Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Learning Mixtures of Gaussian Processes through Random Projection
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Clusters functional data from Gaussian process mixtures by projecting curves onto many one-dimensional random functions, fitting a univariate GMM to each projection, and combining the resulting base clusterings through weighted ensemble clustering.
Problem
Learning latent cluster labels and mixture parameters for functional data generated from a Gaussian process mixture, avoiding the cubic cost and local optima of EM-based GP mixture estimation.
Approach
Projection coefficients of GP-mixture functions onto any function follow a univariate GMM, so multiple random 1-D projections each yield a base clustering; these are aggregated via an overlap-weighted co-association ensemble, with theoretical guarantees on separation, identifiability and polynomial learnability.
Key results
- GPmix ranks in top three on the 12 simulated scenarios and is top performer in 6 of 12 (AMI and ARI).
- GPmix outperforms the other six algorithms on 8 of 10 real datasets in AMI/ARI.
- GPmix clusters each real dataset in under a second (e.g., SYM 551 ms vs 9803 ms for FEM).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GPmix instead of the strongest listed baseline | Functional-data clustering · ArrowHead | AMI: 0.25 -> 0.37 | Helped |
| Use GPmix instead of the strongest listed baseline | Functional-data clustering · CBF | AMI: 0.53 -> 0.84 | Helped |
| Use GPmix instead of the strongest listed baseline | Functional-data clustering · DiatomSizeReduction | AMI: 0.82 -> 0.94 | Helped |
| Use GPmix instead of the strongest listed baseline | Functional-data clustering · FaceFour | ARI: 0.54 -> 0.76 | Helped |
| Use GPmix instead of the strongest listed baseline | Functional-data clustering · Meat | AMI: 0.93 -> 0.70 | Hurt |
| Use GPmix instead of the strongest listed baseline | Functional-data clustering · Symbols | ARI: 0.80 -> 0.66 | Hurt |
| Use GPmix instead of the strongest listed baseline | Functional-data clustering · Functional-data clustering across real datasets | runtime: 551 milliseconds -> 1.2M | Helped |
Surprising findings
- On scenario J, where component GPs share the same mean function, all seven algorithms fail, consistent with the identifiability theory.
- The method remains effective on non-Gaussian functional data in the numerical study, despite the theory assuming GP components.
Limitations
- Theoretical guarantees rely on Gaussian process assumptions and well-separated components; identifiability fails when mean functions coincide (scenario J).
- Relies on smoothing of raw curves and on choosing projection functions and number of clusters via BIC/AIC or validation indices, with configuration tuned by grid search on ARI/AMI.
- Real-data comparisons use the best of ten runs per algorithm, which may favor the method.
Experimental setup
Datasets: 12 simulated GP mixture scenarios (A-L) 10 UEA & UCR time series datasets (ArrowHead, BirdChicken, CBF, DiatomSizeReduction, ECG200, FaceFour, GunPoint, Meat, S
Benchmarks: 12 simulated scenarios 10 UEA & UCR real datasets
Metrics: ARI AMI runtime (ms) absolute error in number of clusters
Baselines: FEM HDD clu FC KM ADP
Builds on: Gaussian process mixture models (Seitz 2021 prior pooling) random projection for high-dimensional GMMs (Dasgupta 1999) Moitra & Valiant 2010 polynomial learnability of GMMs Cuesta-Albertos et al. 2007 random projection theorem Maitra & Melnykov 2010 overlap measure
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