DIFFRAC swMATH ID: 23902 Software Authors: F. Bach; Z. Harchaoui Description: F. Bach and Z. Harchaoui. DIFFRAC : a discriminative and flexible framework for clustering. We present a novel linear clustering framework (DIFFRAC) which relies on a lin- ear discriminative cost function and a convex relaxation of a combinatorial op- timization problem. The large convex optimization problem is solved through a sequence of lower dimensional singular value decompositions. This framework has several attractive properties: (1) although apparently similar to K-means, it exhibits superior clustering performance than K-means, in particular in terms of robustness to noise. (2) It can be readily extended to non linear clustering if the discriminative cost function is based on positive definite kernels, and can then be seen as an alternative to spectral clustering. (3) Prior information on the partition is easily incorporated, leading to state-of-the-art performance for semi-supervised learning, for clustering or classification. We present empirical evaluations of our algorithms on synthetic and real medium-scale datasets Homepage: https://www.di.ens.fr/~fbach/diffrac_nips.pdf Related Software: SciPy; MixMatch; MBCbook; t-SNE; PyTorch; CIFAR; Megaman; Python; LIBSVM; PRMLT; Manopt; k-means++; ImageNet; FastICA; CVX; AR face Cited in: 5 Publications all top 5 Cited by 13 Authors 2 Sugiyama, Masashi 1 Bach, Francis R. 1 Chen, Jie 1 Flammarion, Nicolas 1 Hachiya, Hirotaka 1 Harchaoui, Zaid 1 Jones, Corinne 1 Kimura, Manabu 1 Niu, Gang 1 Palaniappan, Balamurugan 1 Roulet, Vincent 1 Saad, Yousef 1 Yamada, Makoto Cited in 5 Serials 1 Neural Computation 1 Numerical Linear Algebra with Applications 1 Entropy 1 Journal of Machine Learning Research (JMLR) 1 Statistics and Computing Cited in 4 Fields 4 Statistics (62-XX) 2 Computer science (68-XX) 1 Numerical analysis (65-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year