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This paper introduces the individual-heterogeneous sub-Gaussian mixture model (IHSGMM), which extends traditional GMMs by assigning each data point its own heterogeneity parameter to account for varying scales within clusters. They propose a spectral method for clustering under the IHSGMM, providing theoretical guarantees of exact cluster recovery even in high-dimensional regimes. Experiments on synthetic and real-world data show the proposed method outperforms standard GMM clustering algorithms.
Overcome the limitations of Gaussian Mixture Models by modeling individual data point heterogeneity, leading to more accurate clustering in real-world scenarios.
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.