Sparsest factor analysis for clustering variables: a matrix decomposition approach

We propose a new procedure for sparse factor analysis (FA) such that each variable loads only one common factor. Thus, the loading matrix has a single nonzero element in each row and zeros elsewhere. Such a loading matrix is the sparsest possible for certain number of variables and common factors. For this reason, the proposed method is named sparsest FA (SSFA). It may also be called FA-based variable clustering, since the variables loading the same common factor can be classified into a cluster. In SSFA, all model parts of FA (common factors, their correlations, loadings, unique factors, and unique variances) are treated as fixed unknown parameter matrices and their least squares function is minimized through specific data matrix decomposition. A useful feature of the algorithm is that the matrix of common factor scores is re-parameterized using QR decomposition in order to efficiently estimate factor correlations. A simulation study shows that the proposed procedure can exactly identify the true sparsest models. Real data examples demonstrate the usefulness of the variable clustering performed by SSFA

Orthogonal rotation in PCAMIX

Kiers (1991) considered the orthogonal rotation in PCAMIX, a principal component method for a mixture of qualitative and quantitative variables. PCAMIX includes the ordinary principal component analysis (PCA) and multiple correspondence analysis (MCA) as special cases. In this paper, we give a new presentation of PCAMIX where the principal components and the squared loadings are obtained from a Singular Value Decomposition. The loadings of the quantitative variables and the principal coordinates of the categories of the qualitative variables are also obtained directly. In this context, we propose a computationaly efficient procedure for varimax rotation in PCAMIX and a direct solution for the optimal angle of rotation. A simulation study shows the good computational behavior of the proposed algorithm. An application on a real data set illustrates the interest of using rotation in MCA. All source codes are available in the R package "PCAmixdata"

Individual differences in metabolomics: individualised responses and between-metabolite relationships

Many metabolomics studies aim to find ‘biomarkers’: sets of molecules that are consistently elevated or decreased upon experimental manipulation. Biological effects, however, often manifest themselves along a continuum of individual differences between the biological replicates in the experiment. Such differences are overlooked or even diminished by methods in standard use for metabolomics, although they may contain a wealth of information on the experiment. Properly understanding individual differences is crucial for generating knowledge in fields like personalised medicine, evolution and ecology. We propose to use simultaneous component analysis with individual differences constraints (SCA-IND), a data analysis method from psychology that focuses on these differences. This method constructs axes along the natural biochemical differences between biological replicates, comparable to principal components. The model may shed light on changes in the individual differences between experimental groups, but also on whether these differences correspond to, e.g., responders and non-responders or to distinct chemotypes. Moreover, SCA-IND reveals the individuals that respond most to a manipulation and are best suited for further experimentation. The method is illustrated by the analysis of individual differences in the metabolic response of cabbage plants to herbivory. The model reveals individual differences in the response to shoot herbivory, where two ‘response chemotypes’ may be identified. In the response to root herbivory the model shows that individual plants differ strongly in response dynamics. Thereby SCA-IND provides a hitherto unavailable view on the chemical diversity of the induced plant response, that greatly increases understanding of the system

A flexible framework for sparse simultaneous component based data integration

<p>Abstract</p> <p>1 Background</p> <p>High throughput data are complex and methods that reveal structure underlying the data are most useful. Principal component analysis, frequently implemented as a singular value decomposition, is a popular technique in this respect. Nowadays often the challenge is to reveal structure in several sources of information (e.g., transcriptomics, proteomics) that are available for the same biological entities under study. Simultaneous component methods are most promising in this respect. However, the interpretation of the principal and simultaneous components is often daunting because contributions of each of the biomolecules (transcripts, proteins) have to be taken into account.</p> <p>2 Results</p> <p>We propose a sparse simultaneous component method that makes many of the parameters redundant by shrinking them to zero. It includes principal component analysis, sparse principal component analysis, and ordinary simultaneous component analysis as special cases. Several penalties can be tuned that account in different ways for the block structure present in the integrated data. This yields known sparse approaches as the lasso, the ridge penalty, the elastic net, the group lasso, sparse group lasso, and elitist lasso. In addition, the algorithmic results can be easily transposed to the context of regression. Metabolomics data obtained with two measurement platforms for the same set of <it>Escherichia coli </it>samples are used to illustrate the proposed methodology and the properties of different penalties with respect to sparseness across and within data blocks.</p> <p>3 Conclusion</p> <p>Sparse simultaneous component analysis is a useful method for data integration: First, simultaneous analyses of multiple blocks offer advantages over sequential and separate analyses and second, interpretation of the results is highly facilitated by their sparseness. The approach offered is flexible and allows to take the block structure in different ways into account. As such, structures can be found that are exclusively tied to one data platform (group lasso approach) as well as structures that involve all data platforms (Elitist lasso approach).</p> <p>4 Availability</p> <p>The additional file contains a MATLAB implementation of the sparse simultaneous component method.</p

Distorted body representations are robust to differences in experimental instructions

Several recent reports have shown that even healthy adults maintain highly distorted representations of the size and shape of their body. These distortions have been shown to be highly consistent across different study designs and dependent measures. However, previous studies have found that visual judgments of size can be modulated by the experimental instructions used, for example, by asking for judgments of the participant’s subjective experience of stimulus size (i.e., apparent instructions) versus judgments of actual stimulus properties (i.e., objective instructions). Previous studies investigating internal body representations have relied exclusively on ‘apparent’ instructions. Here, we investigated whether apparent versus objective instructions modulate findings of distorted body representations underlying position sense (Exp. 1), tactile distance perception (Exp. 2), as well as the conscious body image (Exp. 3). Our results replicate the characteristic distortions previously reported for each of these tasks and further show that these distortions are not affected by instruction type (i.e., apparent vs. objective). These results show that the distortions measured with these paradigms are robust to differences in instructions and do not reflect a dissociation between perception and belief

A LC-MS metabolomics approach to investigate the effect of raw apple intake in the rat plasma metabolome

Fruit and vegetable consumption has been associated with several health benefits; however the mechanisms are largely unknown at the biochemical level. Our research aims to investigate whether plasma metabolome profiling can reflect biological effects after feeding rats with raw apple by using an untargeted UPLC-ESI-TOF-MS based metabolomics approach in both positive and negative mode. Eighty young male rats were randomised into groups receiving daily 0, 5 or 10 g fresh apple slices, respectively, for 13 weeks. During weeks 3-6 some of the animals were receiving 4 mg/ml 1,2-dimethylhydrazine dihydrochloride (DMH) once a week. Plasma samples were taken at the end of the intervention and among all groups, about half the animals were 12 h fasted. An initial ANOVA-simultaneous component analysis with a three-factor or two-factor design was employed in order to isolate potential metabolic variations related to the consumption of fresh apples. Partial least squares-discriminant analysis was then applied in order to select discriminative features between plasma metabolites in control versus apple fed rats and partial least squares modelling to reveal possible dose response. The findings indicate that in laboratory rats apple feeding may alter the microbial amino acid fermentation, lowering toxic metabolites from amino acids metabolism and increasing metabolism into more protective products. It may also delay lipid and amino acid catabolism, gluconeogenesis, affect other features of the transition from the postprandial to the fasting state and affect steroid metabolism by suppressing the plasma level of stress corticosteroids, certain mineralocorticoids and oxidised bile acid metabolites. Several new hypotheses regarding the cause of health effects from apple intake can be generated from this study for further testing in humans. © 2013 Springer Science+Business Media New York