All-pole centroids in the Wasserstein metric with applications to clustering of spectral densities
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arXiv
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| Format: | Preprint |
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2026
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| author | Pallewela, Rumeshika Elvander, Filip |
| author_facet | Pallewela, Rumeshika Elvander, Filip |
| contents | In this work, we propose a method for computing centroids, or barycenters, in the spectral Wasserstein-2 metric for sets of power spectral densities, where the barycenters are restricted to belong to the set of all-pole spectra with a certain model order. This may be interpreted as finding an autoregressive representative for sets of second-order stationary Gaussian processes. While Wasserstein, or optimal transport, barycenters have been successfully used earlier in problems of spectral estimation and clustering, the resulting barycenters are non-parametric and the complexity of representing and storing them depends on, e.g., the choice of discretization grid. In contrast, the herein proposed method yields compact, low-dimensional, and interpretable spectral centroids that can be used in downstream tasks. Computing the all-pole centroids corresponds to solving a non-convex optimization problem in the model parameters, and we present a gradient descent scheme for addressing this. Although convergence to a globally optimal point cannot be guaranteed, the sub-optimality of the obtained centroids can be quantified. The proposed method is illustrated on a problem of phoneme classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14583 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | All-pole centroids in the Wasserstein metric with applications to clustering of spectral densities Pallewela, Rumeshika Elvander, Filip Signal Processing In this work, we propose a method for computing centroids, or barycenters, in the spectral Wasserstein-2 metric for sets of power spectral densities, where the barycenters are restricted to belong to the set of all-pole spectra with a certain model order. This may be interpreted as finding an autoregressive representative for sets of second-order stationary Gaussian processes. While Wasserstein, or optimal transport, barycenters have been successfully used earlier in problems of spectral estimation and clustering, the resulting barycenters are non-parametric and the complexity of representing and storing them depends on, e.g., the choice of discretization grid. In contrast, the herein proposed method yields compact, low-dimensional, and interpretable spectral centroids that can be used in downstream tasks. Computing the all-pole centroids corresponds to solving a non-convex optimization problem in the model parameters, and we present a gradient descent scheme for addressing this. Although convergence to a globally optimal point cannot be guaranteed, the sub-optimality of the obtained centroids can be quantified. The proposed method is illustrated on a problem of phoneme classification. |
| title | All-pole centroids in the Wasserstein metric with applications to clustering of spectral densities |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2602.14583 |