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It is well known that, in the presence of outliers, the single linkage algorithm generally fails to identify clusters. In this paper, we construct a new version of this algorithm, less sensitive to outliers, and study both its theoretical properties and its practical behavior. In particular, we provide an oracle-type inequality which guarantees that our procedure recovers clusters with high probability under mild assumptions on the distribution of the outliers. Using this inequality, we prove the consistency of our method and exhibit rates of convergence in various situations. The performance of this approach is also assessed through simulation studies. A thorough comparison with several classical clustering algorithms on simulated data is presented. [ABSTRACT FROM AUTHOR]

• We present the SSLE approach for Bayesian model inversion based on SSE and SLE. • Posterior quantities are obtained analytically from the SSLE coefficients. • The original SSE algorithm is enhanced with an active learning enrichment scheme. • This method generalizes and drastically improves the efficiency of the SLE approach. • We showcase the method on three problems of different complexity and dimensionality. In this paper we propose a new sampling-free approach to solve Bayesian model inversion problems that is an extension of the previously proposed spectral likelihood expansions (SLE) method. Our approach, called stochastic spectral likelihood embedding (SSLE), uses the recently presented stochastic spectral embedding (SSE) method for local spectral expansion refinement to approximate the likelihood function at the core of Bayesian inversion problems. We show that, similar to SLE, this approach results in analytical expressions for key statistics of the Bayesian posterior distribution, such as evidence, posterior moments and posterior marginals , by direct post-processing of the expansion coefficients. Because SSLE and SSE rely on the direct approximation of the likelihood function, they are in a way independent of the computational/mathematical complexity of the forward model. We further enhance the efficiency of SSLE by introducing a likelihood specific adaptive sample enrichment scheme. To showcase the performance of the proposed SSLE, we solve three problems that exhibit different kinds of complexity in the likelihood function: multimodality, high posterior concentration and high nominal dimensionality. We demonstrate how SSLE significantly improves on SLE, and present it as a promising alternative to existing inversion frameworks. [ABSTRACT FROM AUTHOR]