Neural Information Processing Systems http://nips.cc/

Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced k -cut of the graph, are either based on greedy techniques or heuristics which have weak connection to the original motivation of minimizing the normalized cut. In this paper we propose a new tight continuous relaxation for any balanced k -cut problem and show that a related recently proposed relaxation is in most cases loose leading to poor performance in practice. For the optimization of our tight continuous relaxation we propose a new algorithm for the difficult sum-of-ratios minimization problem which achieves monotonic descent. Extensive comparisons show that our method outperforms all existing approaches for ratio cut and other balanced k -cut criteria.

Appendix to "Auxiliary T ask Reweighting for Minimum-data Learning" S is the optimal parameter. Concretely, with Jensen's inequality, we have Z ( S; α) is small). See the remark below for more discussion on the validity of the assumption. In Section 2.4, we propose a two-stage algorithm, where we update the task weights with Langevin This simplified version is summarized in Algorithm 1. For all results, we repeat experiments for three times and report the average performance.

Such pairwise comparison data is easy to collect, as typically discussed in the learning-to-rank scenario, and does not break the anonymity of data.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors present a novel non-parametric Bayesian model for unsupervised clustering. The model uses a two level hierarchy of Dirichlet process priors to handle clusters which may be multi-modal, skewed and/or heavy tailed. The authors present a collapsed Gibbs sampler for inference which exploits the conjugacy of the model. The authors do an excellent job of motivating the model by explaining the deficiencies of the standard infinite mixture of Gaussians.

In many modern applications from, for example, bioinformatics and computer vision, samples have multiple feature representations coming from different data sources. Multiview learning algorithms try to exploit all these available information to obtain a better learner in such scenarios. In this paper, we propose a novel multiple kernel learning algorithm that extends kernel k -means clustering to the multiview setting, which combines kernels calculated on the views in a localized way to better capture sample-specific characteristics of the data. We demonstrate the better performance of our localized data fusion approach on a human colon and rectal cancer data set by clustering patients. Our method finds more relevant prognostic patient groups than global data fusion methods when we evaluate the results with respect to three commonly used clinical biomarkers.