K-OPLS package: kernel-based orthogonal projections to latent structures for prediction and interpretation in feature space

Abstract

Background: Kernel-based classification and regression methods have been successfully applied to modelling a wide variety of biological data. The Kernel-based Orthogonal Projections to Latent Structures (K-OPLS) method offers unique properties facilitating separate modelling of predictive variation and structured noise in the feature space. While providing prediction results similar to other kernel-based methods, K-OPLS features enhanced interpretational capabilities; allowing detection of unanticipated systematic variation in the data such as instrumental drift, batch variability or unexpected biological variation.

Results: We demonstrate an implementation of the K-OPLS algorithm for MATLAB and R, licensed under the GNU GPL and available at http://www.sourceforge.net/projects/kopls/. The package includes essential functionality and documentation for model evaluation (using cross-validation), training and prediction of future samples. Incorporated is also a set of diagnostic tools and plot functions to simplify the visualisation of data, e.g. for detecting trends or for identification of outlying samples. The utility of the software package is demonstrated by means of a metabolic profiling data set from a biological study of hybrid aspen.

Conclusion: The properties of the K-OPLS method are well suited for analysis of biological data, which in conjunction with the availability of the outlined open-source package provides a comprehensive solution for kernel-based analysis in bioinformatics applications.

Figure 1

K-OPLS model properties of the NMR-based metabolic profiling data set. Each point represents a measured observation (biological sample).The size of each glyph in the figure is proportional to the internode number 1–8, denoting a growth gradient. In (A), the K-OPLS predictive score vector t¹_p is plotted against the first Y-orthogonal score vector t¹_o. In (B), the first K-OPLS Y-orthogonal score vector t¹_o is plotted against the second Y-orthogonal score vector t²_o. An approximate joint internode gradient, formed by a linear combination of both vectors, is shown using the dashed arrow. In (C), the first K-OPLS Y-orthogonal score vector t¹_o is plotted against the second Y-orthogonal score vector t²_o only for the mutant samples, colour-coded by biological replicate. Biological replicate A displays a deviating behaviour compared to biological replicates B and C; trajectory shown by the dashed line. In (D), the first KPLS latent variable t₁ is plotted against the second latent variable t₂. The discriminatory direction is now a linear combination of both of the latent variables.