Non-negative matrix factorization (NMF) is an effective model in converting data into non-negative coefficient representation whose discriminative ability is usually enhanced to be used for diverse pattern recognition tasks. In NMF-based clustering, we often need to perform K-means on the learned coefficient as postprocessing step to get the final cluster assignments. This breaks the connection between the feature learning and recognition stages. In this paper, we propose to learn the non-negative coefficient matrix based on which we jointly perform fuzzy clustering, by viewing that each column of the dictionary matrix as a concept of each cluster. As a result, we formulate a new fuzzy clustering model, termed Joint Non-negative and Fuzzy Coding with Graph regularization (G-JNFC), and design an effective optimization method to solve it under the alternating direction optimization framework. Besides the convergence and computational complexity analysis on G-JNFC, we conduct extensive experiments on both synthetic and representative benchmark data sets. The results show that the proposed G-JNFC model is effective in data clustering.

非负矩阵分解（NMF）是将数据转换为非负系数表示形式的有效模型，其判别能力通常得到增强，可用于各种模式识别任务。在基于NMF的群集中，我们经常需要执行K-表示将学习到的系数作为后处理步骤以获取最终的聚类分配。这打破了特征学习和识别阶段之间的联系。在本文中，我们建议通过将字典矩阵的每一列视为每个聚类的概念来学习我们共同执行模糊聚类的非负系数矩阵。结果，我们建立了一个新的模糊聚类模型，称为图正则化联合非负和模糊编码（G-JNFC），并设计了一种有效的优化方法，以在交替方向优化框架下对其进行求解。除了对G-JNFC进行收敛和计算复杂度分析外，我们还在合成基准数据集和代表性基准数据集上进行了广泛的实验。