Projected Fuzzy C-Means Clustering Algorithm with Instance Penalty

At present, high-dimensional data clustering has become a vital research field in machine learning. Traditional clustering algorithms cannot perform well on high-dimensional data, where the clustering task is usually divided into two stages: dimensionality reduction first and clustering later. In general, the existing high-dimensional clustering methods usually have the following shortcomings: (1) the two-stage strategy splits the connection between clustering and dimensionality reduction; (2) these algorithms do not consider the impact of anomalous instances in high-dimensional data on clustering performance. Therefore, to address these problems, a projected fuzzy c-means clustering algorithm with instance penalty (PCIP) is proposed. Firstly, we construct an instance penalty matrix and assign an instance penalty coefficient to each sample. Secondly, a model for clustering high-dimensional data is constructed by integrating fuzzy c-means clustering (FCM) and principal component analysis (PCA). The proposed model can perform dimensionality reduction and clustering simultaneously. In addition, the time complexity of the proposed algorithm is linearly related to the number of samples n, which can efficiently deal with large data sets. Finally, extensive experiments demonstrate the effectiveness of the proposed algorithm.