Individual-heterogeneous sub-Gaussian Mixture Models
This addresses clustering challenges in real-world data where homogeneity assumptions fail, though it appears incremental as it builds on mixture models with added flexibility.
The paper tackled the problem of clustering data with varying scales or intensities by introducing an individual-heterogeneous sub-Gaussian mixture model, and it achieved exact recovery of cluster labels under mild conditions, outperforming existing algorithms in experiments.
The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the individual-heterogeneous sub-Gaussian mixture model, a flexible framework that assigns each observation its own heterogeneity parameter, thereby explicitly capturing the heterogeneity inherent in practical applications. Built upon this model, we propose an efficient spectral method that provably achieves exact recovery of the true cluster labels under mild separation conditions, even in high-dimensional settings where the number of features far exceeds the number of samples. Numerical experiments on both synthetic and real data demonstrate that our method consistently outperforms existing clustering algorithms, including those designed for classical Gaussian mixture models.