title: EnsCat: clustering of categorical data via ensembling.
abstract: BACKGROUND
  Clustering is a widely used collection of unsupervised learning techniques for identifying natural classes within a data set. It is often used in bioinformatics to infer population substructure. Genomic data are often categorical and high dimensional, e.g., long sequences of nucleotides. This makes inference challenging: The distance metric is often not well-defined on categorical data; running time for computations using high dimensional data can be considerable; and the Curse of Dimensionality often impedes the interpretation of the results. Up to the present, however, the literature and software addressing clustering for categorical data has not yet led to a standard approach.
  
  
  RESULTS
  We present software for an ensemble method that performs well in comparison with other methods regardless of the dimensionality of the data. In an ensemble method a variety of instantiations of a statistical object are found and then combined into a consensus value. It has been known for decades that ensembling generally outperforms the components that comprise it in many settings. Here, we apply this ensembling principle to clustering. We begin by generating many hierarchical clusterings with different clustering sizes. When the dimension of the data is high, we also randomly select subspaces also of variable size, to generate clusterings. Then, we combine these clusterings into a single membership matrix and use this to obtain a new, ensembled dissimilarity matrix using Hamming distance.
  
  
  CONCLUSIONS
  Ensemble clustering, as implemented in R and called EnsCat, gives more clearly separated clusters than other clustering techniques for categorical data. The latest version with manual and examples is available at https://github.com/jlp2duke/EnsCat .
authors.affiliation: Department of Statistics, University of Nebraska-Lincoln, Lincoln, NE, USA.
authors.forename: Bertrand S
authors.initials: BS
authors.lastname: Clarke
authors.affiliation: Department of Natural and Applied Sciences, University of Wisconsin Madison, Iowa City, IA, USA.
authors.forename: Saeid
authors.initials: S
authors.lastname: Amiri
authors.affiliation: Department of Statistics, University of Nebraska-Lincoln, Lincoln, NE, USA. jclarke3@unl.edu.|Department of Food Science and Technology, University of Nebraska-Lincoln, Lincoln, NE, USA. jclarke3@unl.edu.
authors.forename: Jennifer L
authors.identifier: http://orcid.org/0000-0002-2723-7249
authors.initials: JL
authors.lastname: Clarke
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D019295:Computational Biology / Q000379:methods*; D023281:Genomics / Q000379:methods; D012984:Software
keywords: Categorical data; Clustering; Ensembling methods; High dimensional data