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

Description Usage Arguments Value Note See Also Examples

sTrainSeq is supposed to perform sequential 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, each training cycle consisting of: i) randomly choose one input vector; ii) determine the winner hexagon/rectangle (BMH) according to minimum distance of codebook matrix to the input vector; ii) update the codebook matrix of the BMH and its neighbors via updating formula (see "Note" below for details). It also returns an object of class "sMap".

1	sTrainSeq(sMap, data, sTrain, seed = 825, 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"
`seed`	an integer specifying the seed
`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) = m_i(t) + α(t)*h_{wi}(t)*[x(t)-m_i(t)], where

t denotes the training time/step
i and w stand for the hexagon/rectangle i and the winner BMH w, respectively
x(t) is an input vector randomly choosen (from the input data) at time t
m_i(t) and m_i(t+1) are respectively the prototype vectors of the hexagon i at time t and t+1
α(t) is the learning rate at time t. There are three types of learning rate functions:
- For "linear" function, α(t)=α_0*(1-t/T)
- For "power" function, α(t)=α_0*(0.005/α_0)^{t/T}
- For "invert" function, α(t)=α_0/(1+100*t/T)
- Where α_0 is the initial learing rate (typically, α_0=0.5 at "rough" stage, α_0=0.05 at "finetune" stage), T is the length of training time/step (often being set to input data length, i.e., the total number of rows)
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, algorithm="sequential",
stage="rough")

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

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

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