$k$-means: Fighting against Degeneracy in Sequential Monte Carlo with an Application to Tracking
This addresses a practical issue in particle filtering for tracking applications, but it is incremental as it builds on existing SMC methods.
The paper tackles degeneracy in Sequential Monte Carlo (SMC) methods, where particles collapse onto a single one, by proposing a Stochastic SMC algorithm that uses k-means clustering to initialize centers from collapsed particles and adjust weights, resulting in better performance than vanilla algorithms.
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.