A novel semi-supervised clustering algorithm based on ridge regression with optimal scaling

Ridge regression has broad applicability in machine learning owing to its elegant closed-form solution. However, its extension to semi-supervised clustering faces challenges, involving the reconciliation of constrained continuous and discrete matrices, and the avoidance of trivial solutions, even under uncorrelated constraints. To this end, we propose an optimal scaling strategy for the indicator matrix, which is able to dynamically bridge the scale discrepancy between the input and the output, preserving the integrity of the discrete solutions without relaxed approximation, and preventing the trivial solutions that arise from the binary indicator matrix. Furthermore, an advanced coordinate descent technique is employed to directly obtain discrete solutions in one step while remaining seamlessly compatible with the label information. Extensive experiments on two synthetic datasets and twelve public datasets demonstrate the preeminence of our proposed model.