A taxonomy framework for unsupervised outlier detection techniques for multi-type data sets

The term "outlier" can generally be defined as an observation that is significantly different from the other values in a data set. The outliers may be instances of error or indicate events. The task of outlier detection aims at identifying such outliers in order to improve the analysis of data and further discover interesting and useful knowledge about unusual events within numerous applications domains. In this paper, we report on contemporary unsupervised outlier detection techniques for multiple types of data sets and provide a comprehensive taxonomy framework and two decision trees to select the most suitable technique based on data set. Furthermore, we highlight the advantages, disadvantages and performance issues of each class of outlier detection techniques under this taxonomy framework

Multi-Fibers Bundles as a new model for high-dimensional Spacetimes

Around 1920, Kaluza and Klein had the idea to add a fifth dimension to the classical 4-dimensional spacetime of general relativity to create a geometric theory of gravitation and electromagnetism. Today, theoretical evidences, like string theory, suggest the need for a spacetime with more than five dimensions. We want to present in this paper a mathematical structure generalizing the fiber bundle structure to the case of a product fiber of the form $F=S \times W$, that enable the possible definition of multiple naturally defined fibers at each point of the manifold, on which therefore one can define objects that depend only on one of the components of the global fiber. Although we do not pretend here to model precisely other known physical interactions, we present this geometric structure as a possible way to model or encode deviations from standard 4-dimensional General Relativity, or "dark" effects such as dark matter or energy ; (we refer to the authors' article [3] ). Also this geometry was a starting point for the second author's new approach to a geometric unification of General Relativity and Quantum Physics ( see [23]).Comment: 16 pages. Extract of another work emphasizing a mathematical aspect. Added :details on notations, correction in the last theorem. arXiv admin note: text overlap with arXiv:1010.1516; substantial text overlap with arXiv:1709.0417

TS2PACK: A Two-Level Tabu Search for the Three-dimensional Bin Packing Problem

Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first-level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representation of the packing, proposed by Fekete and Schepers, which reduces the size of the search space. We also introduce a general method to increase the size of the associated neighborhoods, and thus the quality of the search, without increasing the overall complexity of the algorithm. Extensive computational results on benchmark problem instances show the effectiveness of the proposed approach, obtaining better results compared to the existing one