Lauri Heinonen’s research while affiliated with University of Turku and other places

This work discusses weighted kernel point projection (WKPP), a new method for embedding metric space or kernel data. WKPP is based on an iteratively weighted generalization of multidimensional scaling and kernel principal component analysis, and one of its main uses is outlier detection. After a detailed derivation of the method and its algorithm, we give theoretical guarantees regarding its convergence and outlier detection capabilities. Additionally, as one of our mathematical contributions, we give a novel characterization of kernelizability, connecting it also to the classical kernel literature. In our empirical examples, WKPP is benchmarked with respect to several competing outlier detection methods, using various different datasets. The obtained results show that WKPP is computationally fast, while simultaneously achieving performance comparable to state-of-the-art methods.

This work presents sparse invariant coordinate analysis, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate analysis, which is presented in such a form that a LASSO-type penalty can be applied to promote sparsity. Robustness is achieved by using robust scatter matrices. In the first part of the paper, the background and building blocks: scatter matrices, measures of robustness, ICS and independent component analysis, are carefully introduced. Then the proposed new method and its algorithm are derived and presented. This part also includes a consistency result for a general case of sparse ICS-like methods. The performance of SICS in identifying sparse independent component loadings is investigated with simulations. The method is also illustrated with example in constructing sparse causal graphs.