ajive: Angle based Joint and Individual Variation Explained

Author: Iain Carmichael
License: MIT

Additional documentation, examples and code revisions are coming soon. For questions, issues or feature requests please reach out to Iain: [email protected].

Overview

Angle based Joint and Individual Variation Explained (AJIVE) is a dimensionality reduction algorithm for the multi-block setting i.e. (K) different data matrices, with the same set of observations and (possibly) different numbers of variables. AJIVE finds joint modes of variation which are common to all (K) data blocks as well as modes of individual variation which are specific to each block. For a detailed discussion of AJIVE see Angle-Based Joint and Individual Variation Explained.

A python version of this package can be found here.

Installation

The ajive package is currently available using devtools

# install.packages('devtools')
devtools::install_github("idc9/r_jive")

Example

Consider the following two block toy example: the first block has 200 observations (rows) and 100 variables; the second block has the same set of 200 observations and 500 variables (similar to Figure 2 of the AJIVE paper).

library(ajive)

# sample a toy dataset with true joint rank of 1
blocks <- sample_toy_data(n=200, dx=100, dy=500)

data_blocks_heatmap(blocks, show_color_bar=FALSE)

After selecting the initial signal ranks we can compute the AJIVE decomposition using the ajive function.

initial_signal_ranks <- c(2, 3) # set by looking at scree plots
jive_results <- ajive(blocks, initial_signal_ranks, 
                      n_wedin_samples = 100, n_rand_dir_samples = 100)

# estimated joint rank
jive_results$joint_rank
#> [1] 1

The heatmap below shows that AJIVE separates the joint and individual signals for this toy data set.

decomposition_heatmaps(blocks, jive_results)

Using notation from Section 3 of the AJIVE paper (where u means scores and v means loadings) we can get the jive data out as follows

# common normalized scores
dim(jive_results$joint_scores)
#> [1] 200   1

# Full matrix representation of the joint signal for the first block
dim(jive_results$block_decomps[[1]][['joint']][['full']])
#> [1] 200 100

# joint block specific scores for the first block
dim(jive_results$block_decomps[[1]][['joint']][['u']])
#> [1] 200   1

# joint block specific loadings for the first block
dim(jive_results$block_decomps[[1]][['joint']][['v']])
#> [1] 100   1

# individual block specific scores for the second block
dim(jive_results$block_decomps[[2]][['individual']][['u']])
#> [1] 200   2

Help and Support

Additional documentation, examples and code revisions are coming soon. For questions, issues or feature requests please reach out to Iain: [email protected].

Documentation

The source code is located on github: https://github.com/idc9/r_jive. Currently the best math reference is the AJIVE paper.

Testing

Testing is done using the testthat package.

Contributing

We welcome contributions to make this a stronger package: data examples, bug fixes, spelling errors, new features, etc.

Citation