Convex clustering and recovery of partially observed data
We propose a convex clustering and reconstruction algorithm for data with missing entries. The algorithm uses a similarity measure between every pair of points to cluster and recover the data. The cluster centres can be recovered reliably when the ground-truth similarity matrix is available. Moreover, the similarity matrix can also be reliably estimated from the partially observed data, when the clusters are well-separated and the coherence of the difference between points from different clusters is low. The algorithm performs well using the estimated similarity matrix on a simulated dataset. The method is also successful in reconstructing images from under-sampled Fourier data.