sTrainBatch: Function to implement training via batch algorithm
In supraHex: supraHex: a supra-hexagonal map for analysing tabular omics data

Description Usage Arguments Value Note See Also Examples

sTrainBatch is supposed to perform batch training algorithm. It requires three inputs: a "sMap" or "sInit" object, input data, and a "sTrain" object specifying training environment. The training is implemented iteratively, but instead of choosing a single input vector, the whole input matrix is used. In each training cycle, the whole input matrix first land in the map through identifying the corresponding winner hexagon/rectangle (BMH), and then the codebook matrix is updated via updating formula (see "Note" below for details). It returns an object of class "sMap".

1	sTrainBatch(sMap, data, sTrain, verbose = TRUE)

`sMap`	an object of class "sMap" or "sInit"
`data`	a data frame or matrix of input data
`sTrain`	an object of class "sTrain"
`verbose`	logical to indicate whether the messages will be displayed in the screen. By default, it sets to TRUE for display

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

nHex: the total number of hexagons/rectanges in the grid
xdim: x-dimension of the grid
ydim: y-dimension of the grid
r: the hypothetical radius of the grid
lattice: the grid lattice
shape: the grid shape
coord: a matrix of nHex x 2, with each row corresponding to the coordinates of a hexagon/rectangle in the 2D map grid
ig: the igraph object
init: an initialisation method
neighKernel: the training neighborhood kernel
codebook: a codebook matrix of nHex x ncol(data), with each row corresponding to a prototype vector in input high-dimensional space
call: the call that produced this result

Updating formula is: m_i(t+1) = \frac{∑_{j=1}^{dlen}h_{wi}(t)x_j}{∑_{j=1}^{dlen}h_{wi}(t)}, where

t denotes the training time/step
x_j is an input vector j from the input data matrix (with dlen rows in total)
i and w stand for the hexagon/rectangle i and the winner BMH w, respectively
m_i(t+1) is the prototype vector of the hexagon i at time t+1
h_{wi}(t) is the neighborhood kernel, a non-increasing function of i) the distance d_{wi} between the hexagon/rectangle i and the winner BMH w, and ii) the radius δ_t at time t. There are five kernels available:
- For "gaussian" kernel, h_{wi}(t)=e^{-d_{wi}^2/(2*δ_t^2)}
- For "cutguassian" kernel, h_{wi}(t)=e^{-d_{wi}^2/(2*δ_t^2)}*(d_{wi} ≤ δ_t)
- For "bubble" kernel, h_{wi}(t)=(d_{wi} ≤ δ_t)
- For "ep" kernel, h_{wi}(t)=(1-d_{wi}^2/δ_t^2)*(d_{wi} ≤ δ_t)
- For "gamma" kernel, h_{wi}(t)=1/Γ(d_{wi}^2/(4*δ_t^2)+2)

sTrainology, visKernels

# 1) generate an iid normal random matrix of 100x10 
data <- matrix( rnorm(100*10,mean=0,sd=1), nrow=100, ncol=10)

# 2) from this input matrix, determine nHex=5*sqrt(nrow(data))=50, 
# but it returns nHex=61, via "sHexGrid(nHex=50)", to make sure a supra-hexagonal grid
sTopol <- sTopology(data=data, lattice="hexa", shape="suprahex")

# 3) initialise the codebook matrix using "uniform" method
sI <- sInitial(data=data, sTopol=sTopol, init="uniform")

# 4) define trainology at "rough" stage
sT_rough <- sTrainology(sMap=sI, data=data, stage="rough")

# 5) training at "rough" stage
sM_rough <- sTrainBatch(sMap=sI, data=data, sTrain=sT_rough)

# 6) define trainology at "finetune" stage
sT_finetune <- sTrainology(sMap=sI, data=data, stage="finetune")

# 7) training at "finetune" stage
sM_finetune <- sTrainBatch(sMap=sM_rough, data=data, sTrain=sT_rough)