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Subset Simulation is a Markov chain Monte Carlo method used to compute small failure probabilities in structural reliability problems. This is done by iteratively sampling from nested subsets in the input space of a performance function, i.e. a function describing the behaviour of a physical system. When the performance function has features such as multimodality or rapidly changing output, it is not uncommon for Subset Simulation to suffer from ergodicity problems. To address these problems, this paper proposes a new framework that enhances Subset Simulation with niching, a concept from the field of evolutionary multimodal optimisation. Niching subset simulation dynamically partitions the input space using support vector machines, and recursively begins anew in each set of the partition. A new niching technique, which uses community detection methods and is specifically designed for high-dimensional problems, is also introduced. It is shown that Niching Subset Simulation is robust against ergodicty problems and can also offer additional insight into the topology of challenging reliability problems.