Sparse Regularization in Fuzzy $c$ -Means for High-Dimensional Data Clustering
针对高维数据聚类中特征选择困难的问题，提出一种带稀疏正则化的模糊c均值模型，通过将目标函数改写为加权组间平方和形式并对权重施加ℓq范数惩罚，使无关特征权重归零，在合成和真实数据集上表现优于现有方法。
In high-dimensional data clustering practices, the cluster structure is commonly assumed to be confined to a limited number of relevant features, rather than the entire feature set. However, for high-dimensional data, identifying the relevant features and discovering the cluster structure are still challenging problems. To solve these problems, this paper proposes a novel fuzzy c-means (FCM) model with sparse regularization (ℓq(0<q≤1)-norm regularization), by reformulating the FCM objective function into the weighted between-cluster sum of square form and imposing the sparse regularization on the weights. An algorithm is also developed to explicitly solve the proposed model. Compared with the existing clustering models, the proposed model can shrink the weights of irrelevant features (noisy features) to exact zero, and also can be efficiently solved in analytic forms when q = 1,1/2. Experiments on both synthetic and real-world data sets show that the proposed approach outperforms the existing clustering approaches.