## Electronic Journal of Statistics

### Statistical properties of convex clustering

#### Abstract

In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and $k$-means clustering. In addition, we derive the range of the tuning parameter for convex clustering that yields a non-trivial solution. We also provide an unbiased estimator of the degrees of freedom, and provide a finite sample bound for the prediction error for convex clustering. We compare convex clustering to some traditional clustering methods in simulation studies.

#### Article information

Source
Electron. J. Statist., Volume 9, Number 2 (2015), 2324-2347.

Dates
First available in Project Euclid: 14 October 2015

https://projecteuclid.org/euclid.ejs/1444828331

Digital Object Identifier
doi:10.1214/15-EJS1074

Mathematical Reviews number (MathSciNet)
MR3411231

Zentralblatt MATH identifier
1336.62193

#### Citation

Tan, Kean Ming; Witten, Daniela. Statistical properties of convex clustering. Electron. J. Statist. 9 (2015), no. 2, 2324--2347. doi:10.1214/15-EJS1074. https://projecteuclid.org/euclid.ejs/1444828331

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