R: Relevance Network for (r)CCA and (s)PLS regression

network {mixOmics} | R Documentation

## Relevance Network for (r)CCA and (s)PLS regression

### Description

Display relevance associations network for (regularized) canonical correlation analysis and (sparse) PLS regression. The function avoids the intensive computation of Pearson correlation matrices on large data set by calculating instead a pair-wise similarity matrix directly obtained from the latent components of our integrative approaches (CCA, PLS, block.pls methods). The similarity value between a pair of variables is obtained by calculating the sum of the correlations between the original variables and each of the latent components of the model. The values in the similarity matrix can be seen as a robust approximation of the Pearson correlation (see González et al. 2012 for a mathematical demonstration and exact formula). The advantage of relevance networks is their ability to simultaneously represent positive and negative correlations, which are missed by methods based on Euclidean distances or mutual information. Those networks are bipartite and thus only a link between two variables of different types can be represented. The network can be saved in a .glm format using the `igraph` package, the function `write.graph` and extracting the output `object$gR`, see details.

### Usage

    network(mat,
    comp = NULL,
    blocks = c(1,2),
    cutoff = NULL,
    row.names = TRUE,
    col.names = TRUE,
    block.var.names = TRUE,
    color.node = NULL,
    shape.node = NULL,
    cex.node.name = 1,
    color.edge = color.GreenRed(100),
    lty.edge = "solid",
    lwd.edge = 1,
    show.edge.labels = FALSE,
    cex.edge.label = 1,
    show.color.key = TRUE,
    symkey = TRUE,
    keysize = c(1, 1),
    keysize.label = 1,
    breaks,
    interactive = FALSE,
    layout.fun = NULL,
    save = NULL,
    name.save = NULL)

### Arguments

`mat` | numeric matrix of values to be represented.
`comp` | atomic or vector of positive integers. The components to adequately account for the data association. Defaults to `comp = 1`.
`cutoff` | numeric value between `0` and `1`. The tuning threshold for the relevant associations network (see Details).
`row.names, col.names` | character vector containing the names of X- and Y-variables.
`color.node` | vector of length two, the colors of the X and Y nodes (see Details).
`shape.node` | character vector of length two, the shape of the X and Y nodes (see Details).
`color.edge` | vector of colors or character string specifying the colors function to using to color the edges, set to default to `color.GreenRed(100)` but other palettes can be chosen (see Details and Examples).
`lty.edge` | character vector of length two, the line type for the edges (see Details).
`lwd.edge` | vector of length two, the line width of the edges (see Details).
`show.edge.labels` | logical. If `TRUE`, plot association values as edge labels (defaults to `FALSE`).
`show.color.key` | boolean. If `TRUE` a color key should be plotted.
`symkey` | boolean indicating whether the color key should be made symmetric about 0. Defaults to `TRUE`.
`keysize` | numeric value indicating the size of the color key.
`keysize.label` | vector of length 1, indicating the size of the labels and title of the color key.
`breaks` | (optional) either a numeric vector indicating the splitting points for binning `mat` into colors, or a integer number of break points to be used, in which case the break points will be spaced equally between `min(mat)` and `max(mat)`.
`interactive` | logical. If `TRUE`, a scrollbar is created to change the cutoff value interactively (defaults to `FALSE`). See Details.
`save` | should the plot be saved ? If so, argument to be set either to `'jpeg'`, `'tiff'`, `'png'` or `'pdf'`.
`name.save` | character string giving the name of the saved file.
`cex.edge.label` | the font size for the edge labels.
`cex.node.name` | the font size for the node labels.
`blocks` | a vector indicating the block variables to display.
`block.var.names` | either a list of vector components for variable names in each block or FALSE for no names. If TRUE, the columns names of the blocks are used as names.
`layout.fun` | a function. It specifies how the vertices will be placed on the graph. See help(layout) in the igraph package. Defaults to layout.fruchterman.reingold.

### Details

`network` allows to infer large-scale association networks between the X and Y datasets in `rcc` or `spls`. The output is a graph where each X- and Y-variable corresponds to a node and the edges included in the graph portray associations between them.

In `rcc`, to identify X-Y pairs showing relevant associations, `network` calculate a similarity measure between X and Y variables in a pair-wise manner: the scalar product value between every pairs of vectors in dimension `length(comp)` representing the variables X and Y on the axis defined by Z_i with i in `comp`, where Z_i is the equiangular vector between the i-th X and Y canonical variate.

In `spls`, if `object$mode` is `regression`, the similarity measure between X and Y variables is given by the scalar product value between every pairs of vectors in dimension `length(comp)` representing the variables X and Y on the axis defined by U_i with i in `comp`, where U_i is the i-th X variate. If `object$mode` is `canonical` then X and Y are represented on the axis defined by U_i and V_i respectively.

Variable pairs with a high similarity measure (in absolute value) are considered as relevant. By changing the cutoff, one can tune the relevance of the associations to include or exclude relationships in the network.

`interactive=TRUE` open two device, one for association network, one for scrollbar, and define an interactive process: by clicking either at each end ('-' or '+') of the scrollbar or at middle portion of this. The position of the slider indicate which is the ‘cutoff’ value associated to the display network.

The network can be saved in a .glm format using the igraph package, the function `write.graph` and extracting the output `obkect$gR`.

The interactive process is terminated by clicking the second button and selecting ‘Stop’ from the menu, or from the ‘Stop’ menu on the graphics window.

The `color.node` is a vector of length two, of any of the three kind of `R` colors, i.e., either a color name (an element of `colors()`), a hexadecimal string of the form `"#rrggbb"`, or an integer `i` meaning `palette()[i]`. `color.node[1]` and `color.node[2]` give the color for filled nodes of the X- and Y-variables respectively. Defaults to `c("white", "white")`.

`color.edge` give the color to edges with colors corresponding to the values in `mat`. Defaults to `color.GreenRed(100)` for negative (green) and positive (red) correlations. We also propose other palettes of colors, such as `color.jet` and `color.spectral`, see help on those functions, and examples below. Other palette of colors from the stats package can be used too.

`shape.node[1]` and `shape.node[2]` provide the shape of the nodes associate to X- and Y-variables respectively. Current acceptable values are `"circle"` and `"rectangle"`. Defaults to `c("circle", "rectangle")`.

`lty.edge[1]` and `lty.egde[2]` give the line type to edges with positive and negative weight respectively. Can be one of `"solid"`, `"dashed"`, `"dotted"`, `"dotdash"`, `"longdash"` and `"twodash"`. Defaults to `c("solid", "solid")`.

`lwd.edge[1]` and `lwd.edge[2]` provide the line width to edges with positive and negative weight respectively. This attribute is of type double with a default of `c(1, 1)`.

### Value

`network` return a list containing the following components:

`M` | the correlation matrix used by `network`.
`gR` | a `graph` object to save the graph for cytoscape use (requires to load the igraph package).

### Warning

If the number of variables is high, the generation of the network generation can take some time.

### Author(s)

Ignacio González and Kim-Anh Lê Cao.

### References

Mathematical definition: González I., Lê Cao K-A., Davis, M.J. and Déjean, S. (2012). Visualising associations between paired omics data sets. J. Data Mining 5:19. http://www.biodatamining.org/content/5/1/19/abstract

Examples and illustrations:

Rohart F, Gautier B, Singh A, Lê Cao K-A. mixOmics: an R package for 'omics feature selection and multiple data integration. PLoS Comput Biol 13(11): e1005752

Relevance networks:

Butte, A. J., Tamayo, P., Slonim, D., Golub, T. R. and Kohane, I. S. (2000). Discovering functional relationships between RNA expression and chemotherapeutic susceptibility using relevance networks. Proceedings of the National Academy of Sciences of the USA 97, 12182-12186.

Moriyama, M., Hoshida, Y., Otsuka, M., Nishimura, S., Kato, N., Goto, T., Taniguchi, H., Shiratori, Y., Seki, N. and Omata, M. (2003). Relevance Network between Chemosensitivity and Transcriptome in Human Hepatoma Cells. Molecular Cancer Therapeutics 2, 199-205.

### See Also

`plotVar`, `cim`, `color.GreenRed`, `color.jet`, `color.spectral` and http: //www.mixOmics.org for more details.

### Examples

    ## network representation for objects of class 'rcc'
    data(nutrimouse)
    X <- nutrimouse$lipid
    Y <- nutrimouse$gene
    nutri.res <- rcc(X, Y, ncomp = 3, lambda1 = 0.064, lambda2 = 0.008)

    ## Not run:
    # may not work on the Linux version, use Windows instead
    # sometimes with Rstudio might not work because of margin issues,
    # in that case save it as an image
    jpeg('example1-network.jpeg', res = 600, width = 4000, height = 4000)
    network(nutri.res, comp = 1:3, cutoff = 0.6)
    dev.off()

    ## End(Not run)

    ## Changing the attributes of the network
    ## Not run:
    # sometimes with Rstudio might not work because of margin issues,
    # in that case save it as an image
    jpeg('example2-network.jpeg')
    network(nutri.res, comp = 1:3, cutoff = 0.45,
    color.node = c("mistyrose", "lightcyan"),
    shape.node = c("circle", "rectangle"),
    color.edge = color.jet(100),
    lty.edge = "solid", lwd.edge = 2,
    show.edge.labels = FALSE)
    dev.off()

    ## End(Not run)

    ## interactive 'cutoff'
    ## Not run:
    network(nutri.res, comp = 1:3, cutoff = 0.55, interactive = TRUE)
    ## select the 'cutoff' and "see" the new network

    ## End(Not run)

    ## network representation for objects of class 'spls'
    data(liver.toxicity)
    X <- liver.toxicity$gene
    Y <- liver.toxicity$clinic
    toxicity.spls <- spls(X, Y, ncomp = 3, keepX = c(50, 50, 50),
    keepY = c(10, 10, 10))
    ## Not run:
    # sometimes with Rstudio might not work because of margin issues,
    # in that case save it as an image
    jpeg('example3-network.jpeg')
    network(toxicity.spls, comp = 1:3, cutoff = 0.8,
    color.node = c("mistyrose", "lightcyan"),
    shape.node = c("rectangle", "circle"),
    color.edge = color.spectral(100),
    lty.edge = "solid", lwd.edge =  1,
    show.edge.labels = FALSE, interactive = FALSE)
    dev.off()

    ## End(Not run)

[Package mixOmics version 6.3.2 Index]