2018/02/20 by Yancheng Yuan, Defeng Sun, Yuan, Yancheng +3 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Algorithm #Artificial intelligence #Canopy clustering algorithm #Cluster analysis #Computer science #Correlation clustering #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine learning #Mathematical optimization #Mathematics #Maxima and minima #Optimization and Control (math.OC) #Optimization and Variational Analysis #Regular polygon #Relaxation (psychology) #Scalability #Scale (ratio) #Sparse and Compressive Sensing Techniques #Stability (learning theory) #cs.LG #math.OC
paper · pdf · doi:10.48550/arxiv.1802.07091
published in arXiv (Cornell University) (Cornell University)
arxiv created 2018/02/20 · openalex publication_date 2018/02/20 · arxiv updated 2018/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as clustering path), which is a convex relaxation of hierarchical clustering model, has been proposed in [7] and [5] Although numerical algorithms like ADMM and AMA are proposed to solve convex clustering model [2], it is known to be very challenging to solve large-scale problems. In this paper, we propose a semi-smooth Newton based augmented Lagrangian method for large-scale convex clustering problems. Extensive numerical experiments on both simulated and real data demonstrate that our algorithm is highly efficient and robust for solving large-scale problems. Moreover, the numerical results also show the superior performance and scalability of our algorithm compared to existing first-order methods.