Diabetes is a chronic, metabolic disease characterized by elevated levels of blood glucose (or blood sugar), which leads over time to serious damage to the heart, blood vessels, eyes, kidneys and nerves.
Diabetes
Diabetes is a global health crisis that has seen a dramatic rise in recent years. According to World Health Organization in 2021, it ranked among the top 10 causes of death worldwide, with a staggering 95% increase since 2000.
represents the conditional probability density function of the dataset given \({\bf p}\), where \(C({\bf p})\) is the normalizing constant for the probability density function.
Background of BCVI
Let \(r_k(\bf x)\) be a ratio adjusted from a CVI defined as
\[
r_k(\bf x) = \begin{cases}
\dfrac{GI(k)-\min_j GI(j)}{\sum_{i=2}^K (GI(i)-\min_j GI(j))} \text{ for Condition A, } \\
\dfrac{\max_j GI(j)- GI(k)}{\sum_{i=2}^K (\max_j GI(j) - GI(i))} \text{ for Condition B, } \\
\end{cases}
\qquad(2)\]
where GI represents an arbitrary CVI.
Condition A: The largest value of the GI indicates the optimal number of clusters.
Condition B: The smallest value of the GI indicates the optimal number of clusters.
It is clear that \(0\le r_k(\bf x) \le 1\).
Dirichlet prior
Here, we assume that \({\bf p}\) follows a Dirichlet prior distribution with parameters \({\bf \alpha} = (\alpha_2,\ldots,\alpha_K)\) with the probability density function
Let \(K \in \mathbb{N}\) and \({\bf r(x)} = (r_2({\bf x}),\ldots,r_K({\bf x}))\), where \(r_k({\bf x})\) is defined as in (1). Assuming that \({\bf x}\) follows the distribution described in (2), the posterior distribution of \({\bf p}\) has the probability density function:
The default alpha value corresponds to the case where \(\alpha_k=1\) for all k. This is used when users want the results to rely only on underlying CVIs.
Alpha
# Selecting each alpha between 0 to 30 is recommended. # If we consider k from 2 to 10aalpha =c(25,25,25,25,25,5,5,5,5)
How to apply
# Determine alpha based on our knowledge# Consider k from 2 to 10aalpha =c(25,25,25,25,25,5,5,5,5)set.seed(50)B.WI =B_Wvalid(x =scale(clustdata), kmax =10, method ="kmeans",corr ="pearson",nstart =10, sampling =1, NCstart =TRUE,alpha = aalpha, mult.alpha =1/2)B.WI
It provides a valuable database for healthcare professionals, supporting informed decision-making, developing treatment strategies, and enhancing drug efficacy.
Highlighted Features for BCVI
Novel and unique concept: BCVI allows users to specify their desired range for the final number of clusters.
Flexibility: BCVI allows users to flexibly set parameters according to their needs and select any clustering algorithms and underlying CVIs of their choice.
Drawbacks
It relies on the quality of underlying indices.
It is only effective when underlying indices are present, providing meaningful options for ranking local peaks for the final number of clusters.
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Installation
install.packages("BayesCVI")library(BayesCVI)
Function
help(package ="BayesCVI")# Data in function # B1_data - B7_data