Function to reorder component planes

Description

sCompReorder is supposed to reorder component planes for the input map/data. It returns an object of class "sReorder". It is realized by using a new map grid (with sheet shape consisting of a rectangular lattice) to train component plane vectors (either column-wise vectors of codebook/data matrix or the covariance matrix thereof). As a result, similar component planes are placed closer to each other. It is highly recommend to use trained map (i.e. codebook matrix) as input if data matrix is hugely big to save computational costs.

Usage

sCompReorder(sMap, 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

sMap
an object of class "sMap" or input data frame/matrix
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 difine 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. See sDistance for details
init
an initialisation method. It can be one of "uniform", "sample" and "linear" initialisation methods
algorithm
the training algorithm. It can be one of "sequential" and "batch" algorithm. By default, it uses 'sequential' algorithm. If the input data contains a large number of samples but not a great amount of zero entries, then it is reasonable to use 'batch' algorithm for its fast computations (probably also without the compromise of accuracy)
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

All component planes are uniquely placed within a "sheet"-shape rectangle grid:

  • Each component plane 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 compoments are hit in the same rectangular lattice, the worse one is always sacrificed by moving to the next best one till all components 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 an iid normal random matrix of 100x10 data <- matrix( rnorm(100*10,mean=0,sd=1), nrow=100, ncol=10) colnames(data) <- paste(rep('S',10), seq(1:10), sep="") # 2) get trained using by default setup sMap <- sPipeline(data=data)
Start at 2017-03-27 18:54:50 First, define topology of a map grid (2017-03-27 18:54:50)... Second, initialise the codebook matrix (61 X 10) using 'linear' initialisation, given a topology and input data (2017-03-27 18:54:50)... Third, get training at the rough stage (2017-03-27 18:54:50)... 1 out of 7 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 2 out of 7 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 3 out of 7 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 4 out of 7 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 5 out of 7 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 6 out of 7 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 7 out of 7 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) Fourth, get training at the finetune stage (2017-03-27 18:54:50)... 1 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 2 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 3 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 4 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 5 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 6 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 7 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 8 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 9 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 10 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 11 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 12 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 13 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 14 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 15 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 16 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 17 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 18 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 19 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 20 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 21 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 22 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 23 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 24 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) 25 out of 25 (2017-03-27 18:54:50) updated (2017-03-27 18:54:50) Next, identify the best-matching hexagon/rectangle for the input data (2017-03-27 18:54:50)... Finally, append the response data (hits and mqe) into the sMap object (2017-03-27 18:54:50)... Below are the summaries of the training results: dimension of input data: 100x10 xy-dimension of map grid: xdim=9, ydim=9, r=5 grid lattice: hexa grid shape: suprahex dimension of grid coord: 61x2 initialisation method: linear dimension of codebook matrix: 61x10 mean quantization error: 4.92761300512866 Below are the details of trainology: training algorithm: batch alpha type: invert training neighborhood kernel: gaussian trainlength (x input data length): 7 at rough stage; 25 at finetune stage radius (at rough stage): from 3 to 1 radius (at finetune stage): from 1 to 1 End at 2017-03-27 18:54:50 Runtime in total is: 0 secs
# 3) reorder component planes in different ways # 3a) directly using column-wise vectors of codebook matrix sReorder <- sCompReorder(sMap=sMap, amplifier=2, metric="none")
Start at 2017-03-27 18:54:50 First, define topology of a map grid (2017-03-27 18:54:50)... Second, initialise the codebook matrix (20 X 61) using 'linear' initialisation, given a topology and input data (2017-03-27 18:54:50)... Third, get training at the rough stage (2017-03-27 18:54:50)... 1 out of 200 (2017-03-27 18:54:50) 20 out of 200 (2017-03-27 18:54:50) 40 out of 200 (2017-03-27 18:54:50) 60 out of 200 (2017-03-27 18:54:50) 80 out of 200 (2017-03-27 18:54:50) 100 out of 200 (2017-03-27 18:54:50) 120 out of 200 (2017-03-27 18:54:50) 140 out of 200 (2017-03-27 18:54:50) 160 out of 200 (2017-03-27 18:54:50) 180 out of 200 (2017-03-27 18:54:50) 200 out of 200 (2017-03-27 18:54:50) Fourth, get training at the finetune stage (2017-03-27 18:54:50)... 1 out of 800 (2017-03-27 18:54:50) 80 out of 800 (2017-03-27 18:54:50) 160 out of 800 (2017-03-27 18:54:50) 240 out of 800 (2017-03-27 18:54:50) 320 out of 800 (2017-03-27 18:54:50) 400 out of 800 (2017-03-27 18:54:50) 480 out of 800 (2017-03-27 18:54:50) 560 out of 800 (2017-03-27 18:54:50) 640 out of 800 (2017-03-27 18:54:51) 720 out of 800 (2017-03-27 18:54:51) 800 out of 800 (2017-03-27 18:54:51) Next, identify the best-matching hexagon/rectangle for the input data (2017-03-27 18:54:51)... Finally, append the response data (hits and mqe) into the sMap object (2017-03-27 18:54:51)... Below are the summaries of the training results: dimension of input data: 10x61 xy-dimension of map grid: xdim=5, ydim=4, r=3 grid lattice: rect grid shape: sheet dimension of grid coord: 20x2 initialisation method: linear dimension of codebook matrix: 20x61 mean quantization error: 5.50070826203008 Below are the details of trainology: training algorithm: sequential alpha type: invert training neighborhood kernel: gaussian trainlength (x input data length): 20 at rough stage; 80 at finetune stage radius (at rough stage): from 1 to 1 radius (at finetune stage): from 1 to 1 End at 2017-03-27 18:54:51 Runtime in total is: 1 secs
# 3b) according to covariance matrix of pearson correlation of codebook matrix sReorder <- sCompReorder(sMap=sMap, amplifier=2, metric="pearson")
Start at 2017-03-27 18:54:51 First, define topology of a map grid (2017-03-27 18:54:51)... Second, initialise the codebook matrix (20 X 10) using 'linear' initialisation, given a topology and input data (2017-03-27 18:54:51)... Third, get training at the rough stage (2017-03-27 18:54:51)... 1 out of 200 (2017-03-27 18:54:51) 20 out of 200 (2017-03-27 18:54:51) 40 out of 200 (2017-03-27 18:54:51) 60 out of 200 (2017-03-27 18:54:51) 80 out of 200 (2017-03-27 18:54:51) 100 out of 200 (2017-03-27 18:54:51) 120 out of 200 (2017-03-27 18:54:51) 140 out of 200 (2017-03-27 18:54:51) 160 out of 200 (2017-03-27 18:54:51) 180 out of 200 (2017-03-27 18:54:51) 200 out of 200 (2017-03-27 18:54:51) Fourth, get training at the finetune stage (2017-03-27 18:54:51)... 1 out of 800 (2017-03-27 18:54:51) 80 out of 800 (2017-03-27 18:54:51) 160 out of 800 (2017-03-27 18:54:51) 240 out of 800 (2017-03-27 18:54:51) 320 out of 800 (2017-03-27 18:54:51) 400 out of 800 (2017-03-27 18:54:51) 480 out of 800 (2017-03-27 18:54:51) 560 out of 800 (2017-03-27 18:54:51) 640 out of 800 (2017-03-27 18:54:51) 720 out of 800 (2017-03-27 18:54:51) 800 out of 800 (2017-03-27 18:54:51) Next, identify the best-matching hexagon/rectangle for the input data (2017-03-27 18:54:51)... Finally, append the response data (hits and mqe) into the sMap object (2017-03-27 18:54:51)... Below are the summaries of the training results: dimension of input data: 10x10 xy-dimension of map grid: xdim=5, ydim=4, r=3 grid lattice: rect grid shape: sheet dimension of grid coord: 20x2 initialisation method: linear dimension of codebook matrix: 20x10 mean quantization error: 0.548597803172487 Below are the details of trainology: training algorithm: sequential alpha type: invert training neighborhood kernel: gaussian trainlength (x input data length): 20 at rough stage; 80 at finetune stage radius (at rough stage): from 1 to 1 radius (at finetune stage): from 1 to 1 End at 2017-03-27 18:54:51 Runtime in total is: 0 secs
# 3c) according to covariance matrix of pearson correlation of input matrix sReorder <- sCompReorder(sMap=data, amplifier=2, metric="pearson")
Start at 2017-03-27 18:54:51 First, define topology of a map grid (2017-03-27 18:54:51)... Second, initialise the codebook matrix (20 X 10) using 'linear' initialisation, given a topology and input data (2017-03-27 18:54:51)... Third, get training at the rough stage (2017-03-27 18:54:51)... 1 out of 200 (2017-03-27 18:54:51) 20 out of 200 (2017-03-27 18:54:51) 40 out of 200 (2017-03-27 18:54:51) 60 out of 200 (2017-03-27 18:54:51) 80 out of 200 (2017-03-27 18:54:51) 100 out of 200 (2017-03-27 18:54:51) 120 out of 200 (2017-03-27 18:54:51) 140 out of 200 (2017-03-27 18:54:51) 160 out of 200 (2017-03-27 18:54:51) 180 out of 200 (2017-03-27 18:54:51) 200 out of 200 (2017-03-27 18:54:51) Fourth, get training at the finetune stage (2017-03-27 18:54:51)... 1 out of 800 (2017-03-27 18:54:51) 80 out of 800 (2017-03-27 18:54:51) 160 out of 800 (2017-03-27 18:54:51) 240 out of 800 (2017-03-27 18:54:51) 320 out of 800 (2017-03-27 18:54:51) 400 out of 800 (2017-03-27 18:54:51) 480 out of 800 (2017-03-27 18:54:51) 560 out of 800 (2017-03-27 18:54:51) 640 out of 800 (2017-03-27 18:54:51) 720 out of 800 (2017-03-27 18:54:51) 800 out of 800 (2017-03-27 18:54:51) Next, identify the best-matching hexagon/rectangle for the input data (2017-03-27 18:54:51)... Finally, append the response data (hits and mqe) into the sMap object (2017-03-27 18:54:51)... Below are the summaries of the training results: dimension of input data: 10x10 xy-dimension of map grid: xdim=5, ydim=4, r=3 grid lattice: rect grid shape: sheet dimension of grid coord: 20x2 initialisation method: linear dimension of codebook matrix: 20x10 mean quantization error: 0.56538206631514 Below are the details of trainology: training algorithm: sequential alpha type: invert training neighborhood kernel: gaussian trainlength (x input data length): 20 at rough stage; 80 at finetune stage radius (at rough stage): from 1 to 1 radius (at finetune stage): from 1 to 1 End at 2017-03-27 18:54:51 Runtime in total is: 0 secs