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Probabilistic neural networks for diagnosis of Alzheimer's disease using conventional and wavelet coherence
Journal of Neuroscience Methods 197 (2011) 165–170
Contents lists available at ScienceDirect
Journal of Neuroscience Methods journal homepage: www.elsevier.com/locate/jneumeth
Probabilistic neural networks for diagnosis of Alzheimer’s disease using conventional and wavelet coherence Ziad Sankari a , Hojjat Adeli b,∗ a
Departments of Biomedical Engineering, Electrical and Computer Engineering, 470 Hitchcock Hall, 2070 Neil Avenue, Ohio State University, Columbus, OH 43210, USA Departments of Biomedical Engineering, Biomedical Informatics, Civil and Environmental Engineering and Geodetic Science, Electrical and Computer Engineering, Neurological Surgery, and Neuroscience, 470 Hitchcock Hall, 2070 Neil Avenue, Ohio State University, Columbus, OH 43210, USA b
a r t i c l e
i n f o
Article history: Received 27 September 2010 Received in revised form 22 January 2011 Accepted 25 January 2011 Keywords: Alzheimer’s disease EEG Neural networks
a b s t r a c t Recently, the authors presented an EEG (electroencephalogram) coherence study of the Alzheimer’s disease (AD) and found statistically significant differences between AD and control groups. In this paper a probabilistic neural network (PNN) model is presented for classification of AD and healthy controls using features extracted in coherence and wavelet coherence studies on cortical connectivity in AD. The model is verified using EEGs obtained from 20 AD probable patients and 7 healthy/control subjects based on a standard 10–20 electrode configuration on the scalp. It is shown that extracting features from EEG sub-bands using coherence, as a measure of cortical connectivity, can discriminate AD patients from healthy controls effectively when a mixed band classification model is applied. For the data set used a classification accuracy of 100% is achieved using the conventional coherence and a spread parameter of the Gaussian function in a particular range found in this research. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Recently, Sankari et al. (in press) presented an EEG coherence study of the Alzheimer’s disease (AD) and found statistically significant differences between AD and control groups. A drawback of the conventional coherence is that only spectral components are observed without taking into account any temporal information. Time-frequency analysis methods can be used to study the changes in cortical connectivity over time. Sankari and Adeli (in press) present a wavelet coherence investigation of EEG readings acquired from AD patients and healthy controls, as the first attempt to use wavelet coherence to distinguish between AD and controls. This method provides better temporal and spectral information leading to improved results. The study shows a set of statistically significant differences in the wavelet coherence among AD and controls. Temporo-central regions show a significant decrease in wavelet coherence in AD in the delta band. Parietal and central regions show a significant decrease in cortical connectivity of AD with most of their neighbors in the theta and alpha bands. It is concluded that feature extraction via wavelet coherence provides a larger set of statistically significant differences between AD and controls.
∗ Corresponding author. Tel.: +1 614 292 7929. E-mail address: [email protected] (H. Adeli). 0165-0270/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2011.01.027
A number of neural network (NN) models have been developed for pattern recognition and classification since mid-1980s. They include the backpropagation NN developed in the late 1980s (Rumelhart et al., 1986; Hung and Adeli, 1993), counterpropagation NN (Adeli and Park, 1995a; Sirca and Adeli, 2001; Dharia and Adeli, 2003), adaptive conjugate gradient neural network algorithm (Adeli and Hung, 1993, 1994; Adeli and Samant, 2000), recurrent NN (Samant and Adeli, 2001; Puscasu et al., 2009), radial basis function NN (RBNN) (Adeli and Karim, 2000; Karim and Adeli, 2002, 2003; Ghosh-Dastidar et al., 2008; Savitha et al., 2009), wavelet NN (Ghosh-Dastidar and Adeli, 2003; Adeli and Jiang, 2006; Zou et al., 2008), spiking NN (Ghosh-Dastidar and Adeli, 2007; Rossello et al., 2009; Ghosh-Dastidar and Adeli, 2009a,b), neural dynamics models (Adeli and Park, 1995b,c, 1996; Park and Adeli, 1995, 1997; Adeli and Karim, 1997a,b; Karim and Adeli, 1999; Adeli and Kim, 2001; Tashakori and Adeli, 2002; Ahmadkhanlou and Adeli, 2005), neuro-genetic models (Jiang and Adeli, 2008; Elragal, 2009), and the probabilistic neural network (PNN) (Specht, 1990). PNN is often used for classification purposes (Adeli and Panakkat, 2009). In this research, a PNN model is presented for classification of AD and healthy controls. The model uses features the authors extracted in two previous research studies on cortical connectivity in AD. Fig. 1 shows the various steps in the model. PNN is applied to the extracted features most distinguishing the two groups based the lowest p-value obtained in the one way analysis of variance (ANOVA) statistical test.
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Z. Sankari, H. Adeli / Journal of Neuroscience Methods 197 (2011) 165–170
Band-limited EEG
EEG Sub-bands
Ir
I1
A1H
Feature Extraction (Conventional coherence or wavelet coherence)
A2H
Pattern Layer
AhH
Input layer
A1AD A2AD
Summation Layer
Σ
AdAD
Σ
Output
O
Fig. 2. Architecture of PNN for diagnosis of AD.
Classification (PNN)
Decision (AD/Control) Fig. 1. AD diagnosis model.
2. Data acquisition EEGs are obtained from 20 AD probable patients (average age of 74) diagnosed with probable AD as per NINCDS-ADRDA and DSM-III-R criteria and 7 healthy (control) subjects (average age of 71) using a standard 10–20 electrode configuration on the scalp (Pritchard et al., 1991). Recordings from 19 scalp electrodes: Fp2, Fp1, F7, F3, Fz, F4, F8, T3, C3, Cz, C4, T4, T5, P3, Pz, P4, T6, O2, O1 are taken while subjects’ eyes are closed. Temporal behavior is examined by accumulating data at a sampling rate of 128 Hz for epochs of 8 s, resulting in time series of 1024 data points. Digital conversion of the measured analog signal is accomplished with an 8 bit digitizer. A band-pass filter (0.1–30 Hz, −12 dB/octave roll-off) is used to filter the frequency band of interest. EEGs are visually inspected and discriminated to eliminate those time series which contain optical and muscular artifacts. 3. Methods 3.1. Mathematical basis A PNN is made up of four layers: an input layer, a pattern layer, a summation layer, and an output layer with a single node. Fig. 2 shows the architecture of the PNN for diagnosis of AD. The input layer consists of r input nodes. In Fig. 2, h and d are the numbers of healthy and AD training vectors respectively. The pattern layer estimates the probability density function (PDF) of the input vector I using the Parzen window method. The Parzen window method is a non-parametric classifier that creates an estimate of the input PDF by superposition of a number of windows that are replicas of a particular function. In this research, the Gaussian function is used as the Parzen window. The Gaussian function is commonly used to represent data with normal distribution. The probability density function of features in this research has a similar shape to that of normally distributed data. In the pattern
layer, the Euclidean distance between the input vector I and the training vector T, an indication of closeness of the input and the training vectors, is used as the argument of the Gaussian function to estimate the input PDF. Thus, the output of the ith neuron belonging to the cth class, Aic , in the pattern layer is expressed as follows: Aic =
1 (2)r/2 sr
exp −
||I − T ic ||2 2s2
(1)
where Tic is the ith training vector corresponding to the cth class, and s is the spread of the Gaussian function. In Fig. 2, c is denoted with subscripts “H” for healthy and “AD” for the Alzheimer’s disease. The spread parameter s controls the size and shape of the Gaussian PDF. As s increases, the Gaussian window becomes wider and vice versa. An input which is close to the training data is represented by a value for Aic close to one. The estimated PDF is used to compute the Bayesian likelihood ratio and classify the input accordingly. In the summation layer, the outputs of the pattern layer corresponding to class c, Aic , are added together at node c (H or AD) as follows: Ac =
1 (2)r/2 sr
i=N i=1
||I − Tic ||2 exp − 2s2
(2)
where N = h in the neuron corresponding to the healthy class and N = d in the neuron corresponding to the AD class. The PNN model classifies the input vector into a specific class based on the maximum probability or the Bayes’ rule. The output O in the output layer indicates which class the input vector belongs to based on the maximum of the values in the two neurons of the summation layer. The influence of the spread parameter s on the effectiveness of the PNN model for diagnosis of AD is investigated in this research. 3.2. Feature extraction Band-limited EEG is sub-divided into four physiological bands commonly used by physiologists and neurologists: delta (0–4 Hz), theta (4–8 Hz), alpha (8–12 Hz) and beta (12–30 Hz). Each of the sub-bands relates to a particular functional and physiological part of the brain. Only the most promising features are selected. In the coherence study, 11 statistically significant promising features with the lowest p values (p values of less than 0.001) were found for diagnosis of AD. They are electrode pairs T5–Fp1, T5–F3 and T5–C4 in the delta band, electrode pairs Pz–F4 and Pz–T3 in the theta band, electrode pairs P4–FP2, P4–F3 and P4–Fz in the alpha band, and electrode pairs T3–F7, T3–F3 and T3–T5 in the beta band (Table 1).
Z. Sankari, H. Adeli / Journal of Neuroscience Methods 197 (2011) 165–170
167
Table 1 Features extracted within each band using conventional coherence and wavelet coherence. Band Method
Delta
Theta
Alpha
Beta
Conventional coherence Wavelet coherence
T5–Fp1, T5–F3 and T5–C4 T5–T3, T5–P3, T6–O2, and T5–C3
Pz–F4 and Pz–T3
P4–FP2, P4–F3 and P4–Fz Pz–C3, C3–Fz, F4–Cz, F3–C3, Fz–C3, and Cz–P3
T3–F7, T3–F3 and T3–T5 Cz–F3, Cz–Fz, T5–O1, F3–Cz, Fz–Cz, and C4–T6
T5–T3, P4–Cz, T3–C3, C3–Fz, C4–F4, and Cz–Fz
In the wavelet coherence study, 22 statistically significant features were found having the lowest p values (p-values of less than 0.001). They are electrode pairs T5–T3, T5–P3, T6–O2, and T5–C3 in the delta band, T5–T3, P4–Cz, T3–C3, C3–Fz, C4–F4, and Cz–Fz, in the theta band, Pz–C3, C3–Fz, F4–Cz, F3–C3, Fz–C3, and Cz–P3 in the alpha band, and Cz–F3, Cz–Fz, T5–O1, F3–Cz, Fz–Cz, and C4–T6 in the beta band (Table 1). Each one of the two sets of features is used as mixed band input to a PNN to classify the data into two classes: AD and control subjects. As such, for mixed-band classification the number of input nodes, r (Fig. 2), is equal to 11 for the case of conventional coherence and 22 for the case of wavelet coherence. A similar study is also made using features within each EEG band separately. For example, the four wavelet coherence values of electrode pairs T5–T3, T5–P3, T6–O2, and T5–C3 in the delta band (Table 1) are used as input features in the PNN model. As such, there are 4 + 4 = 8 such studies in the single band investigation phase. In these single-band classifications, the number of features within each band, r, can vary between 2 and 6, depending on how many ‘promising’ features (p value < 0.001) are present within each of these bands.
Fig. 3. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the delta band of the conventional coherence.
3.3. Training The PNN model was trained by randomly dividing the available set of data (20 AD and 7 healthy) into a training set and a testing set. The training set contains features extracted from 3 healthy subjects and 10 AD patients. The testing set is then composed of 4 healthy and 10 AD patients. This process is repeated 100 times and the average values are reported in the performance assessment presented in the next section. The performance of the PNN model is evaluated for different values of the spread parameter, s, to determine a range of optimal values. 4. Results Fig. 4. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the theta band of the conventional coherence.
4.1. Statistical measures to evaluate the model The results are evaluated using three statistical measures from the number of correct and incorrect predictions: detection rate or probability of detection PD , false alarm rate PF , and the misdetection rate PM . The detection rate, PD , is defined as the number of AD subjects identified correctly, Nc , divided by the total number of AD subjects NAD : PD =
NC NAD
(3)
The false alarm rate, PF , is defined as the number of healthy controls identified incorrectly as AD, Nf , divided by the total number of healthy subjects Nh : PF =
Nf Nh
(4)
The misdetection rate PM is defined as the number of AD subjects identified as healthy, Nm , divided by the total number of AD subjects
NAD : PM =
Nm = 1 − PD NAD
(5)
4.2. Classification with conventional coherence Fig. 3 shows the values of misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the delta band. A tradeoff pattern between PM and PF is noted in this figure. The misdetection rate decreases with an increase in the value of the spread parameter. In this band 100% detection (no misdetection) is obtained at s = 0.22 with a false alarm rate as low as 44%. Fig. 4 shows the values of misdetection and false alarm rates as a function of the spread parameter in the theta band. Similar to what is observed in the delta band (Fig. 3) the misdetection rate decreases with an increase in the value of the spread parameter,
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Fig. 5. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the alpha band of the conventional coherence.
Fig. 7. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter using mixed band features of the conventional coherence.
Fig. 6. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the beta band of the conventional coherence.
Fig. 8. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the delta band of the wavelet coherence.
whereas the false alarm rate increases with an increase in the value of the spread parameter. The same observation is noted in the alpha and beta bands. In the theta band, 100% detection (no misdetection) is obtained at s = 0.30 with a false alarm rate of 45%. Fig. 5 shows the values of misdetection and false alarm rates as a function of the spread parameter in the alpha band. In this band, 100% detection (no misdetection) is obtained at s = 0.32 with a false alarm rate of 42%. Fig. 6 shows the values of misdetection and false alarm rates as a function of the spread parameter in the beta band. In this band, 100% detection (no misdetection) is obtained at s = 0.30 with a false alarm rate of 58.75%. In all cases where single band features were investigated, a tradeoff between the misdetection and the false alarm rates is observed. Finally, the 11 statistically significant features identified in all bands are used as input to the PNN model (mixed band feature detection). Fig. 7 shows the misdetection and false alarm rates as a function of the spread value s using mixed band features of the conventional coherence. A detection rate of 100% with a false alarm rate of 0% is obtained for spread values s in the range 0.32–0.42.
parameter. In this band, a misdetection rate of 5.9% (detection rate of 94.1%) is obtained at s = 0.45 with a false alarm rate of 57.75%. Fig. 9 shows the values of misdetection and false alarm rates as a function of the spread parameter in the theta band. A misdetection rate of 3.9% (detection rate of 96.1%) is obtained at s = 0.35 for an improved false alarm rate of 20% compared with the conventional coherence.
4.3. Classification with wavelet coherence Fig. 8 shows the values of misdetection and false alarm rates as a function of the spread parameter in the delta band. The misdetection rate decreases with an increase in the value of the spread
Fig. 9. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the theta band of the wavelet coherence.
Z. Sankari, H. Adeli / Journal of Neuroscience Methods 197 (2011) 165–170
Fig. 10 shows the values of misdetection and false alarm rates as a function of the spread parameter in the alpha band. A misdetection rate of 4.1% (detection rate of 95.9%) is obtained at s = 0.18 for an improved false alarm rate of 10.75% compared with the conventional coherence. Fig. 11 shows the values of misdetection and false alarm rates as a function of the spread parameter in the beta band. No misdetection rate (or 100% detection rate) is obtained at s = 0.38 for an improved false alarm rate of 37% compared with the conventional coherence. Similar to what is observed in the conventional coherence study, a tradeoff exists between the misdetection and false alarm rates. In all but the alpha band, the false alarm rate is relatively steady over a large range of the spread parameter despite the decrease in the misdetection rate. Finally, the features identified in all bands are used as input to the PNN model. The model performs worse than in the case of conventional coherence features as seen in Fig. 12. The best performance for the mixed band case, PD = 100% and PF = 18.25% is observed for a spread value s = 0.05. The model, however, maintains a steady misdetection and false alarm rates for a larger range of the spread parameter s. 5. Discussion In the single-band case PNN yields similar results for both conventional coherence and wavelet coherence in the delta band.
Fig. 10. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the alpha band of the wavelet coherence.
169
Fig. 12. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter using mixed band features of the wavelet coherence.
Wavelet coherence shows improved performance in the theta, alpha and beta bands. This is predictable since the dimension of information in wavelet coherence is larger, accounting for changes in both time and frequency concurrently. Features extracted in the beta band appear to be the worst performing for both conventional and wavelet coherence using the PNN classification model. A possible explanation of this observation is the large bandwidth in the beta band where resolution of information decreases significantly as the band undergoes more and more processing, especially when compared with the other bands with smaller bandwidth. The results of single-band analysis for both conventional and wavelet coherence, however, are not accurate enough for AD diagnostic applications. Even though the wavelet coherence method yields a larger set of statistically significant differences between AD subjects and controls, the conventional coherence features in the mixed band case perform better than those obtained from the wavelet coherence method. In fact, for the given set of data, a classification accuracy of 100% with 0% false alarm rate is achieved using the conventional method at a spread value, s, between 0.32 and 0.42. A possible explanation why wavelet coherence does not perform as well in the mixed band analysis is the limited variability between the wavelet coherence fractions of AD and control groups within different bands, which results in poor PNN classification. It is also observed in this research that as s increases, the false alarm rate increases and misdetection rate decreases. This phenomenon is explained by the fact that the spread parameter controls the shape of the Gaussian function used in estimating the PDF of the input data. As the spread value decreases, the Gaussian curve becomes very narrow and discrimination among elements that do not belong to the training set becomes more difficult, the AD cases can not be well detected and, hence, misdetection rate increases. 6. Conclusion
Fig. 11. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the beta band of the wavelet coherence.
This study demonstrates that extracting EEG features using coherence, as a measure of cortical connectivity, can discriminate AD patients from healthy controls effectively especially when the mixed band classification model is applied. This research suggests that coherence studies can provide statistically significant features which help classify between AD and healthy subjects. In this research, for the data set used, a classification accuracy of 100% is achieved using conventional coherence and a spread parameter in a particular range found. A larger sample size and a more variant data set are needed in order to generalize the findings of this
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research. Multiple types of dementia can also be compared using the techniques developed on this research to investigate the efficacy of the methods used. The ultimate objective of the research is to provide a clinically useful tool to diagnose AD at an early stage using surface EEG. Acknowledgements The authors would like to thank Dr. Dennis Duke of Florida State University and Dr. Kerry Coburn of Mercer University for providing EEG data for this research project. References Adeli H, Hung SL. A concurrent adaptive conjugate gradient learning algorithm on MIMD machines. J Supercomp Appl 1993;7:155–66. Adeli H, Hung SL. An adaptive conjugate gradient learning algorithm for effective training of multilayer neural networks. Appl Math Comp 1994;62:81–102. Adeli H, Jiang X. dynamic fuzzy wavelet neural network model for structural system identification. J Struct Eng-ASCE 2006;132:102–11. Adeli H, Karim A. Neural network model for optimization of cold-formed steel beams. J Struct Eng-ASCE 1997a;123(11):1535–43. Adeli H, Karim A. Scheduling/cost optimization and neural dynamics model for construction. J Construct Eng M 1997b;123:450–8. Adeli H, Karim A. Fuzzy-wavelet RBFNN model for freeway incident detection. J Transp Eng-ASCE 2000;126:464–71. Adeli H, Kim H. Cost optimization of composite floors using the neural dynamics model. Commun Numer Methods Eng 2001;17:771–87. Adeli H, Panakkat A. A probabilistic neural network for earthquake magnitude prediction. Neural Netw 2009;22:1018–24. Adeli H, Park HS. Counter propagation neural network in structural engineering. J Struct Eng-ASCE 1995a;121:1205–12. Adeli H, Park HS. A neural dynamics model for structural optimization-theory. Comput Struct 1995b;57:383–90. Adeli H, Park HS. Optimization of space structures by neural dynamics. Neural Netw 1995c;8:769–81. Adeli H, Park HS. Fully automated design of superhighrise building structure by a hybrid AI model on a massively parallel machine. AI Magazine 1996;17:87– 93. Adeli H, Samant A. An adaptive conjugate gradient neural network–wavelet model for traffic incident detection. Comput Aided Civil Infrastruct Eng 2000;15:251–60. Ahmadkhanlou F, Adeli H. Optimum cost design of reinforced concrete slabs using neural dynamics model. Eng Appl Artif Intel 2005;18(1):65–72. Dharia A, Adeli H. Neural network model for rapid forecasting of freeway link travel time. Eng Appl Artif Intel 2003;16(7–8):607–13.
Elragal HM. Improving neural networks prediction accuracy using particle swarm optimization combiner. Int J Neural Syst 2009;19(5):387–93. Ghosh-Dastidar S, Adeli H. Wavelet-clustering-neural network model for freeway incident detection. Comput Aided Civil Infrastruct Eng 2003;18(5):325–38. Ghosh-Dastidar S, Adeli H. Improved Spiking neural networks for EEG classification and epilepsy and seizure detection. Integr Comput Aid E 2007;14(3):187–212. Ghosh-Dastidar S, Adeli H. Spiking neural networks. Int J Neural Syst 2009a;19(4):295–308. Ghosh-Dastidar S, Adeli H. A new supervised learning algorithm for multiple spiking neural networks with application in epilepsy and seizure detection. Neural Netw 2009b;22:1419–31. Ghosh-Dastidar S, Adeli H, Dadmehr N. Principal component analysis-enhanced cosine radial basis function neural network for robust epilepsy and seizure detection. IEEE Trans Bio-med Eng 2008;55(2):512–8. Hung SL, Adeli H. Parallel backpropagation learning algorithms on cray Y-MP8/864 supercomputer. Neurocomputing 1993;5(6):287–302. Jiang X, Adeli H. Neuro-genetic algorithm for nonlinear active control of highrise buildings. Int J Numer Methods Eng 2008;75(8):770–86. Karim A, Adeli H. CONSCOM: an OO construction scheduling and change management system. J Construct Eng M 1999;125(5):368–76. Karim A, Adeli H. Comparison of the fuzzy-wavelet RBFNN freeway incident detection model with the California algorithm. J Transp Eng-ASCE 2002;128(1):21–30. Karim A, Adeli H. Radial basis function neural network for work zone capacity and queue estimation. J Transp Eng-ASCE 2003;129(5):494–503. Park HS, Adeli H. A neural dynamics model for structural optimization-application to plastic design of structures. Comput Struct 1995;57(3):391–9. Pritchard WS, Duke DW, Coburn KL. Altered EEG dynamical responsivity associated with normal aging and probable Alzheimer’s disease. Dementia 1991;2:102–5. Puscasu G, Codres B, Stancu A, Murariu G. Nonlinear system identification based on internal recurrent neural networks. Int J Neural Syst 2009;19(2):115–25. Rossello JL, Canals V, Morro A, Verd J. Chaos-based mixed signal implementation of spiking neurons. Int J Neural Syst 2009;19(6):465–71. Rumelhart DE, McClellarnd JL, The PDP Research Group. Parallel distributed processing: Exploration in the microstructure of cognition. Cambridge: MIT Press; 1986. Samant A, Adeli H. Enhancing neural network incident detection algorithms using wavelets. Comput Aided Civil Infrastruct Eng 2001;16(4):239–45. Sankari Z, Adeli H, Adeli A. Intrahemispheric, interhemispheric and distal EEG coherence in Alzheimer’s disease. Clin Neurophysiol; in press. Sankari Z, Adeli H. Wavelet coherence model for diagnosis of Alzheimer’s disease. Clin Neurophysiol; in press, doi:10.1016/j.clinph.2010.09.008. Savitha R, Suresh S, Sundararajan N. A fully complex-valued radial basis function network and its learning algorithm. Int J Neural Syst 2009;19(4):253–67. Sirca G, Adeli H. Neural network model for uplift load capacity of metal roof panels. J Struct Eng-ASCE 2001;127(11):1276–85. Specht DF. Probabilistic neural networks. Neural Netw 1990;3(1):109–18. Tashakori AR, Adeli H. Optimum design of cold-formed steel space structures using neural dynamic model. J Construct Steel Res 2002;58(12):1545–66. Zou W, Chi Z, Lo KC. Improvement of image classification using wavelet coefficients with structured-based neural network. Int J Neural Syst 2008;18(3):195–205.
Contents lists available at ScienceDirect
Journal of Neuroscience Methods journal homepage: www.elsevier.com/locate/jneumeth
Probabilistic neural networks for diagnosis of Alzheimer’s disease using conventional and wavelet coherence Ziad Sankari a , Hojjat Adeli b,∗ a
Departments of Biomedical Engineering, Electrical and Computer Engineering, 470 Hitchcock Hall, 2070 Neil Avenue, Ohio State University, Columbus, OH 43210, USA Departments of Biomedical Engineering, Biomedical Informatics, Civil and Environmental Engineering and Geodetic Science, Electrical and Computer Engineering, Neurological Surgery, and Neuroscience, 470 Hitchcock Hall, 2070 Neil Avenue, Ohio State University, Columbus, OH 43210, USA b
a r t i c l e
i n f o
Article history: Received 27 September 2010 Received in revised form 22 January 2011 Accepted 25 January 2011 Keywords: Alzheimer’s disease EEG Neural networks
a b s t r a c t Recently, the authors presented an EEG (electroencephalogram) coherence study of the Alzheimer’s disease (AD) and found statistically significant differences between AD and control groups. In this paper a probabilistic neural network (PNN) model is presented for classification of AD and healthy controls using features extracted in coherence and wavelet coherence studies on cortical connectivity in AD. The model is verified using EEGs obtained from 20 AD probable patients and 7 healthy/control subjects based on a standard 10–20 electrode configuration on the scalp. It is shown that extracting features from EEG sub-bands using coherence, as a measure of cortical connectivity, can discriminate AD patients from healthy controls effectively when a mixed band classification model is applied. For the data set used a classification accuracy of 100% is achieved using the conventional coherence and a spread parameter of the Gaussian function in a particular range found in this research. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Recently, Sankari et al. (in press) presented an EEG coherence study of the Alzheimer’s disease (AD) and found statistically significant differences between AD and control groups. A drawback of the conventional coherence is that only spectral components are observed without taking into account any temporal information. Time-frequency analysis methods can be used to study the changes in cortical connectivity over time. Sankari and Adeli (in press) present a wavelet coherence investigation of EEG readings acquired from AD patients and healthy controls, as the first attempt to use wavelet coherence to distinguish between AD and controls. This method provides better temporal and spectral information leading to improved results. The study shows a set of statistically significant differences in the wavelet coherence among AD and controls. Temporo-central regions show a significant decrease in wavelet coherence in AD in the delta band. Parietal and central regions show a significant decrease in cortical connectivity of AD with most of their neighbors in the theta and alpha bands. It is concluded that feature extraction via wavelet coherence provides a larger set of statistically significant differences between AD and controls.
∗ Corresponding author. Tel.: +1 614 292 7929. E-mail address: [email protected] (H. Adeli). 0165-0270/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2011.01.027
A number of neural network (NN) models have been developed for pattern recognition and classification since mid-1980s. They include the backpropagation NN developed in the late 1980s (Rumelhart et al., 1986; Hung and Adeli, 1993), counterpropagation NN (Adeli and Park, 1995a; Sirca and Adeli, 2001; Dharia and Adeli, 2003), adaptive conjugate gradient neural network algorithm (Adeli and Hung, 1993, 1994; Adeli and Samant, 2000), recurrent NN (Samant and Adeli, 2001; Puscasu et al., 2009), radial basis function NN (RBNN) (Adeli and Karim, 2000; Karim and Adeli, 2002, 2003; Ghosh-Dastidar et al., 2008; Savitha et al., 2009), wavelet NN (Ghosh-Dastidar and Adeli, 2003; Adeli and Jiang, 2006; Zou et al., 2008), spiking NN (Ghosh-Dastidar and Adeli, 2007; Rossello et al., 2009; Ghosh-Dastidar and Adeli, 2009a,b), neural dynamics models (Adeli and Park, 1995b,c, 1996; Park and Adeli, 1995, 1997; Adeli and Karim, 1997a,b; Karim and Adeli, 1999; Adeli and Kim, 2001; Tashakori and Adeli, 2002; Ahmadkhanlou and Adeli, 2005), neuro-genetic models (Jiang and Adeli, 2008; Elragal, 2009), and the probabilistic neural network (PNN) (Specht, 1990). PNN is often used for classification purposes (Adeli and Panakkat, 2009). In this research, a PNN model is presented for classification of AD and healthy controls. The model uses features the authors extracted in two previous research studies on cortical connectivity in AD. Fig. 1 shows the various steps in the model. PNN is applied to the extracted features most distinguishing the two groups based the lowest p-value obtained in the one way analysis of variance (ANOVA) statistical test.
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Z. Sankari, H. Adeli / Journal of Neuroscience Methods 197 (2011) 165–170
Band-limited EEG
EEG Sub-bands
Ir
I1
A1H
Feature Extraction (Conventional coherence or wavelet coherence)
A2H
Pattern Layer
AhH
Input layer
A1AD A2AD
Summation Layer
Σ
AdAD
Σ
Output
O
Fig. 2. Architecture of PNN for diagnosis of AD.
Classification (PNN)
Decision (AD/Control) Fig. 1. AD diagnosis model.
2. Data acquisition EEGs are obtained from 20 AD probable patients (average age of 74) diagnosed with probable AD as per NINCDS-ADRDA and DSM-III-R criteria and 7 healthy (control) subjects (average age of 71) using a standard 10–20 electrode configuration on the scalp (Pritchard et al., 1991). Recordings from 19 scalp electrodes: Fp2, Fp1, F7, F3, Fz, F4, F8, T3, C3, Cz, C4, T4, T5, P3, Pz, P4, T6, O2, O1 are taken while subjects’ eyes are closed. Temporal behavior is examined by accumulating data at a sampling rate of 128 Hz for epochs of 8 s, resulting in time series of 1024 data points. Digital conversion of the measured analog signal is accomplished with an 8 bit digitizer. A band-pass filter (0.1–30 Hz, −12 dB/octave roll-off) is used to filter the frequency band of interest. EEGs are visually inspected and discriminated to eliminate those time series which contain optical and muscular artifacts. 3. Methods 3.1. Mathematical basis A PNN is made up of four layers: an input layer, a pattern layer, a summation layer, and an output layer with a single node. Fig. 2 shows the architecture of the PNN for diagnosis of AD. The input layer consists of r input nodes. In Fig. 2, h and d are the numbers of healthy and AD training vectors respectively. The pattern layer estimates the probability density function (PDF) of the input vector I using the Parzen window method. The Parzen window method is a non-parametric classifier that creates an estimate of the input PDF by superposition of a number of windows that are replicas of a particular function. In this research, the Gaussian function is used as the Parzen window. The Gaussian function is commonly used to represent data with normal distribution. The probability density function of features in this research has a similar shape to that of normally distributed data. In the pattern
layer, the Euclidean distance between the input vector I and the training vector T, an indication of closeness of the input and the training vectors, is used as the argument of the Gaussian function to estimate the input PDF. Thus, the output of the ith neuron belonging to the cth class, Aic , in the pattern layer is expressed as follows: Aic =
1 (2)r/2 sr
exp −
||I − T ic ||2 2s2
(1)
where Tic is the ith training vector corresponding to the cth class, and s is the spread of the Gaussian function. In Fig. 2, c is denoted with subscripts “H” for healthy and “AD” for the Alzheimer’s disease. The spread parameter s controls the size and shape of the Gaussian PDF. As s increases, the Gaussian window becomes wider and vice versa. An input which is close to the training data is represented by a value for Aic close to one. The estimated PDF is used to compute the Bayesian likelihood ratio and classify the input accordingly. In the summation layer, the outputs of the pattern layer corresponding to class c, Aic , are added together at node c (H or AD) as follows: Ac =
1 (2)r/2 sr
i=N i=1
||I − Tic ||2 exp − 2s2
(2)
where N = h in the neuron corresponding to the healthy class and N = d in the neuron corresponding to the AD class. The PNN model classifies the input vector into a specific class based on the maximum probability or the Bayes’ rule. The output O in the output layer indicates which class the input vector belongs to based on the maximum of the values in the two neurons of the summation layer. The influence of the spread parameter s on the effectiveness of the PNN model for diagnosis of AD is investigated in this research. 3.2. Feature extraction Band-limited EEG is sub-divided into four physiological bands commonly used by physiologists and neurologists: delta (0–4 Hz), theta (4–8 Hz), alpha (8–12 Hz) and beta (12–30 Hz). Each of the sub-bands relates to a particular functional and physiological part of the brain. Only the most promising features are selected. In the coherence study, 11 statistically significant promising features with the lowest p values (p values of less than 0.001) were found for diagnosis of AD. They are electrode pairs T5–Fp1, T5–F3 and T5–C4 in the delta band, electrode pairs Pz–F4 and Pz–T3 in the theta band, electrode pairs P4–FP2, P4–F3 and P4–Fz in the alpha band, and electrode pairs T3–F7, T3–F3 and T3–T5 in the beta band (Table 1).
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Table 1 Features extracted within each band using conventional coherence and wavelet coherence. Band Method
Delta
Theta
Alpha
Beta
Conventional coherence Wavelet coherence
T5–Fp1, T5–F3 and T5–C4 T5–T3, T5–P3, T6–O2, and T5–C3
Pz–F4 and Pz–T3
P4–FP2, P4–F3 and P4–Fz Pz–C3, C3–Fz, F4–Cz, F3–C3, Fz–C3, and Cz–P3
T3–F7, T3–F3 and T3–T5 Cz–F3, Cz–Fz, T5–O1, F3–Cz, Fz–Cz, and C4–T6
T5–T3, P4–Cz, T3–C3, C3–Fz, C4–F4, and Cz–Fz
In the wavelet coherence study, 22 statistically significant features were found having the lowest p values (p-values of less than 0.001). They are electrode pairs T5–T3, T5–P3, T6–O2, and T5–C3 in the delta band, T5–T3, P4–Cz, T3–C3, C3–Fz, C4–F4, and Cz–Fz, in the theta band, Pz–C3, C3–Fz, F4–Cz, F3–C3, Fz–C3, and Cz–P3 in the alpha band, and Cz–F3, Cz–Fz, T5–O1, F3–Cz, Fz–Cz, and C4–T6 in the beta band (Table 1). Each one of the two sets of features is used as mixed band input to a PNN to classify the data into two classes: AD and control subjects. As such, for mixed-band classification the number of input nodes, r (Fig. 2), is equal to 11 for the case of conventional coherence and 22 for the case of wavelet coherence. A similar study is also made using features within each EEG band separately. For example, the four wavelet coherence values of electrode pairs T5–T3, T5–P3, T6–O2, and T5–C3 in the delta band (Table 1) are used as input features in the PNN model. As such, there are 4 + 4 = 8 such studies in the single band investigation phase. In these single-band classifications, the number of features within each band, r, can vary between 2 and 6, depending on how many ‘promising’ features (p value < 0.001) are present within each of these bands.
Fig. 3. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the delta band of the conventional coherence.
3.3. Training The PNN model was trained by randomly dividing the available set of data (20 AD and 7 healthy) into a training set and a testing set. The training set contains features extracted from 3 healthy subjects and 10 AD patients. The testing set is then composed of 4 healthy and 10 AD patients. This process is repeated 100 times and the average values are reported in the performance assessment presented in the next section. The performance of the PNN model is evaluated for different values of the spread parameter, s, to determine a range of optimal values. 4. Results Fig. 4. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the theta band of the conventional coherence.
4.1. Statistical measures to evaluate the model The results are evaluated using three statistical measures from the number of correct and incorrect predictions: detection rate or probability of detection PD , false alarm rate PF , and the misdetection rate PM . The detection rate, PD , is defined as the number of AD subjects identified correctly, Nc , divided by the total number of AD subjects NAD : PD =
NC NAD
(3)
The false alarm rate, PF , is defined as the number of healthy controls identified incorrectly as AD, Nf , divided by the total number of healthy subjects Nh : PF =
Nf Nh
(4)
The misdetection rate PM is defined as the number of AD subjects identified as healthy, Nm , divided by the total number of AD subjects
NAD : PM =
Nm = 1 − PD NAD
(5)
4.2. Classification with conventional coherence Fig. 3 shows the values of misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the delta band. A tradeoff pattern between PM and PF is noted in this figure. The misdetection rate decreases with an increase in the value of the spread parameter. In this band 100% detection (no misdetection) is obtained at s = 0.22 with a false alarm rate as low as 44%. Fig. 4 shows the values of misdetection and false alarm rates as a function of the spread parameter in the theta band. Similar to what is observed in the delta band (Fig. 3) the misdetection rate decreases with an increase in the value of the spread parameter,
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Fig. 5. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the alpha band of the conventional coherence.
Fig. 7. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter using mixed band features of the conventional coherence.
Fig. 6. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the beta band of the conventional coherence.
Fig. 8. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the delta band of the wavelet coherence.
whereas the false alarm rate increases with an increase in the value of the spread parameter. The same observation is noted in the alpha and beta bands. In the theta band, 100% detection (no misdetection) is obtained at s = 0.30 with a false alarm rate of 45%. Fig. 5 shows the values of misdetection and false alarm rates as a function of the spread parameter in the alpha band. In this band, 100% detection (no misdetection) is obtained at s = 0.32 with a false alarm rate of 42%. Fig. 6 shows the values of misdetection and false alarm rates as a function of the spread parameter in the beta band. In this band, 100% detection (no misdetection) is obtained at s = 0.30 with a false alarm rate of 58.75%. In all cases where single band features were investigated, a tradeoff between the misdetection and the false alarm rates is observed. Finally, the 11 statistically significant features identified in all bands are used as input to the PNN model (mixed band feature detection). Fig. 7 shows the misdetection and false alarm rates as a function of the spread value s using mixed band features of the conventional coherence. A detection rate of 100% with a false alarm rate of 0% is obtained for spread values s in the range 0.32–0.42.
parameter. In this band, a misdetection rate of 5.9% (detection rate of 94.1%) is obtained at s = 0.45 with a false alarm rate of 57.75%. Fig. 9 shows the values of misdetection and false alarm rates as a function of the spread parameter in the theta band. A misdetection rate of 3.9% (detection rate of 96.1%) is obtained at s = 0.35 for an improved false alarm rate of 20% compared with the conventional coherence.
4.3. Classification with wavelet coherence Fig. 8 shows the values of misdetection and false alarm rates as a function of the spread parameter in the delta band. The misdetection rate decreases with an increase in the value of the spread
Fig. 9. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the theta band of the wavelet coherence.
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Fig. 10 shows the values of misdetection and false alarm rates as a function of the spread parameter in the alpha band. A misdetection rate of 4.1% (detection rate of 95.9%) is obtained at s = 0.18 for an improved false alarm rate of 10.75% compared with the conventional coherence. Fig. 11 shows the values of misdetection and false alarm rates as a function of the spread parameter in the beta band. No misdetection rate (or 100% detection rate) is obtained at s = 0.38 for an improved false alarm rate of 37% compared with the conventional coherence. Similar to what is observed in the conventional coherence study, a tradeoff exists between the misdetection and false alarm rates. In all but the alpha band, the false alarm rate is relatively steady over a large range of the spread parameter despite the decrease in the misdetection rate. Finally, the features identified in all bands are used as input to the PNN model. The model performs worse than in the case of conventional coherence features as seen in Fig. 12. The best performance for the mixed band case, PD = 100% and PF = 18.25% is observed for a spread value s = 0.05. The model, however, maintains a steady misdetection and false alarm rates for a larger range of the spread parameter s. 5. Discussion In the single-band case PNN yields similar results for both conventional coherence and wavelet coherence in the delta band.
Fig. 10. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the alpha band of the wavelet coherence.
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Fig. 12. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter using mixed band features of the wavelet coherence.
Wavelet coherence shows improved performance in the theta, alpha and beta bands. This is predictable since the dimension of information in wavelet coherence is larger, accounting for changes in both time and frequency concurrently. Features extracted in the beta band appear to be the worst performing for both conventional and wavelet coherence using the PNN classification model. A possible explanation of this observation is the large bandwidth in the beta band where resolution of information decreases significantly as the band undergoes more and more processing, especially when compared with the other bands with smaller bandwidth. The results of single-band analysis for both conventional and wavelet coherence, however, are not accurate enough for AD diagnostic applications. Even though the wavelet coherence method yields a larger set of statistically significant differences between AD subjects and controls, the conventional coherence features in the mixed band case perform better than those obtained from the wavelet coherence method. In fact, for the given set of data, a classification accuracy of 100% with 0% false alarm rate is achieved using the conventional method at a spread value, s, between 0.32 and 0.42. A possible explanation why wavelet coherence does not perform as well in the mixed band analysis is the limited variability between the wavelet coherence fractions of AD and control groups within different bands, which results in poor PNN classification. It is also observed in this research that as s increases, the false alarm rate increases and misdetection rate decreases. This phenomenon is explained by the fact that the spread parameter controls the shape of the Gaussian function used in estimating the PDF of the input data. As the spread value decreases, the Gaussian curve becomes very narrow and discrimination among elements that do not belong to the training set becomes more difficult, the AD cases can not be well detected and, hence, misdetection rate increases. 6. Conclusion
Fig. 11. Misdetection and false alarm rates (PM and PF ) as a function of the spread parameter in the beta band of the wavelet coherence.
This study demonstrates that extracting EEG features using coherence, as a measure of cortical connectivity, can discriminate AD patients from healthy controls effectively especially when the mixed band classification model is applied. This research suggests that coherence studies can provide statistically significant features which help classify between AD and healthy subjects. In this research, for the data set used, a classification accuracy of 100% is achieved using conventional coherence and a spread parameter in a particular range found. A larger sample size and a more variant data set are needed in order to generalize the findings of this
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