  For regular particle filter algorithm or Sequential Monte Carlo (SMC)
methods, the initial weights are traditionally dependent on the proposed
distribution, the posterior distribution at the current timestamp in the
sampled sequence, and the target is the posterior distribution of the previous
timestamp. This is technically correct, but leads to algorithms which usually
have practical issues with degeneracy, where all particles eventually collapse
onto a single particle. In this paper, we propose and evaluate using $k$ means
clustering to attack and even take advantage of this degeneracy. Specifically,
we propose a Stochastic SMC algorithm which initializes the set of $k$ means,
providing the initial centers chosen from the collapsed particles. To fight
against degeneracy, we adjust the regular SMC weights, mediated by cluster
proportions, and then correct them to retain the same expectation as before. We
experimentally demonstrate that our approach has better performance than
vanilla algorithms.
