Proceedings of the 17th Iranian Conference of Biomedical Engineering (ICBME2010), 3-4 November 2010

Application of Local Linear Neuro-Fuzzy Model in Prediction of Mean Arterial Blood Pressure Time

Series Amin Janghorbanil, Abdollah Arasteh1, Mohammad Hassan Moradi1

1 Amirkabir University of Technology Tehran, Iran

E-mail: A.Janghorbani@aut.ac.ir.a_arasteh@aut.ac.ir.mhmoradi@aut.ac.ir

Abstract-predicting the future behavior of human's biosignals

can help clinicians to prevent occurrence of physiological disorders such as hypotension, hypertension, epilepsy, etc. In addition this prediction helps clinicians to buy some time in order

to select a more effective treatment for physiological disorders without exposing the patient to additional risks of delay in receiving treatment. In this paper a local linear neuro-fuzzy model was applied to predict mean arterial pressure time series. In order to evaluate the accuracy of prediction, Normalized Mean Square Error (NMSE) was chosen as an error index. 10 mean arterial pressure signals (2.5 hours each) from 10 patients were selected for training and prediction. Mean of NMSE for

these signals was 0.023 in train and 0.0514 in test.

Keyword: Time Series, Prediction, Local Linear Model, Neuro­Fuzzy, Local Linear Model Tree (LoLiMoT) algorithm

I. INTRODUCTION

Time series prediction is one of the interesting researches that is widely used in engineering, economy, financial management, medicine and many other fields. There are several methods that have been applied for prediction of various time series. ARIMA models are traditional and classic methods for prediction of time series; these methods are based on linear systems and are not suitable for prediction of real world nonlinear time series [1]. Artificial neural networks have overcome nonlinear nature of time series and became one of powerful tools for prediction of various nonlinear and nonstationary time series such as financial time series [2] and other natural time series such as wind speed time series [3]. In addition, Support Vector Machine (SVM) is also used for prediction of various time series such as financial and chaotic time series in many studies [4].

In the recent years in many researches neuro-fuzzy models have been utilized for prediction of nonlinear and chaotic time series and also for nonlinear and complex system identification [5]. Neuro-fuzzy model is a gray box modeling technique that has ability to use transparency of rule based fuzzy system with learning capability of neural networks which has been shown good ability in time series prediction. One of the nuero-fuzzy models is local linear neuro-fuzzy model that has been used in several studies for time series prediction and nonlinear system identification [6] - [8]. This method has been widely used for

prediction of chaotic time series such as solar activities [9], [10].

In medicine the physiological time series contain useful information about health of patients and are one of the best tools for monitoring physiological state of them. So prediction of future behavior of physiological time series can help patients and clinicians to prevent occurrence of physiological disorders and predict the future physiological state of patients. In addition this prediction helps clinicians to buy some time in order to select a more effective treatment for physiological disorders such as epilepsy, hypotension, hypertension, etc without exposing the patient to additional risks of delay in receiving treatment. To achieve this aim, Minfein et al [11] applied a local wavelet SVM model to model EEG and used the model for predicting future values of the signal and occurrence of seizure. Atoufi et al [12] applied a local linear neuro-fuzzy model for modeling EEG and prediction of future values of EEG time series. Insung et al [13] applied neural networks in order to design and implement human biosignal data prediction system.

Hypotension is one of the physiological disorders with high mortality rate that predicting occurrence of it can help clinician to diagnose the cause of this physiological disorder and select appropriate treatment based on this diagnosis. In this study a local linear neuro-fuzzy model was applied in order to predict future values of mean arterial blood pressure time series which helps clinician to forecast occurrence of hypotension or hypertension before onset of them.

Remainder of this paper is organized as follows: In the following section the neuro-fuzzy model that was used for modeling of blood pressure time series is illustrated. In section 3 the experimental results are presented. Finally, section 4 discusses the experimental results and concludes the paper with a few suggestions about future studies.

II. LOCAL LINEAR NEURO-FUZZY MODEL

A. Structure of neuro-Juzzy model Local linear modeling technique is based on dividing a

complex modeling problem into a number of smaller and simpler submodels such as linear models, which are identified independently and simply [14].

978-1-4244-7484-4110/$26.00 ©2010 IEEE

Local linear neuro-fuzzy model can be described with a network structure. In this network each neuron realizes a local linear model (LLM) and an associated validity function that determines the validity region of LLMs. The network structure of the local linear neuro-fuzzy model is depicted in Fig.I. This model is a neuro-fuzzy model with linear neuron in the output layer that calculates LLM output from the input vector and a hidden layer which determines the weight of LLM output in final network output, according to Eq.l and Eq.2 [14].

(1)

(2)

In which'!:!. = [uj,u2, • • • ,up] is the p dimensional input

vector of the model, W ij is /' LLM parameter of neuron ilh, M

is number of LLMs and ¢i is normalized Gaussian validity

function of neuron i/h with:

(3)

Figure I: Network structure of local linear neuro-fuzzy model with M neuron andp input

Each neuron of this network can be considered as a fuzzy rule in which the nonlinear parameters of Gaussian validity

functions, center (cij) and standard deviation «(J" ij ), are

parameters of hidden layer and represent the rule premises and

LLM parameters ( W ij ) represent the rule consequents.

Optimization or learning methods are used to adjust these parameters [8].

B. Parameter optimization of rule cosequents

Global optimization of Mx(P+l) LLM parameters can be obtained by least square optimization technique. Assume that.!:!: is the parameter vector that contains all parameters of LLMs:

T W = [WID' WII···, WIP' W2D,···, W2P' •••• , WMP] (4)

and X is the associated regression matrix for N measured data sample:

X = [X SlIb X SlIb X 'lib ] I , 2 , ••• , M

in which :

X.�lb= I

¢;(u(l)) ¢;(u(2))

U,(lM(u(1)) u,(2M(u(2))

u/lM(u(1)) up(2M(u(2))

Therefore the model output can obtain from Eq.7.

y=Xw So LLM parameters can be obtained from Eq.8 [1]:

w=(XTXtXTy in which y is measured process output.

C. Parameter optimization of rule premises

(5)

(6)

(7)

(8)

An incremental learning algorithm called local linear model tree algorithm, was applied in order to optimize the validity function parameters. For this purpose the input space is divided into smaller hypercubic subspaces and center of each hypercube is selected as center of LLM validity function. Standard deviation of LLM validity function is proportional to the hypercube extension. In each iteration the worst performing LLM is determined to be divided. All the possible divisions in the p dimensional input space are checked and the best is done. The LLM is divided into two equal halves on the selected input dimension and forms two independent LLMs with associated validity functions. The algorithm can be described in 4 steps [14]:

1. Start with initial model: start with a single LLM. Construct the validity function for this LLM and estimate the LLM parameters of the model. Set

M to initial number of LLMs (M=l if no LLM is defined initially)

2. Find the worst LLM: calculate loss function e.g. NMES of all the LLMs and find the worst LLM based on the loss function

3. Check all divisions: the worst LLM is considered for further refinement. The hypercube of this LLM is split into two halves with an axis orthogonal spilt. Divisions in all dimensions are tried. For each division all these steps are carried out:

a) Construction of multidimensional validity functions for both new hypercubes

b) Local estimation of the rule consequent parameters for both newly generated LLMs

c) Calculation of total loss function for current overall model

4. Select the best division: from p alternative of divisions, the division which minimizes the overall loss function of the model is selected and its associated validity function, LLM is adopted for the model and the number of LLM is increased by 1 (M=M+ 1).

5. Check for algorithm convergence: if the convergence criterion is satisfied the algorithm terminates otherwise continues from step2.

Four iterations of local linear model tree (LoLiMoT) algorithm for two dimensional input space is depicted in Fig.2.

lI,

I. ileralion h � 4� ltn'2 V l , lffi' 2 2.\

2. ileralion 2-2 lI�

�,� ¥ lI2 .. �-1 3'2 � 3. lIerallon f'..7 3-3 lI, � II � b

n o, &�":'; Figure 2: Four iteration of local linear model tree (LoLiMoT) algorithm

for two dimensional input space

III. EXPERIMENTAL RESULT

The proposed method was applied for prediction of m.ean arterial pressure time series. 1000 samples of each Mi\P tune series were selected for training and 8000 samples of It were used for test and prediction.

[MAP(t-5),MAP(t-4),MAP(t-3),MAP(t-2),M,AP(t-1)} vect?r was given to the neuro-fuzzy model. as the . mput vector: m order to predict next value of MAP tune series . Nor�ahzed mean square error (NMSE) is selected for evaluatIOn of prediction accuracy which is defined as:

NMSE =

[-,-=,-�_(Y_- 5'_)2 ] L(Y-ji)2 i=!

(9)

2.5 hours of MAP time series from 10 patients were selected for prediction task. Mean of NMSE for predic�ion of MAP time series from 10 patients was 0.023 for tram and 0.0514 for test. In Fig.3 and FigA measured MAP time series and predicted MAP time series with local �inear. �euro-fuzzy model and absolute prediction error of them m trammg and test is depicted respectively.

66

64

620 100 200 3()() 400 000 sample

3_5

3

2.5

sample

(b) Figure 3: a) Measured and predicted MAP time series (train)

(NMSE=O.03)

b) Absolute prediction error (train)

IV. CONCLUSION

In this study a local linear neuro-fuzzy model was applied in order to predict future values of MAP time series that can help patients to prevent occurrence of hypotension or hypertension or help clinicians to select appropriate treatment for these physiological disorders. This method was applied for prediction of MAP time series from ten patients and finally acceptable NMSE was achieved for one step ahead prediction of MAP time series. The mean of NMSE for prediction of MAP time series belong to 10 patients, was 0.023 for train and 0.0514 for test. For future studies preprocessing techniques such as PCA or wavelet transform can be applied to time series and local linear neuro-fuzzy model can be utilized for prediction of each PCA or wavelet coefficient and finally by combination of predicted PCAs or wavelet coefficients predicted values are achieved and in this manner horizon of prediction may be increased.

test 90

85

80

75

70

� 55

50

45 0 1000 2000 3000 4000 5000 6000 7000 0000 9000

sampel

(a)

35

30

25

20

g w 15

10

1000 2000 3000 4000 5000 6000 7000 0000 9000 sampel

(b)

REFERENCES

Figure 4: a) Measured and predicted MAP time series (test)

(NMSE=0.06)

b) Absolute prediction error (test)

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[6] I.Mohammadzaman "Predictive Control of an Electromagnetic Suspension System Based on Locally Linear Model Tree and Subset Selection" The 9th International Workshop on Advanced Motion Control Turkey 2006 .

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[8] M. Nosrati Maralloo" Long Term Electrical Load Forecasting via a Neurofuzzy Model" 14th International CSI computer Conference. tehran 20-21 Oct. 2009

[9] 1. Sharifi " Multi-step prediction of Dst index using singular spectrum analysis and locally linear neurofuzzy modeling" Earth Planets Space, vo158, pp: 331-341, 2006

[10] AGholipour " Predicting Chaotic Time Series Using Neural and Neurofuzzy Models: A Comparative Study." Springer Neural Processing Letters. 2006

[II] M.Shen " A Prediction Approach for Multichannel EEG Signals Modeling Using Local Wavelet SVM" IEEE Trans. Instrum. Meas, Vol 59, NoS. 2010

[12] B.Atoufi " A Survey of Multi-Channel Prediction of EEG Signal in Different EEG States: Normal, Pre-Seizure, and Seizure" 17th international conference on Computer Science and Information Technologies ,2009, Yerevan, Armenia

[13] I. Jung" Neural network based human biosignal data prediction system" World Congress on Medical Physics and Biomedical Engineering 2006 IFBME proceedings Volume 6, Track 24.pp: 3709-3713

[14] O. Nelles, Local linear Neuro-fuzzy Model in Nonlinear system identification from Classical Approaches to Neural Networks and Fuzzy Models , Springer Verlag, Berlin,200I.pp:341 :389

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