Model-based clustering of categorical data based on the Hamming distance
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929402967752704 |
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| author | Argiento, Raffaele Filippi-Mazzola, Edoardo Paci, Lucia |
| author_facet | Argiento, Raffaele Filippi-Mazzola, Edoardo Paci, Lucia |
| contents | A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family are then considered as kernels of a finite mixture model with an unknown number of components.
Conjugate Bayesian inference has been derived for the parameters of the Hamming distribution model. The mixture is framed in a Bayesian nonparametric setting, and a transdimensional blocked Gibbs sampler is developed to provide full Bayesian inference on the number of clusters, their structure, and the group-specific parameters, facilitating the computation with respect to customary reversible jump algorithms. The proposed model encompasses a parsimonious latent class model as a special case when the number of components is fixed. Model performances are assessed via a simulation study and reference datasets, showing improvements in clustering recovery over existing approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_04746 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Model-based clustering of categorical data based on the Hamming distance Argiento, Raffaele Filippi-Mazzola, Edoardo Paci, Lucia Methodology A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family are then considered as kernels of a finite mixture model with an unknown number of components. Conjugate Bayesian inference has been derived for the parameters of the Hamming distribution model. The mixture is framed in a Bayesian nonparametric setting, and a transdimensional blocked Gibbs sampler is developed to provide full Bayesian inference on the number of clusters, their structure, and the group-specific parameters, facilitating the computation with respect to customary reversible jump algorithms. The proposed model encompasses a parsimonious latent class model as a special case when the number of components is fixed. Model performances are assessed via a simulation study and reference datasets, showing improvements in clustering recovery over existing approaches. |
| title | Model-based clustering of categorical data based on the Hamming distance |
| topic | Methodology |
| url | https://arxiv.org/abs/2212.04746 |