Function to reorder the multiple graph colorings within a sheet-shape rectangle grid

Description

dNetReorder is reorder the multiple graph colorings within a sheet-shape rectangle grid

Usage

dNetReorder(g, data, feature = c("node", "edge"), node.normalise = c("none", "degree"), 
  xdim = NULL, ydim = NULL, amplifier = NULL, metric = c("none", "pearson", "spearman", 
          "kendall", "euclidean", "manhattan", "cos", "mi"), init = c("linear", "uniform", 
          "sample"), algorithm = c("sequential", "batch"), alphaType = c("invert", 
          "linear", "power"), neighKernel = c("gaussian", "bubble", "cutgaussian", 
          "ep", "gamma"))

Arguments

g
an object of class "igraph" or "graphNEL"
data
an input data matrix used to color-code vertices/nodes. One column corresponds to one graph node coloring. The input matrix must have row names, and these names should include all node names of input graph, i.e. V(g)$name, since there is a mapping operation. After mapping, the length of the patern vector should be the same as the number of nodes of input graph. The way of how to color-code is to map values in the pattern onto the whole colormap (see the next arguments: colormap, ncolors, zlim and colorbar)
feature
the type of the features used. It can be one of either 'edge' for the edge feature or 'node' for the node feature. See 'Note' for explanations.
node.normalise
the normalisation of the nodes. It can be one of either 'none' for no normalisation or 'degree' for a node being penalised by its degree.
xdim
an integer specifying x-dimension of the grid
ydim
an integer specifying y-dimension of the grid
amplifier
an integer specifying the amplifier (3 by default) of the number of component planes. The product of the component number and the amplifier constitutes the number of rectangles in the sheet grid
metric
distance metric used to define the similarity between component planes. It can be "none", which means directly using column-wise vectors of codebook/data matrix. Otherwise, first calculate the covariance matrix from the codebook/data matrix. The distance metric used for calculating the covariance matrix between component planes can be: "pearson" for pearson correlation, "spearman" for spearman rank correlation, "kendall" for kendall tau rank correlation, "euclidean" for euclidean distance, "manhattan" for cityblock distance, "cos" for cosine similarity, "mi" for mutual information.
init
an initialisation method. It can be one of "uniform", "sample" and "linear" initialisation methods
algorithm
the training algorithm. Currently, only "sequential" algorithm has been implemented
alphaType
the alpha type. It can be one of "invert", "linear" and "power" alpha types
neighKernel
the training neighbor kernel. It can be one of "gaussian", "bubble", "cutgaussian", "ep" and "gamma" kernels

Value

an object of class "sReorder", a list with following components:

  • nHex: the total number of rectanges in the grid
  • xdim: x-dimension of the grid
  • ydim: y-dimension of the grid
  • uOrder: the unique order/placement for each component plane that is reordered to the "sheet"-shape grid with rectangular lattice
  • coord: a matrix of nHex x 2, with each row corresponding to the coordinates of each "uOrder" rectangle in the 2D map grid
  • call: the call that produced this result

Note

According to which features are used and whether nodes should be penalised by degrees, the feature data are constructed differently from the input data and input graph:

  • When the node features are used, the feature data is the input data (or penalised data) with the same dimension.
  • When the edge featrues are used, each entry (i.e. given an edge and a sample) in the feature data is the absolute difference between its two-end nodes (or after being penalised).
  • After that, the constructed feature are subject to sample correlation analysis by supraHex. That is, a map grid (with sheet shape consisting of a rectangular lattice) is used to train either column-wise vectors of the feature data matrix or the covariance matrix thereof.
  • As a result, similar samples are placed closer to each other within this map grid. More precisely, to ensure the unique placement, each sample mapped to the "sheet"-shape grid with rectangular lattice is determinied iteratively in an order from the best matched to the next compromised one. If multiple samples are hit in the same rectangular lattice, the worse one is always sacrificed by moving to the next best one till all samples are placed somewhere exclusively on their own.

The size of "sheet"-shape rectangle grid depends on the input arguments:

  • How the input parameters are used to determine nHex is taken priority in the following order: "xdim & ydim" > "nHex" > "data".
  • If both of xdim and ydim are given, nHex=xdim*ydim.
  • If only data is input, nHex=5*sqrt(dlen), where dlen is the number of rows of the input data.
  • After nHex is determined, xy-dimensions of rectangle grid are then determined according to the square root of the two biggest eigenvalues of the input data.

Examples

# 1) generate a random graph according to the ER model g <- erdos.renyi.game(100, 1/100) # 2) produce the induced subgraph only based on the nodes in query subg <- dNetInduce(g, V(g), knn=0) # 3) reorder the module with vertices being color-coded by input data nnodes <- vcount(subg) nsamples <- 10 data <- matrix(runif(nnodes*nsamples), nrow=nnodes, ncol=nsamples) rownames(data) <- V(subg)$name sReorder <- dNetReorder(g=subg, data, feature="node", node.normalise="none")
Start at 2017-03-27 19:58:07 First, define topology of a map grid (2017-03-27 19:58:07)... Second, initialise the codebook matrix (36 X 14) using 'linear' initialisation, given a topology and input data (2017-03-27 19:58:07)... Third, get training at the rough stage (2017-03-27 19:58:07)... 1 out of 360 (2017-03-27 19:58:07) 36 out of 360 (2017-03-27 19:58:07) 72 out of 360 (2017-03-27 19:58:07) 108 out of 360 (2017-03-27 19:58:07) 144 out of 360 (2017-03-27 19:58:07) 180 out of 360 (2017-03-27 19:58:07) 216 out of 360 (2017-03-27 19:58:07) 252 out of 360 (2017-03-27 19:58:07) 288 out of 360 (2017-03-27 19:58:07) 324 out of 360 (2017-03-27 19:58:07) 360 out of 360 (2017-03-27 19:58:07) Fourth, get training at the finetune stage (2017-03-27 19:58:07)... 1 out of 1440 (2017-03-27 19:58:07) 144 out of 1440 (2017-03-27 19:58:08) 288 out of 1440 (2017-03-27 19:58:08) 432 out of 1440 (2017-03-27 19:58:08) 576 out of 1440 (2017-03-27 19:58:08) 720 out of 1440 (2017-03-27 19:58:08) 864 out of 1440 (2017-03-27 19:58:08) 1008 out of 1440 (2017-03-27 19:58:08) 1152 out of 1440 (2017-03-27 19:58:08) 1296 out of 1440 (2017-03-27 19:58:08) 1440 out of 1440 (2017-03-27 19:58:08) Next, identify the best-matching hexagon/rectangle for the input data (2017-03-27 19:58:08)... Finally, append the response data (hits and mqe) into the sMap object (2017-03-27 19:58:08)... Below are the summaries of the training results: dimension of input data: 10x14 xy-dimension of map grid: xdim=6, ydim=6, r=3 grid lattice: rect grid shape: sheet dimension of grid coord: 36x2 initialisation method: linear dimension of codebook matrix: 36x14 mean quantization error: 0.363916075119665 Below are the details of trainology: training algorithm: sequential alpha type: invert training neighborhood kernel: gaussian trainlength (x input data length): 36 at rough stage; 144 at finetune stage radius (at rough stage): from 1 to 1 radius (at finetune stage): from 1 to 1 End at 2017-03-27 19:58:08 Runtime in total is: 1 secs

Source code

dNetReorder.r

Source man

dNetReorder.Rd dNetReorder.pdf

See also

visNetReorder