We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X1,...,Xn. We perform exact clustering with high probability using a convex semidefinite estimator that interprets as a corrected, relaxed version of K-means. The estimator is analyzed through a non-asymptotic framework and showed to be optimal or near-optimal in recovering the partition. Furthermore, its performances are shown to be adaptive to the problem's effective dimension, as well as to K the unknown number of groups in this partition. We illustrate the method's performances in comparison to other classical clustering algorithms with numerical experiments on simulated high-dimensional data.

We illustrate the method's performances in comparison

The paper proposes a semidefinite relaxation for K-means clustering with isotropic and non-isotropic mixtures of sub-gaussian distributions in both high and low-dimensions. The paper has a good technical analysis of the methods proposed in it. There are some supporting empirical experiments too. However, one thing would have been useful to see was how computation time scales with both p and n. The empirical experiments considered n 30, which is pretty small for many application situations.

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

Open relation extraction is the task of extracting open-domain relation facts from natural language sentences. Existing works either utilize heuristics or distant-supervised annotations to train a supervised classifier over pre-defined relations, or adopt unsupervised methods with additional assumptions that have less discriminative power. In this work, we proposed a self-supervised framework named SelfORE, which exploits weak, self-supervised signals by leveraging large pretrained language model for adaptive clustering on contextualized relational features, and bootstraps the self-supervised signals by improving contextualized features in relation classification. Experimental results on three datasets show the effectiveness and robustness of SelfORE on open-domain Relation Extraction when comparing with competitive baselines. Source code is available at https://github.com/THU-BPM/SelfORE.

We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X1,...,Xn. We perform exact clustering with high probability using a convex semidefinite estimator that interprets as a corrected, relaxed version of K-means. The estimator is analyzed through a non-asymptotic framework and showed to be optimal or near-optimal in recovering the partition. Furthermore, its performances are shown to be adaptive to the problem's effective dimension, as well as to K the unknown number of groups in this partition. We illustrate the method's performances in comparison to other classical clustering algorithms with numerical experiments on simulated high-dimensional data.

We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X1,...,Xn. We perform exact clustering with high probability using a convex semidefinite estimator that interprets as a corrected, relaxed version of K-means. The estimator is analyzed through a non-asymptotic framework and showed to be optimal or near-optimal in recovering the partition. Furthermore, its performances are shown to be adaptive to the problem’s effective dimension, as well as to K the unknown number of groups in this partition. We illustrate the method’s performances in comparison to other classical clustering algorithms with numerical experiments on simulated high-dimensional data.