Fast Clustering via Anchor Label Alignment and Transition Probabilities

Anchor-based clustering techniques have gained considerable attention for their efficiency and ability to capture representative information. However, traditional methods often suffer from separate stages of spectral feature extraction and discretization, leading to critical information loss and reduced clustering performance. Additionally, most existing models require tuning of hyperparameters introduced by various regularization terms, limiting their practicality. To address these issues, we propose a novel method that aligns anchor-to-anchor transition probabilities via the correlation of anchor labels, and implicitly incorporates objectives of maximizing intra-cluster similarity and balanced clustering, called FC-ALATP. The regularization parameter does not require manual tuning, which be updated in closed form. Moreover, the optimization stage scales linearly with the number of anchors; specifically, two solvers, projected gradient descent (PGD) and fast coordinate descent (fast CD), are developed. Extensive experiments demonstrate that fast CD out-performs PGD, and FC-ALATP achieves superior performance over other anchor-based models with less time cost.