G. Ferrari-Trecate and M. Muselli. Single-linkage clustering for optimal classification in piecewise affine regression. IFAC Conference on the Analysis and Design of Hybrid Systems (ADHS 03) , 2003. St. Malo, France, 16-18 June.
When performing regression with piecewise affine maps, the mostchallenging task is to classify the data points, i.e. to correctlyattribute a data point to the affine submodel that most likelygenerated it. In this paper, we consider a regression schemesimilar to the one proposed in (Ferrari-Trecate et al., 2001,2003) that reducesthe classification step to a clustering problem in presence ofoutliers. However, instead of the K-means procedure adoptedin (Ferrari-Trecate et al., 2001,2003), we propose the use of single-linkageclustering that estimates automatically the number of submodelscomposing the piecewise affine map.Moreover we prove that, under mild assumptions on the data set,single-linkage clustering can guarantee optimal classification inpresence of bounded noise.