We present a novel clustering method, SON clustering, formulated as a convex optimization problem. The method is based on over-parameterization and uses a sum-of-norms regularization to control the trade-o between the model t and the number of clusters. Hence, the number of clusters can be automatically adapted to best describe the data, and need not to be specied a priori. We apply SON clustering to cluster the particles in a particle lter, an application where the number of clusters is often unknown and time varying, making SON clustering an attractive alternative. ABSTRACTWe present a novel clustering method, SON clustering, formulated as a convex optimization problem. The method is based on overparameterization and uses a sum-of-norms regularization to control the trade-off between the model fit and the number of clusters. Hence, the number of clusters can be automatically adapted to best describe the data, and need not to be specified a priori. We apply SON clustering to cluster the particles in a particle filter, an application where the number of clusters is often unknown and time varying, making SON clustering an attractive alternative.

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Sequential Monte Carlo (SMC) methods, such as the particle filter, are by now one of the standard computational techniques for addressing the filtering problem in general state-space models. However, many applications require post-processing of data offline. In such scenarios the smoothing problem-in which all the available data is used to compute state estimates-is of central interest. We consider the smoothing problem for a class of conditionally linear Gaussian models. We present a forward-backward-type Rao-Blackwellized particle smoother (RBPS) that is able to exploit the tractable substructure present in these models. Akin to the well known Rao-Blackwellized particle filter, the proposed RBPS marginalizes out a conditionally tractable subset of state variables, effectively making use of SMC only for the "intractable part" of the model. Compared to existing RBPS, two key features of the proposed method are: (i) it does not require structural approximations of the model, and (ii) the aforementioned marginalization is done both in the forward direction and in the backward direction.

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