A novel signal diagnosis technique using pseudo complex-valued ...

Expert Systems with Applications 38 (2011) 9063–9069

Contents lists available at ScienceDirect

Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

A novel signal diagnosis technique using pseudo complex-valued autoregressive technique A.M. Aibinu ⇑, M.J.E. Salami, A.A. Shafie Department of Mechatronics, International Islamic University Malaysia (IIUM), P.O. Box 10, 50728, Malaysia

a r t i c l e

i n f o

Keywords: Autoregressive model Complex-valued data (CVD) Complex-valued neural network (CVNN) Diabetes Parametric models

a b s t r a c t In this paper, a new method of biomedical signal classification using complex- valued pseudo autoregressive (CAR) modeling approach has been proposed. The CAR coefficients were computed from the synaptic weights and coefficients of a split weight and activation function of a feedforward multilayer complex valued neural network. The performance of the proposed technique has been evaluated using PIMA Indian diabetes dataset with different complex-valued data normalization techniques and four different values of learning rate. An accuracy value of 81.28% has been obtained using this proposed technique. Ó 2011 Published by Elsevier Ltd.

1. Introduction The use of parametric modeling technique in the form of rational system transfer function has been extensively applied to various fields of human endeavor (Aibinu, Salami, & Shafie, 2010a, 2010b, 2010c; Bruce, 2000; Chon & Cohen, 1997; Chon, Hoyer, Armoundas, Holstein-Rathlou, & Marsh, 1999; Hayes, 1996; Marple, 1987; Manolakis, Ingle, & Kogon, 2000; Proakis & Manolakis, 2007). Processes with spectral poles or narrow peaks are preferably modeled with autoregressive (AR) modeling technique whereas moving average (MA) models are suitable for processes with spectral zeros or narrow valleys and autoregressive moving average (ARMA) models are suitable for processes with both narrow peaks and valleys (Broersen, 2009; Kay & Marple, 1981; Priestley, 1981). Areas of application of modeling techniques include but not limited to the field of biomedical signal processing (Bruce, 2000; Chon & Cohen, 1997; Chon et al., 1999; Hayes, 1996; Manolakis et al., 2000; Marple, 1987; Proakis & Manolakis, 2007), digital image processing (Liang & Lauterbur, 2000; Salami, Najeeb, Khalifa, & Arrifin, 2007; Smith, Nichols, Henkelman, & Wood, 1986), building and built environment industry (Aibinu et al., 2008), nuclear plant (Kim, Chang, & Lee, 1993), communication (Fattah & Zhu, 2008; Liang, Wilkes, & Cadzow, 1993) etc. These modeling approaches have been applied to: determine an unknown system by the knowledge of the input and output data (system modeling and identification); to predict the future values based on past output values (linear prediction); to determine the frequency content; to evaluate system response. Autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) have been among the widely used parametric modeling ⇑ Corresponding author. E-mail address: [email protected] (A.M. Aibinu). 0957-4174/$ - see front matter Ó 2011 Published by Elsevier Ltd. doi:10.1016/j.eswa.2010.11.005

techniques. Mathematically, an ARMA model involves representation of a system by the difference equation of the form

yðnÞ ¼ 

p X k¼1

ak yðn  kÞ þ

q X

bk xðn  kÞ

ð1Þ

k¼0

where ak and bk are the model coefficients, p and q are real-valued model order for the AR and MA parts, respectively (Blanchet & Charbut, 2006; Kay, 1988; Kay & Marple, 1981; Lu & Chon, 2001; Makhoul, 1975; Priestley, 1981; Widrow & Stearns, 1985). If the coefficients in (1), are complex number and either y(n) or x(n) are CVD, then the ARMA model is referred to as a complex autoregressive moving average (CARMA) model. Similarly, an AR model involves representation of a system by the difference equation of the form

yðnÞ ¼ 

p X

ak yðn  kÞ þ b0 xðnÞ

ð2Þ

k¼1

Similar to ARMA model, if the coefficients in (2), are complex number and either y(n) or x(n) are CVD, then the model can be referred to as complex autoregressive (CAR) model. The Wold’s decomposition theorem allows any stationary discrete time signal to be decomposed into a deterministic signal and an autoregressive (AR) process of high order, thus an ARMA process can be represented by an AR process of sufficiently high order (Wold, 1938). Similarly, an ARMA process can also be represented by an MA model of sufficiently high order, thus the existence of inter-usage between the three models. Furthermore, from this theorem the issue of model selection reduces to selecting the model that requires the smallest number of parameters and are also easy to compute (Marple, 1987; Proakis & Manolakis, 2007). Several methods have been suggested for ARMA model coefficients determination, these can be broadly divided into two groups, namely optimal and suboptimal techniques (Aibinu,