O2PLS: O2PLS: Two-Way Orthogonal Partial Least Squares

In selbouhaddani/O2PLS: O2PLS: Two-Way Orthogonal Partial Least Squares

Description

This is based on work of (Trygg, Wold, 2003). Includes the O2PLS fit, some misc functions and some cross-validation tools.

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 for interpretation (el Bouhaddani et al, 2016).

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 don't want the fancy output, but only 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 Power-Method 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).

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("O2PLS") 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) where a,ax,ay are vectors of integers. See the help pages. kcv is the number of folds, with kcv = 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.

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. By default y=0.

Citation

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

Bouhaddani, S., Houwing-duistermaat, J., Jongbloed, G., Salo, P., Perola, M., & Uh, H.-W. (2016). Evaluation of O2PLS in Omics data integration. BMC Bioinformatics BMTL Supplement. doi:10.1186/s12859-015-0854-z

The bibtex entry can be obtained with command citation("O2PLS"). 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. http://doi.org/10.1002/cem.775

Author(s)

Said el Bouhaddani ([e-mail]), Jeanine Houwing-Duistermaat ([e-mail]), Geurt Jongbloed ([e-mail]), Szymon Kielbasa ([e-mail]), Hae-Won Uh ([e-mail]).

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

selbouhaddani/O2PLS documentation built on May 29, 2019, 5:53 p.m.