (mCIA) is a multivariate analysis method that can assess relationships and trends in multiple datasets. Recently it has been used for integrative analysis of multiple high-dimensional -omics datasets. However, its estimated loading vectors are non-sparse, which presents challenges for identifying important features and interpreting analysis results. We propose two new mCIA methods: 1) a sparse mCIA method that produces sparse loading estimates and 2) a structured sparse mCIA method that further enables incorporation of structural information among variables such as those from functional genomics. Results Our extensive simulation studies demonstrate the superior performance of the sparse mCIA and structured sparse mCIA methods compared to the existing mCIA in terms of feature selection and estimation accuracy. Application to the integrative analysis of transcriptomics data and proteomics data from a cancer study identified biomarkers that are suggested in the literature related with cancer disease. Conclusion Proposed sparse mCIA achieves simultaneous model estimation and feature selection and yields analysis results that are more interpretable than the existing mCIA. Furthermore, proposed structured sparse mCIA can effectively incorporate prior network information among genes, resulting in improved feature selection and enhanced interpretability.

The Multiple CO-inertia Analysis (MCOA) is a method which makes it possible simultaneously to analyze multiple tables of a multiblock having the same lines (individuals). It stipulates the existence of the auxiliary variables as for the generalized canonical correlation analysis (GCCA). Its numerical stability, its easiness to use and its good properties, make of it a good alternative to the GCCA, which is numerically unstable or not easily interpretable. In this article, we propose a generalization of this method in several multiblocks having the same lines, named: Generalized Multiple CO-inertia Analysis (GMCOA). Properties of this method are given. This method is applied to the sensory analysis. [ABSTRACT FROM AUTHOR]

Abstract Working with weakly congruent markers means that consensus genetic structuring of populations requires methods explicitly devoted to this purpose. The method, which is presented here, belongs to the multivariate analyses. This method consists of different steps. First, single-marker analyses were performed using a version of principal component analysis, which is designed for allelic frequencies (%PCA). Drawing confidence ellipses around the population positions enhances %PCA plots. Second, a multiple co-inertia analysis (MCOA) was performed, which reveals the common features of single-marker analyses, builds a reference structure and makes it possible to compare single-marker structures with this reference through graphical tools. Finally, a typological value is provided for each marker. The typological value measures the efficiency of a marker to structure populations in the same way as other markers. In this study, we evaluate the interest and the efficiency of this method applied to a European and African bovine microsatellite data set. The typological value differs among markers, indicating that some markers are more efficient in displaying a consensus typology than others. Moreover, efficient markers in one collection of populations do not remain efficient in others. The number of markers used in a study is not a sufficient criterion to judge its reliability. "Quantity is not quality".

Abstract Background Unsupervised clustering and outlier detection are important in medical research to understand the distributional composition of a collective of patients. A number of clustering methods exist, also for high-dimensional data after dimension reduction. Clustering and outlier detection may, however, become less robust or contradictory if multiple high-dimensional data sets per patient exist. Such a scenario is given when the focus is on 3-D data of multiple organs per patient, and a high-dimensional feature matrix per organ is extracted. Methods We use principal component analysis (PCA), t-distributed stochastic neighbor embedding (t-SNE) and multiple co-inertia analysis (MCIA) combined with bagplots to study the distribution of multi-organ 3-D data taken by computed tomography scans. After point-set registration of multiple organs from two public data sets, multiple hundred shape features are extracted per organ. While PCA and t-SNE can only be applied to each organ individually, MCIA can project the data of all organs into the same low-dimensional space. Results MCIA is the only approach, here, with which data of all organs can be projected into the same low-dimensional space. We studied how frequently (i.e., by how many organs) a patient was classified to belong to the inner or outer 50% of the population, or as an outlier. Outliers could only be detected with MCIA and PCA. MCIA and t-SNE were more robust in judging the distributional location of a patient in contrast to PCA. Conclusions MCIA is more appropriate and robust in judging the distributional location of a patient in the case of multiple high-dimensional data sets per patient. It is still recommendable to apply PCA or t-SNE in parallel to MCIA to study the location of individual organs.

Motivation Co-inertia analysis (CIA) is a multivariate statistical analysis method that can assess relationships and trends in two sets of data. Recently CIA has been used for an integrative analysis of multiple high-dimensional omics data. However, for classical CIA, all elements in the loading vectors are nonzero, presenting a challenge for the interpretation when analyzing omics data. For other multivariate statistical methods such as canonical correlation analysis (CCA), penalized least squares (PLS), various approaches have been proposed to produce sparse loading vectors via l 1-penalization/constraint. We propose a novel CIA method that uses l 1-penalization to induce sparsity in estimators of loading vectors. Our method simultaneously conducts model fitting and variable selection. Also, we propose another CIA method that incorporates structure/network information such as those from functional genomics, besides using sparsity penalty so that one can get biologically meaningful and interpretable results. Results Extensive simulations demonstrate that our proposed penalized CIA methods achieve the best or close to the best performance compared to the existing CIA method in terms of feature selection and recovery of true loading vectors. Also, we apply our methods to the integrative analysis of gene expression data and protein abundance data from the NCI-60 cancer cell lines. Our analysis of the NCI-60 cancer cell line data reveals meaningful variables for cancer diseases and biologically meaningful results that are consistent with previous studies. Availability and implementation Our algorithms are implemented as an R package which is freely available at: https://www.med.upenn.edu/long-lab/. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

This paper is about the problem of the treatment of ordinal qualitative variables in co-inertia analysis. In the literature, there are different proposals based on the application of known statistical techniques to quantify ordinal variables. Here we propose to use a new procedure for the coding considering the empirical distributions of the variables involved in the analysis. We present an application to a real dataset, comparing the results obtained with the different kinds of quantification. [ABSTRACT FROM AUTHOR]

Aim of this paper is to introduce Gower and Hand's biplot procedures within the Co-Inertia Analysis. Predictive biplots can be considered a good choice for interpretation purposes while interpretative ones are very useful to classify new samples not used for the construction of the main co-inertia axes. [ABSTRACT FROM AUTHOR]

Abstract Background Rapid development of DNA microarray technology has resulted in different laboratories adopting numerous different protocols and technological platforms, which has severely impacted on the comparability of array data. Current cross-platform comparison of microarray gene expression data are usually based on cross-referencing the annotation of each gene transcript represented on the arrays, extracting a list of genes common to all arrays and comparing expression data of this gene subset. Unfortunately, filtering of genes to a subset represented across all arrays often excludes many thousands of genes, because different subsets of genes from the genome are represented on different arrays. We wish to describe the application of a powerful yet simple method for cross-platform comparison of gene expression data. Co-inertia analysis (CIA) is a multivariate method that identifies trends or co-relationships in multiple datasets which contain the same samples. CIA simultaneously finds ordinations (dimension reduction diagrams) from the datasets that are most similar. It does this by finding successive axes from the two datasets with maximum covariance. CIA can be applied to datasets where the number of variables (genes) far exceeds the number of samples (arrays) such is the case with microarray analyses. Results We illustrate the power of CIA for cross-platform analysis of gene expression data by using it to identify the main common relationships in expression profiles on a panel of 60 tumour cell lines from the National Cancer Institute (NCI) which have been subjected to microarray studies using both Affymetrix and spotted cDNA array technology. The co-ordinates of the CIA projections of the cell lines from each dataset are graphed in a bi-plot and are connected by a line, the length of which indicates the divergence between the two datasets. Thus, CIA provides graphical representation of consensus and divergence between the gene expression profiles from different microarray platforms. Secondly, the genes that define the main trends in the analysis can be easily identified. Conclusions CIA is a robust, efficient approach to coupling of gene expression datasets. CIA provides simple graphical representations of the results making it a particularly attractive method for the identification of relationships between large datasets.

The olive fruit fly Bactrocera oleae (Rossi, 1790) poses a significant threat to oliviculture worldwide, despite extensive chemical control measures. The susceptibility of olive (Olea europaea L.) to this pest varies among cultivars, with fruit size being a key factor of interest, as it can be assessed using non-destructive automated technologies. In this study, we investigated the oviposition preferences of the olive fruit fly in six Italian olive cultivars, tracking fertile and sterile punctures in relation to the diametric growth of the drupe. Additionally, we assessed the genetic diversity among cultivars using SSR markers, aiming to uncover a potential correlation between variation in the genetic diversity patterns and infestation levels. The results revealed that the relationship between fruit size and infestation level is non-linear and varies across different cultivars. The co-inertia analysis (COIA) performed on the genetic and infestation datasets revealed possible shared patterns of diversity and relationships between the two datasets. This study emphasizes the complex and diverse nature of the interaction between the olive fruit fly and its host, underscoring the importance of comprehending non-linear relationships to develop accurate genotypic-specific predictions and models.