# Function to implement training via batch algorithm

### Description

`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".

### Usage

1 | ```
sTrainBatch(sMap, data, sTrain, verbose = T)
``` |

### Arguments

`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 |

### Value

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`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`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

### Note

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)*

### See Also

`sTrainology`

, `visKernels`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
# 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)
``` |