A Flexible Outlier Detector Based on a Topology Given by Graph Communities

Acord transformatiu CRUE-CSICOutlier detection is essential for optimal performance of machine learning methods and statistical predictive models. Their detection is especially determinant in small sample size unbalanced problems, since in such settings outliers become highly influential and significantly bias models. This particular experimental settings are usual in medical applications, like diagnosis of rare pathologies, outcome of experimental personalized treatments or pandemic emergencies. In contrast to population-based methods, neighborhood based local approaches compute an outlier score from the neighbors of each sample, are simple flexible methods that have the potential to perform well in small sample size unbalanced problems. A main concern of local approaches is the impact that the computation of each sample neighborhood has on the method performance. Most approaches use a distance in the feature space to define a single neighborhood that requires careful selection of several parameters, like the number of neighbors. This work presents a local approach based on a local measure of the heterogeneity of sample labels in the feature space considered as a topological manifold. Topology is computed using the communities of a weighted graph codifying mutual nearest neighbors in the feature space. This way, we provide with a set of multiple neighborhoods able to describe the structure of complex spaces without parameter fine tuning. The extensive experiments on real-world and synthetic data sets show that our approach outperforms, both, local and global strategies in multi and single view settings

Neural Nearest Neighbors Networks

Non-local methods exploiting the self-similarity of natural signals have been well studied, for example in image analysis and restoration. Existing approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed feature space. The main hurdle in optimizing this feature space w.r.t. application performance is the non-differentiability of the KNN selection rule. To overcome this, we propose a continuous deterministic relaxation of KNN selection that maintains differentiability w.r.t. pairwise distances, but retains the original KNN as the limit of a temperature parameter approaching zero. To exploit our relaxation, we propose the neural nearest neighbors block (N3 block), a novel non-local processing layer that leverages the principle of self-similarity and can be used as building block in modern neural network architectures. We show its effectiveness for the set reasoning task of correspondence classification as well as for image restoration, including image denoising and single image super-resolution, where we outperform strong convolutional neural network (CNN) baselines and recent non-local models that rely on KNN selection in hand-chosen features spaces.Comment: to appear at NIPS*2018, code available at https://github.com/visinf/n3net

Feature Selection and Weighting by Nearest Neighbor Ensembles

In the field of statistical discrimination nearest neighbor methods are a well known, quite simple but successful nonparametric classification tool. In higher dimensions, however, predictive power normally deteriorates. In general, if some covariates are assumed to be noise variables, variable selection is a promising approach. The paper’s main focus is on the development and evaluation of a nearest neighbor ensemble with implicit variable selection. In contrast to other nearest neighbor approaches we are not primarily interested in classification, but in estimating the (posterior) class probabilities. In simulation studies and for real world data the proposed nearest neighbor ensemble is compared to an extended forward/backward variable selection procedure for nearest neighbor classifiers, and some alternative well established classification tools (that offer probability estimates as well). Despite its simple structure, the proposed method’s performance is quite good - especially if relevant covariates can be separated from noise variables. Another advantage of the presented ensemble is the easy identification of interactions that are usually hard to detect. So not simply variable selection but rather some kind of feature selection is performed. The paper is a preprint of an article published in Chemometrics and Intelligent Laboratory Systems. Please use the journal version for citation