This paper focuses on density-based clustering, particularly the Density Peak (DP) algorithm and the one based on density-connectivity DBSCAN; and proposes a new method which takes advantage of the individual strengths of these two methods to yield a density-based hierarchical clustering algorithm. Our investigation begins with formally defining the types of clusters DP and DBSCAN are designed to detect; and then identifies the kinds of distributions that DP and DBSCAN individually fail to detect all clusters in a dataset. These identified weaknesses inspire us to formally define a new kind of clusters and propose a new method called DC-HDP to overcome these weaknesses to identify clusters with arbitrary shapes and varied densities. In addition, the new method produces a richer clustering result in terms of hierarchy or dendrogram for better cluster structures understanding. Our empirical evaluation results show that DC-HDP produces the best clustering results on 14 datasets in comparison with 7 state-of-the-art clustering algorithms.

The questions in a crowdsourcing task typically exhibit varying degrees of difficulty and subjectivity. Their joint effects give rise to the variation in responses to the same question by different crowd-workers. This variation is low when the question is easy to answer and objective, and high when it is difficult and subjective. Unfortunately, current quality control methods for crowdsourcing consider only the question difficulty to account for the variation. As a result,these methods cannot distinguish workers personal preferences for different correct answers of a partially subjective question from their ability/expertise to avoid objectively wrong answers for that question. To address this issue, we present a probabilistic model which (i) explicitly encodes question difficulty as a model parameter and (ii) implicitly encodes question subjectivity via latent preference factors for crowd-workers. We show that question subjectivity induces grouping of crowd-workers, revealed through clustering of their latent preferences. Moreover, we develop a quantitative measure of the subjectivity of a question. Experiments show that our model(1) improves the performance of both quality control for crowd-sourced answers and next answer prediction for crowd-workers,and (2) can potentially provide coherent rankings of questions in terms of their difficulty and subjectivity, so that task providers can refine their designs of the crowdsourcing tasks, e.g. by removing highly subjective questions or inappropriately difficult questions.