约束聚类是指在特定约束条件下的聚类问题，是当前机器学习特别是聚类研究的热点之一。约束聚类中，如何有效地将已知约束条件和聚类相结合构造恰当的模型及算法是研究的重点和难点。根据项目组近期对聚类问题研究的成果，本项目拟通过引入损失度量，将损失函数与已知约束有机地结合来研究约束聚类问题。考虑到约束形式的多样性，本项目将分别从特征级约束、样本级约束和类别级约束对约束聚类进行研究。通过构建这三类约束在聚类中的损失函数，分别提出对应三种约束的聚类模型和混合约束下的聚类模型，并研究相应的理论基础和求解算法，其中特别注重研究具有离散性质的特征、样本和类别约束与类内极大化相似性且类间极小化相似性所构成的混合整数优化模型与算法。最后，我们将上述模型及算法应用于文本聚类问题中，并通过文本聚类的实际需求检验和提高约束聚类模型及算法。本项目探索约束聚类问题中的损失度量、约束优化模型及算法，为约束聚类提供了新的思路。

Constrained clustering is a clustering problem under specific constraints. It is one of the hotspots in machine learning, especially clustering. How to effectively combine the known constraints and clustering to construct the appropriate model and algorithm in constrained clustering is the focus and difficulty of the research. On the basis of our recent researches on clustering, this project intends to introduce the concept of loss measure and combine loss function with known constraints to study constrained clustering. Considering the diversity of constraints, this project will study constrained clustering from feature level constraints, sample level constraints and category level constraints. By constructing the loss function of these three kinds of constraints in clustering, the clustering model corresponding to three kinds of constraints and it under mixed constraints are proposed respectively. The corresponding theory and algorithm are studied. Particular attention is paid to the mixed integer optimization composed of discrete features, sample and category constraints, intra-class maximization similarity and inter-class minimization similarity. Finally, we apply the above models and algorithms to the text clustering problem, and improve them by testing the actual needs of text clustering. This project explores loss measurement, constrained optimization model and algorithm in constrained clustering problem, and provides a new idea for constrained clustering.