OmicsPLS {OmicsPLS}

Data integration with O2PLS: Two-Way Orthogonal Partial Least Squares

Description

The OmicsPLS package is an R package for penalized integration of heterogeneous omics data. The software articles are published in (el Bouhaddani et al, 2018, doi: 10.1186/s12859-018-2371-3) and (Gu et al, 2020, doi: 10.1186/s12859-021-03958-3). OmicsPLS includes the O2PLS fit, the GO2PLS fit, cross-validation tools and some misc functions.

Model and assumptions

Note that the rows of X and Y are the subjects and columns are variables. The number of columns may be different, but the subjects should be the same in both datasets.

The O2PLS model (Trygg & Wold, 2003) decomposes two datasets X and Y into three parts.

• 1. A joint part, representing the relationship between X and Y

• 2. An orthogonal part, representing the unrelated latent variation in X and Y separately.

• 3. A noise part capturing all residual variation.

See also the corresponding paper (el Bouhaddani et al, 2018).

Fitting

The O2PLS fit is done with o2m. For data X and Y you can run o2m(X,Y,n,nx,ny) for an O2PLS fit with n joint and nx, ny orthogonal components. See the help page of o2m for more information on parameters. There are four ways to obtain an O2PLS fit, depending on the dimensionality.

• For the not-too-high dimensional case, you may use o2m with default parameters. E.g. o2m(X,Y,n,nx,ny).

• In case you only want the parameters, you may add stripped = TRUE to obtain a stripped version of o2m which avoids calculating and storing some matrices. E.g. o2m(X,Y,n,nx,ny,stripped=TRUE).

• For high dimensional cases, defined by ncol(X)>p_thresh and ncol(Y)>q_thresh, a NIPALS approach is used which avoids storing large matrices. E.g. o2m(X,Y,n,nx,ny,p_thresh=3000,q_thresh=3000). The thresholds are by default both at 3000 variables.

• If you want a stripped version in the high dimensional case, add stripped = TRUE. E.g. o2m(X,Y,n,nx,ny,stripped=TRUE,p_thresh=3000,q_thresh=3000).

• For GO2PLS, add sparsity = TRUE and specify how many variables or groups to retain. E.g. o2m(X,Y,n,nx,ny,sparse=TRUE,keepx, keepy).

Obtaining results

After fitting an O2PLS model, by running e.g. fit = o2m(X,Y,n,nx,ny), the results can be visualised. Use plot(fit,...) to plot the desired loadings with/without ggplot2. Use summary(fit,...) to see the relative explained variances in the joint/orthogonal parts. Also plotting the joint scores fit$Tt, fit$U and orthogonal scores fit$T_Yosc, fit$U_Xosc are of help.

Cross-validating

Determining the number of components n,nx,ny is an important task. For this we have two methods. See citation("OmicsPLS") for our proposed approach for determining the number of components, implemented in crossval_o2m_adjR2!

• Cross-validation (CV) is done with crossval_o2m and crossval_o2m_adjR2, both have built in parallelization which relies on the parallel package. Usage is something like crossval_o2m(X,Y,a,ax,ay,nr_folds) where a,ax,ay are vectors of integers. See the help pages. nr_folds is the number of folds, with nr_folds = nrow(X) for Leave-One-Out CV.

• For crossval_o2m_adjR2 the same parameters are to be specified. This way of cross-validating is (potentially much) faster than the standard approach. It is also recommended over the standard CV.

• To cross-validate the number of variables to keep, use crossval_sparsity.

S3 methods

There are S3 methods implemented for a fit obtained with o2m, i.e. fit <- o2m(X,Y,n,nx,ny)

• Use plot(fit) to plot the loadings, see above.

• Use loadings(fit) to extract a matrix with loading values

• Use scores(fit) to extract the scores

• Use print and summary to print and summarize the fit object

Imputation

When the data contains missing values, one should impute them prior to using O2PLS. There are many sophisticated approaches available, such as MICE and MissForest, and no one approach is the best for all situations. To still allow users to quickly impute missing values in their data matrix, the impute_matrix function is implemented. It relies on the softImpute function+package and imputes based on the singular value decomposition.

Misc

Also some handy tools are available

• orth(X) is a function to obtain an orthogonalized version of a matrix or vector X.

• ssq(X) is a function to calculate the sum of squares (or squared Frobenius norm) of X. See also vnorm for calculating the norm of each column in X.

• mse(x, y) returns the mean squared difference between two matrices/vectors.

Citation

If you use the OmicsPLS R package in your research, please cite the corresponding software paper:

el Bouhaddani, S., Uh, H.-W., Jongbloed, G., Hayward, C., Klarić, L., Kiełbasa, S. M., & Houwing-Duistermaat, J. (2018). Integrating omics datasets with the OmicsPLS package. BMC Bioinformatics, 19(1). doi: 10.1186/s12859-018-2371-3

The bibtex entry can be obtained with command citation("OmicsPLS"). Thank you!

The original paper proposing O2PLS is

Trygg, J., & Wold, S. (2003). O2-PLS, a two-block (X-Y) latent variable regression (LVR) method with an integral OSC filter. Journal of Chemometrics, 17(1), 53-64. doi: 10.1002/cem.775

Author(s)

Said el Bouhaddani ([e-mail], Twitter: @selbouhaddani), Zhujie Gu, Szymon Kielbasa, Geurt Jongbloed, Jeanine Houwing-Duistermaat, Hae-Won Uh.

Maintainer: Said el Bouhaddani ([e-mail]).