Sparse Membership Affinity Lasso for Fuzzy Clustering

The membership matrix is a key element in fuzzy clustering, enabling novel data representation in multiple clusters. The row vectors of the membership matrix represent each sample's degree of membership to different clusters. Notably, researchers have confirmed the presence of the local affinity among these row vectors, effectively preserving the local structure of the original data distribution. However, in this work, we consider that most sample points have insignificant fuzziness, with fuzziness found primarily in a few clusters, resulting in most membership vectors being sparse. To tackle this issue, we present the sparse, membership-affinity fuzzy clustering model, which leverages the sparsity of the row vectors and its affinity to establish a more appropriate representation, along with an optimization algorithm. Our experimental results on both simulated and real datasets demonstrate that the combination of sparsity and affinity can significantly enhance fuzzy clustering performance over other models.