Lihi Zelnik-manor, Pietro Perona
We study a number of open issues in spectral clustering: (i) Selecting the appropriate scale of analysis, (ii) Handling multi-scale data, (iii) Cluster- ing with irregular background clutter, and, (iv) Finding automatically the number of groups. We ﬁrst propose that a ‘local’ scale should be used to compute the afﬁnity between each pair of points. This local scaling leads to better clustering especially when the data includes multiple scales and when the clusters are placed within a cluttered background. We further suggest exploiting the structure of the eigenvectors to infer automatically the number of groups. This leads to a new algorithm in which the ﬁnal randomly initialized k-means stage is eliminated.