Dynamical systems and nonlinear Kalman filtering applied in classification

In this paper we present an application for the dynamical systems and nonlinear filtering in classification. Described here method constitutes a new proposal for the classification of dynamical objects. This method does not require the expansion of dimensionality of the input vectors used in time series, compared to other methods which multiply inputs. The proposed classifier uses the dynamical systems as its core and nonlinear Kalman filtering as its learning algorithm. Presented herein results are the performance tests of proposed classifier applied in a real life problem - bankruptcy prediction, which is one of the fundamentals application of data mining in finance. The results achieved by the presented method were compared to other very popular classifiers and these experiments prove greater classification accuracy of the proposed method.

[1]  Carlos Serrano-Cinca,et al.  Self organizing neural networks for financial diagnosis , 1996, Decision Support Systems.

[2]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[3]  Edward I. Altman,et al.  FINANCIAL RATIOS, DISCRIMINANT ANALYSIS AND THE PREDICTION OF CORPORATE BANKRUPTCY , 1968 .

[4]  Rudolph van der Merwe,et al.  Sigma-point kalman filters for probabilistic inference in dynamic state-space models , 2004 .

[5]  Cindy Yoshiko Shirata.  Financial Ratios as Predictors of Bankruptcy in Japan : An Empirical Research , 1998 .

[6]  J. Gove,et al.  Application of a dual unscented Kalman filter for simultaneous state and parameter estimation in problems of surface‐atmosphere exchange , 2006 .

[7]  Jeffrey K. Uhlmann,et al.  Nondivergent simultaneous map building and localization using covariance intersection , 1997, Defense, Security, and Sensing.

[8]  James A. Ohlson.  FINANCIAL RATIOS AND THE PROBABILISTIC PREDICTION OF BANKRUPTCY , 1980 .

[9]  Amir F. Atiya,et al.  Bankruptcy prediction for credit risk using neural networks: A survey and new results , 2001, IEEE Trans. Neural Networks.

[10]  D. Simon.  Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches , 2006 .

[11]  J Kurths,et al.  Estimation of parameters and unobserved components for nonlinear systems from noisy time series. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[13]  H. Musoff,et al.  Unscented Kalman Filter , 2015 .

[14]  Chai Quek,et al.  Bank Failure Prediction and Financial Data Reconstruction using Novel Soft-Computing Approaches , 2002 .

[15]  Panayiotis Theodossiou,et al.  Predicting Corporate Financial Distress: A Time-Series CUSUM Methodology , 1998 .

[16]  Shigeo Abe DrEng.  Pattern Classification , 2001, Springer London.

[17]  Kaisa Sere,et al.  The Effect of Sample Size on Different Failure Prediction Methods , 1998 .

[18]  S. Julier,et al.  A General Method for Approximating Nonlinear Transformations of Probability Distributions , 1996 .