## Convex clustering for binary data.(English)Zbl 1459.62109

Summary: We present a new clustering algorithm for multivariate binary data. The new algorithm is based on the convex relaxation of hierarchical clustering, which is achieved by considering the binomial likelihood as a natural distribution for binary data and by formulating convex clustering using a pairwise penalty on prototypes of clusters. Under convex clustering, we show that the typical $$\ell_1$$ pairwise fused penalty results in ineffective cluster formation. In an attempt to promote the clustering performance and select the relevant clustering variables, we propose the penalized maximum likelihood estimation with an $$\ell_2$$ fused penalty on the fusion parameters and an $$\ell_1$$ penalty on the loading matrix. We provide an efficient algorithm to solve the optimization by using majorization-minimization algorithm and alternative direction method of multipliers. Numerical studies confirmed its good performance and real data analysis demonstrates the practical usefulness of the proposed method.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects)

UCI-ml; sparcl
Full Text:

### References:

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