Adaptive Neighbors Graph Learning for Large-Scale Data Clustering using Vector Quantization and Self-Regularization

Abstract

In traditional adaptive neighbors graph learning (ANGL)-based clustering, the time complexity is more than $O\left(n^2\right)$, where $n$ is the number of data points, which is not scalable for large-scale data problems in real applications. Subsequently, ANGL adds a balance regularization to its objective function to avoid the sparse over-fitting problem in the learned similarity graph matrix. Still, the regularization may leads to many weak connections between data points in different clusters. To address these problems, we propose a new fast clustering method, namely, Adaptive Neighbors Graph Learning for Large-Scale Data Clustering using Vector Quantization and Self-Regularization (ANGL-LDC), to perform vector quantization (VQ) on original data and feed the obtained VQ data as the input in the $n\times n$ similarity graph matrix learning. Hence, the $n\times n$ similarity graph matrix learning problem is simplified to weighted $m\times m$ $(m\ll n)$ graph learning problem, where $m$ is the number of distinct points and weight is the duplicate times of distinct points in VQ data. Consequently, the time complexity of ANGL-LDC is much lower than that of ANGL. At the same time, we propose a new ANGL objective function with a graph connection self-regularization mechanism, where the ANGL-LDC objective function will get an infinity value if the value of one graph connection is equal to 1. Therefore, ANGL-LDC naturally avoids obtaining the sparse over-fitting problem since we need to minimize the value of ANGL-LDC’s objective function. Experimental results on synthetic and real-world datasets demonstrate the scalability and effectiveness of ANGL-LDC.