| plot_BCVI {BayesCVI} | R Documentation |
Plots for visualizing BCVI
Description
Plot Bayesian cluster validity index (BCVI) with and without standard deviation error bars and the underlying index.
Usage
plot_BCVI(B.result, mult.err.bar = 2)
Arguments
B.result |
a result from one of the functions |
mult.err.bar |
a multiplier of the stadard deviations to be used for plotting error bars |
Details
BCVI is defined as follows.
Let
r_k(\bf x) = \dfrac{\max_j CVI(j)- CVI(k)}{\sum_{i=2}^K (\max_j CVI(j) - CVI(i))}
for a cluster validity index (CVI) such that the smallest value indicates the optimal number of clusters and
r_k(\bf x) = \dfrac{CVI(k)-\min_j CVI(j)}{\sum_{i=2}^K (CVI(i)-\min_j CVI(j))}
for a CVI such that the largest indicates the optimal number of clusters.
Assume that
f({\bf x}|{\bf p}) = C({\bf p}) \prod_{k=2}^Kp_k^{nr_k(x)}
represents the conditional probability density function of the dataset given \bf p, where C({\bf p}) is the normalizing constant. Assume further that {\bf p} follows a Dirichlet prior distribution with parameters {\bm \alpha} = (\alpha_2,\ldots,\alpha_K). The posterior distribution of \bf p still remains a Dirichlet distribution with parameters (\alpha_2+nr_2({\bf x}),\ldots,\alpha_K+nr_K({\bf x})).
The BCVI is then defined as
BCVI(k) = E[p_k|{\bf x}] = \frac{\alpha_k + nr_k({\bf x})}{\alpha_0+n}
where \alpha_0 = \sum_{k=2}^K \alpha_k.
The variance of p_k can be computed as
Var(p_k|{\bf x}) = \dfrac{(\alpha_k + nr_k(x))(\alpha_0 + n -\alpha_k-nr_k(x))}{(\alpha_0 + n)^2(\alpha_0 + n +1 )}.
Value
plot_index |
a plot of the underlying index for the number of groups from |
plot_BCVI |
a plot of BCVI for the number of groups from |
error_bar_plot |
a plot of BCVI with error bars for the number of groups from |
Author(s)
Nathakhun Wiroonsri and Onthada Preedasawakul
References
N. Wiroonsri, O. Preedasawakul, "A Bayesian cluster validity index", arXiv:2402.02162, 2024.
See Also
B_STRPBM.IDX, B_TANG.IDX, B_XB.IDX, B_Wvalid, B_WP.IDX, B_DB.IDX
Examples
library(BayesCVI)
library(UniversalCVI)
##Soft clustering
# The data included in this package.
data = B7_data[,1:2]
# alpha
aalpha = c(5,5,5,20,20,20,0.5,0.5,0.5)
B.XB = B_XB.IDX(x = scale(data), kmax =10, method = "FCM", fzm = 2,
nstart = 20, iter = 100, alpha = aalpha, mult.alpha = 1/2)
# plot the BCVI
pplot = plot_BCVI(B.XB)
pplot$plot_index
pplot$plot_BCVI
pplot$error_bar_plot
## Hard clustering
# The data included in this package.
data = B2_data[,1:2]
K.STR = STRPBM.IDX(scale(data), kmax = 10, kmin = 2, method = "kmeans",
indexlist = "STR", nstart = 100)
# WP.IDX values
result = K.STR$STR$STR
aalpha = c(20,20,20,5,5,5,0.5,0.5,0.5)
B.STR = BayesCVIs(CVI = result,
n = nrow(data),
kmax = 10,
opt.pt = "max",
alpha = aalpha,
mult.alpha = 1/2)
# plot the BCVI
pplot = plot_BCVI(B.STR)
pplot$plot_index
pplot$plot_BCVI
pplot$error_bar_plot