cumulative_loss: Cumulative Loss
In PACBO: Clustering Online Datasets

Description Usage Arguments Details Value Examples

This function computes the sum of squared Euclidean distance of each observation to its nearest center.

1	cumulative_loss(centers, observations)

`centers`	a matrix containing m centers of length d, where each row corresponds to coordinates of a center.
`observations`	a matrix containing T observations of length d, where each row of the matrix is an observation of length d.

Given a set C of m centers of length d (i.e., C = {c_{1}, c_{2}, …, c_{m}}) and a set X of T observations of length d (i.e., X = {x_{1}, x_{2}, …, x_{T}}), this function computes the sum of squared euclidean distance of each observation in X to its nearest center in C, i.e.,

S_{T}(C) =∑_{t=1,2,…,T} min_{1<= i <= m}|x_{t}-c_{i}|_{2}^{2}.

The sum of squared Euclidean distance of each of T observations in matrix observations to its nearest center within centers.

## generating 4 centers of length 3.
centers <- matrix(1:12, nrow = 4, ncol = 3)
## generating 10 observations of length 3.
observations <- matrix(rmnorm(10, mean = c(0,3,5), varcov = diag(1,3)), nrow = 10)
cumulative_loss(centers, observations)