  Clustering is an essential technique for discovering patterns in data. The
steady increase in amount and complexity of data over the years led to
improvements and development of new clustering algorithms. However, algorithms
that can cluster data with mixed variable types (continuous and categorical)
remain limited, despite the abundance of data with mixed types particularly in
the medical field. Among existing methods for mixed data, some posit
unverifiable distributional assumptions or that the contributions of different
variable types are not well balanced.
  We propose a two-step hybrid density- and partition-based algorithm (HyDaP)
that can detect clusters after variables selection. The first step involves
both density-based and partition-based algorithms to identify the data
structure formed by continuous variables and recognize the important variables
for clustering; the second step involves partition-based algorithm together
with a novel dissimilarity measure we designed for mixed data to obtain
clustering results. Simulations across various scenarios and data structures
were conducted to examine the performance of the HyDaP algorithm compared to
commonly used methods. We also applied the HyDaP algorithm on electronic health
records to identify sepsis phenotypes.
