Principal component analysis is one of the most important and powerful methods in chemometrics as well as in a wealth of other areas. This paper provides a description of how to understand, use, and interpret principal component analysis. The paper focuses on the use of principal component analysis in typical chemometric areas but the results are generally applicable.

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Principal component analysis

Drug discovery and development pipelines are long, complex and depend on numerous factors. Machine learning (ML) approaches provide a set of tools that can improve discovery and decision making for well-specified questions with abundant, high-quality data. Opportunities to apply ML occur in all stages of drug discovery. Examples include target validation, identification of prognostic biomarkers and analysis of digital pathology data in clinical trials. Applications have ranged in context and methodology, with some approaches yielding accurate predictions and insights. The challenges of applying ML lie primarily with the lack of interpretability and repeatability of ML-generated results, which may limit their application. In all areas, systematic and comprehensive high-dimensional data still need to be generated. With ongoing efforts to tackle these issues, as well as increasing awareness of the factors needed to validate ML approaches, the application of ML can promote data-driven decision making and has the potential to speed up the process and reduce failure rates in drug discovery and development. Machine learning has been applied to numerous stages in the drug discovery pipeline. Here, Vamathevan and colleagues discuss the most useful techniques and how machine learning can promote data-driven decision making in drug discovery and development. They highlight major hurdles in the field, such as the required data characteristics for applying machine learning, which will need to be solved as machine learning matures.

Applications of machine learning in drug discovery and development.

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Multiple factor analysis.

Multi-omics studies promise the improved characterization of biological processes across molecular layers. However, methods for the unsupervised integration of the resulting heterogeneous data sets are lacking. We present Multi-Omics Factor Analysis (MOFA), a computational method for discovering the principal sources of variation in multi-omics data sets. MOFA infers a set of (hidden) factors that capture biological and technical sources of variability. It disentangles axes of heterogeneity that are shared across multiple modalities and those specific to individual data modalities. The learnt factors enable a variety of downstream analyses, including identification of sample subgroups, data imputation and the detection of outlier samples. We applied MOFA to a cohort of 200 patient samples of chronic lymphocytic leukaemia, profiled for somatic mutations, RNA expression, DNA methylation and ex vivo drug responses. MOFA identified major dimensions of disease heterogeneity, including immunoglobulin heavy-chain variable region status, trisomy of chromosome 12 and previously underappreciated drivers, such as response to oxidative stress. In a second application, we used MOFA to analyse single-cell multi-omics data, identifying coordinated transcriptional and epigenetic changes along cell differentiation.

https://www.embopress.org/doi/pdf/10.15252/msb.20178124

Multi-Omics Factor Analysis—a framework for unsupervised integration of multi-omics data sets

Driven by high-throughput sequencing techniques, modern genomic and clinical studies are in a strong need of integrative machine learning models for better use of vast volumes of heterogeneous information in the deep understanding of biological systems and the development of predictive models. How data from multiple sources (called multi-view data) are incorporated in a learning system is a key step for successful analysis. In this article, we provide a comprehensive review on omics and clinical data integration techniques, from a machine learning perspective, for various analyses such as prediction, clustering, dimension reduction and association. We shall show that Bayesian models are able to use prior information and model measurements with various distributions; tree-based methods can either build a tree with all features or collectively make a final decision based on trees learned from each view; kernel methods fuse the similarity matrices learned from individual views together for a final similarity matrix or learning model; network-based fusion methods are capable of inferring direct and indirect associations in a heterogeneous network; matrix factorization models have potential to learn interactions among features from different views; and a range of deep neural networks can be integrated in multi-modal learning for capturing the complex mechanism of biological systems.

A review on machine learning principles for multi-view biological data integration.

Factor analysis (FA) provides linear factors that describe the relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe the relationships between groups of variables, where each group represents either a set of related variables or a data set. The model also naturally extends canonical correlation analysis to more than two sets, in a way that is more flexible than previous extensions. Our solution is formulated as a variational inference of a latent variable model with structural sparsity, and it consists of two hierarchical levels: 1) the higher level models the relationships between the groups and 2) the lower models the observed variables given the higher level. We show that the resulting solution solves the group factor analysis (GFA) problem accurately, outperforming alternative FA-based solutions as well as more straightforward implementations of GFA. The method is demonstrated on two life science data sets, one on brain activation and the other on systems biology, illustrating its applicability to the analysis of different types of high-dimensional data sources.

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Group Factor Analysis

Factor analysis provides linear factors that describe relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe relationships between groups of variables, where each group represents either a set of related variables or a data set. The model also naturally extends canonical correlation analysis to more than two sets, in a way that is more flexible than previous extensions. Our solution is formulated as variational inference of a latent variable model with structural sparsity, and it consists of two hierarchical levels: The higher level models the relationships between the groups, whereas the lower models the observed variables given the higher level. We show that the resulting solution solves the group factor analysis problem accurately, outperforming alternative factor analysis based solutions as well as more straightforward implementations of group factor analysis. The method is demonstrated on two life science data sets, one on brain activation and the other on systems biology, illustrating its applicability to the analysis of different types of high-dimensional data sources.

Motivation: Modelling methods that find structure in data are necessary with the current large volumes of genomic data, and there have been various efforts to find subsets of genes exhibiting consistent patterns over subsets of treatments. These biclustering techniques have focused on one data source, often gene expression data. We present a Bayesian approach for joint biclustering of multiple data sources, extending a recent method Group Factor Analysis to have a biclustering interpretation with additional sparsity assumptions. The resulting method enables data-driven detection of linear structure present in parts of the data sources. Results: Our simulation studies show that the proposed method reliably infers biclusters from heterogeneous data sources. We tested the method on data from the NCI-DREAM drug sensitivity prediction challenge, resulting in an excellent prediction accuracy. Moreover, the predictions are based on several biclusters which provide insight into the data sources, in this case on gene expression, DNA methylation, protein abundance, exome sequence, functional connectivity fingerprints and drug sensitivity. Availability and Implementation: http://research.cs.aalto.fi/pml/software/GFAsparse/ Contacts: kerstin.bunte@googlemail.com or samuel.kaski@aalto.fi

Sparse group factor analysis for biclustering of multiple data sources

We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix---tensor factorization problem to arbitrary sets of tensors of any depth, including matrices, can be interpreted as unsupervised multi-view learning from multiple data tensors, and can be generalized to relax the usual trilinear tensor factorization assumptions. The result is a factorization of the set of tensors into factors shared by any subsets of the tensors, and factors private to individual tensors. We demonstrate the performance against existing baselines in multiple tensor factorization tasks in structural toxicogenomics and functional neuroimaging.

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Bayesian multi-tensor factorization

The R package GFA provides a full pipeline for factor analysis of multiple data sources that are represented as matrices with co-occurring samples. It allows learning dependencies between subsets of the data sources, decomposed into latent factors. The package also implements sparse priors for the factorization, providing interpretable biclusters of the multi-source data.

https://jmlr.org/papers/volume18/16-509/16-509.pdf

Eemeli Leppäaho

Papers

Group Factor Analysis

Group Factor Analysis

Sparse group factor analysis for biclustering of multiple data sources

Bayesian multi-tensor factorization

GFA: exploratory analysis of multiple data sources with group factor analysis