Algebraic change-point detection

Elementary techniques from operational calculus, differential algebra, and noncommutative algebra lead to a new approach for change-point detection, which is an important field of investigation in various areas of applied sciences and engineering. Several successful numerical experiments are presented.

[1]  Cédric Join,et al.  Towards New Technical Indicators for Trading Systems and Risk Management , 2009 .

[2]  Hebertt Sira-Ramírez,et al.  Closed-loop parametric identification for continuous-time linear systems via new algebraic techniques , 2007 .

[3]  Mamadou Mboup,et al.  A Volterra filter for neuronal spike detection , 2008 .

[4]  K. Yosida.  Operational Calculus: A Theory of Hyperfunctions , 1984 .

[5]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[6]  J. Mikusiński.  Operational Calculus , 1959 .

[7]  M. Mboup.  Parameter estimation for signals described by differential equations , 2009 .

[8]  F. Ollivier,et al.  Une méthode d'identification pour un système linéaire à retards , 2007 .

[9]  Ken Perlin,et al.  [Computer Graphics]: Three-Dimensional Graphics and Realism , 2022 .

[10]  Tewfik Sari,et al.  Non-standard analysis and representation of reality , 2008, Int. J. Control.

[11]  Emilie Lebarbier,et al.  Detecting multiple change-points in the mean of Gaussian process by model selection , 2005, Signal Process..

[12]  B. E. Brodsky,et al.  Non-Parametric Statistical Diagnosis , 2000 .

[13]  Marc Lavielle,et al.  Using penalized contrasts for the change-point problem , 2005, Signal Process..

[14]  M. Fliess,et al.  Questioning some paradigms of signal processing via concrete examples , 2003 .

[15]  Michel Fliess,et al.  Parameters estimation of systems with delayed and structured entries , 2009, Autom..

[16]  Cédric Join,et al.  Non-linear estimation is easy , 2007, Int. J. Model. Identif. Control..

[17]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[18]  Martin Vetterli,et al.  Wavelet footprints: theory, algorithms, and applications , 2003, IEEE Trans. Signal Process..

[19]  Michel Fliess,et al.  Analyse non standard du bruit , 2006, ArXiv.

[20]  Philippe Flajolet,et al.  Analytic Combinatorics , 2009 .

[21]  Mamadou Mboup,et al.  Analyse et représentation de signaux transitoires : application à la compression, au débruitage et à la détection de ruptures , 2005 .

[22]  吉田 耕作.  Operational calculus: A theory of hyperfunctions , 1984 .

[23]  P. Flajolet,et al.  Analytic Combinatorics: RANDOM STRUCTURES , 2009 .

[24]  B. Brodsky,et al.  Nonparametric Methods in Change Point Problems , 1993 .

[25]  M. Fliess,et al.  An algebraic framework for linear identification , 2003 .

[26]  Michel Fliess.  Critique du rapport signal à bruit en communications numériques -- Questioning the signal to noise ratio in digital communications , 2008, ArXiv.

[27]  Wai-Kai Chen.  Passive and Active Filters: Theory and Implementations , 1986 .

[28]  Cédric Join,et al.  Systematic Risk Analysis: First Steps Towards a New Definition of Beta , 2009 .

[29]  Yoshio Kinokuniya,et al.  On Operational Calculus , 1951 .

[30]  Marius van der Put,et al.  Galois Theory of Linear Differential Equations , 2012 .

[31]  Lotfi Belkoura.  Change point detection with application to the identification of a switching process , 2009, ICONS 2009.

[32]  L. Horváth,et al.  Limit Theorems in Change-Point Analysis , 1997 .

[33]  W. E. Scott.  Operational calculus based on the two-sided Laplace integral , 1951 .

[34]  Jean-Yves Tourneret,et al.  Bayesian off-line detection of multiple change-points corrupted by multiplicative noise: application to SAR image edge detection , 2003, Signal Process..

[35]  Cédric Join,et al.  A delay estimation approach to change-point detection , 2007 .

[36]  Marc Raimondo,et al.  A peaks over threshold model for change-point detection by wavelets , 2004 .

[37]  B. E. Brodsky,et al.  Non-Parametric Statistical Diagnosis: Problems and Methods , 2000 .

[38]  Mamadou Mboup,et al.  Spike Detection and Sorting: Combining Algebraic Differentiations with ICA , 2009, ICA.

[39]  Irène Gijbels,et al.  On the Estimation of Jump Points in Smooth Curves , 1999 .

[40]  J. McConnell,et al.  Noncommutative Noetherian Rings , 2001 .

[41]  Joachim Rudolph,et al.  Ein algebraischer Zugang zur Parameteridentifikation in linearen unendlichdimensionalen Systemen (An Algebraic Approach to Parameter Identification in Linear Infinite Dimensional Systems) , 2007, Autom..