High-Dimensional Range profile geometrical visualization and performance estimation of classification of radar targets via a Gaussian mixture model
Ali Mohammad‐Djafari, Thomas Boulay, Nicolas Gac, Julien Lagoutte · 2013
High-Dimensional Range profile geometrical visualization and performance estimation of classification of radar targets via a Gaussian mixture model Thomas Boulay1,2 , Ali Mohammad-Djafari1 , Nicolas Gac1 , Julien Lagoutte2 1 Laboratoire des Signaux et Syst`emes (L2S, UMR 8506 CNRS - SUPELEC - Univ Paris Sud 11) Sup´elec, Plateau de Moulon, F-91192 Gif-sur-Yvette, FRANCE. 2 THALES AIR SYSTEMS, voie Pierre Gilles de Gennes, 91470 Limours en Hurepoix, FRANCE Emails: [email protected], [email protected], [email protected], [email protected] GSI 2013, MINES ParisTech, Paris, France' & $ % Non Cooperative Target Recognition (NCTR) Formation of range profile Example of range profile ' & $ % Objectives • Visualize high-dimensional range profiles in 2D space • Estimate graphically and analytically classification performances ' & $ % Non Linear Dimension Reduction (NLDR) From high-dimensional space to low-dimensional space xT,i → yT,i xT,i ∈ RM → yT,i ∈ R2 Stochastic Neighbor Embedding (SNE) pj|i = exp −||xT,i − xT,j||2 /(2σ2 i ) k=i exp −||xT,i − xT,k||2/(2σ2 i ) qj|i = exp −||yT,i − yT,j||2 k=i exp −||yT,i �