# Individual-heterogeneous sub-Gaussian Mixture Models Source: [Individual-heterogeneous sub-Gaussian Mixture Models]() Collection index: [llms.txt]() Data updated: 2026-04-09T05:00:04.534Z Authors: Huan Qing Published: 2026-04-07T02:22:51.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Classification on Iris (Misclassification Count)](): Classification; Iris; Misclassification Count: 7. - [Classification on DNA](): Classification; DNA; Misclassification Count: 353. - [Handwritten Digit Classification on USPS (train)](): Handwritten digit classification; usps (train); Error Count: 2027. - [Handwritten Digit Classification on pendigits (train)](): Handwritten digit classification; pendigits (train); Misclassification Rate: 0.25647184414198027. - [Image Segment Classification on segment](): Image Segment Classification; segment; Misclassification Count: 735. - [Satellite Image Classification on satimage (train)](): Satellite Image Classification; satimage (train); Misclassification Count: 1381. - [Classification on Wine (Misclassification Count)](): Classification; Wine; Misclassification Count: 9. - [Classification on Seeds (Misclassification Count)](): Classification; SEEDS; Misclassification Count: 20. ## Original sources and implementation [Original paper]() [PDF]()