Fuzzy c-Means Clustering with Discriminative Projection

The clustering technique plays an important role in data mining and machine learning fields. Clustering for high-dimensional data, such as texts, images, and videos, remains a challenging task due to the existence of many noise features. The widely used methods for this issue focus on mining a effective pattern in high-dimensional data using some dimensionality reduction techniques before clustering. This strategy slightly mitigates the effects of irrelevant and redundant features, but cannot significantly improve the clustering performance because the captured pattern by dimensionality reduction is not directly related to the clustering task. In this paper, we propose a unified framework to achieve discriminative dimensionality reduction and fuzzy clustering for high-dimensional data simultaneously. The proposed framework not only utilizes the clustering results to directly guide or supervise the process of discriminative dimensionality reduction, but also controls the clustering fuzziness more easily by a $F$ -norm regularization term. An efficient optimization algorithm is exploited to address the objective function of our method, which is proved to converge to the local optimal solution in theory. We evaluate the proposed method on three large-scale fine-grained image datasets, including Birds, Flowers, and Cars, for clustering and retrieval two tasks. The experimental results on metrics ACC, NMI, ARI and Recall@K indicate that our method achieves the comparable performance over the state-of-the-art methods.