The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase transition at the Kesten-Stigum threshold is particularly interesting both from a mathematical and an applied standpoint. It states that no estimator based on the network topology can perform substantially better than chance on sparse graphs if the model parameter is below certain threshold. Nevertheless, if we slightly extend the horizon to the ubiquitous semi-supervised setting, such a fundamental limitation will disappear completely. We prove that with arbitrary fraction of the labels revealed, the detection problem is feasible throughout the parameter domain. Moreover, we introduce two efficient algorithms, one combinatorial and one based on optimization, to integrate label information with graph structures. Our work brings a new perspective to stochastic model of networks and semidefinite program research.

Learning distance functions with side information plays a key role in many machine learning and data mining applications. Conventional approaches often assume a Mahalanobis distance function. These approaches are limited in two aspects: (i) they are computationally expensive (even infeasible) for high dimensional data because the size of the metric is in the square of dimensionality; (ii) they assume a fixed metric for the entire input space and therefore are unable to handle heterogeneous data. In this paper, we propose a novel scheme that learns nonlinear Bregman distance functions from side information using a non-parametric approach that is similar to support vector machines. The proposed scheme avoids the assumption of fixed metric because its local distance metric is implicitly derived from the Hessian matrix of a convex function that is used to generate the Bregman distance function.

Clustering is a well-known unsupervised machine learning approach capable of automatically grouping discrete sets of instances with similar characteristics. Constrained clustering is a semi-supervised extension to this process that can be used when expert knowledge is available to indicate constraints that can be exploited. Well-known examples of such constraints are must-link (indicating that two instances belong to the same group) and cannot-link (two instances definitely do not belong together). The research area of constrained clustering has grown significantly over the years with a large variety of new algorithms and more advanced types of constraints being proposed. However, no unifying overview is available to easily understand the wide variety of available methods, constraints and benchmarks. To remedy this, this study presents in-detail the background of constrained clustering and provides a novel ranked taxonomy of the types of constraints that can be used in constrained clustering. In addition, it focuses on the instance-level pairwise constraints, and gives an overview of its applications and its historical context. Finally, it presents a statistical analysis covering 307 constrained clustering methods, categorizes them according to their features, and provides a ranking score indicating which methods have the most potential based on their popularity and validation quality. Finally, based upon this analysis, potential pitfalls and future research directions are provided.

Most dialogue systems in real world rely on predefined intents and answers for QA service, so discovering potential intents from large corpus previously is really important for building such dialogue services. Considering that most scenarios have few intents known already and most intents waiting to be discovered, we focus on semi-supervised text clustering and try to make the proposed method benefit from labeled samples for better overall clustering performance. In this paper, we propose Deep Contrastive Semi-supervised Clustering (DCSC), which aims to cluster text samples in a semi-supervised way and provide grouped intents to operation staff. To make DCSC fully utilize the limited known intents, we propose a two-stage training procedure for DCSC, in which DCSC will be trained on both labeled samples and unlabeled samples, and achieve better text representation and clustering performance. We conduct experiments on two public datasets to compare our model with several popular methods, and the results show DCSC achieve best performance across all datasets and circumstances, indicating the effect of the improvements in our work.

Learning distance functions with side information plays a key role in many machine learning and data mining applications. Conventional approaches often assume a Mahalanobis distance function. These approaches are limited in two aspects: (i) they are computationally expensive (even infeasible) for high dimensional data because the size of the metric is in the square of dimensionality; (ii) they assume a fixed metric for the entire input space and therefore are unable to handle heterogeneous data. In this paper, we propose a novel scheme that learns nonlinear Bregman distance functions from side information using a non-parametric approach that is similar to support vector machines. The proposed scheme avoids the assumption of fixed metric because its local distance metric is implicitly derived from the Hessian matrix of a convex function that is used to generate the Bregman distance function.

Many research studies on distance metric learning (DML) reiterate that the definition of distance between two data points substantially affects clustering tasks. Recently, variety of DML methods have been proposed to improve the accuracy of clustering by learning a distance metric; however, most of them only perform a linear transformation, which yields insignificant to non-linear separable data. This study proposes a DML method which provides an integration of kernelization technique with Mahalanobis-based DML. Thus, non-linear transformation of the distance metric can be performed. Moreover, a cluster validity index is optimized by an evolutionary algorithm. The empirical results on semi-supervised clustering suggest the promising result on both synthetic and real-world data set.