Search results for "Gower"
showing 2 items of 2 documents
Large-scale nonlinear dimensionality reduction for network intrusion detection
2017
International audience; Network intrusion detection (NID) is a complex classification problem. In this paper, we combine classification with recent and scalable nonlinear dimensionality reduction (NLDR) methods. Classification and DR are not necessarily adversarial, provided adequate cluster magnification occurring in NLDR methods like $t$-SNE: DR mitigates the curse of dimensionality, while cluster magnification can maintain class separability. We demonstrate experimentally the effectiveness of the approach by analyzing and comparing results on the big KDD99 dataset, using both NLDR quality assessment and classification rate for SVMs and random forests. Since data involves features of mixe…
On several notions of complexity of polynomial progressions
2021
For a polynomial progression $$(x,\; x+P_1(y),\; \ldots,\; x+P_{t}(y)),$$ we define four notions of complexity: Host-Kra complexity, Weyl complexity, true complexity and algebraic complexity. The first two describe the smallest characteristic factor of the progression, the third one refers to the smallest-degree Gowers norm controlling the progression, and the fourth one concerns algebraic relations between terms of the progressions. We conjecture that these four notions are equivalent, which would give a purely algebraic criterion for determining the smallest Host-Kra factor or the smallest Gowers norm controlling a given progression. We prove this conjecture for all progressions whose ter…