Using Benford s Law to Detect Anomalies in Electroencephalogram: An Application to Detecting Alzheimer s Disease

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1 Using Benford s Law to Detect Anomalies in Electroencephalogram: An Application to Detecting Alzheimer s Disease Santosh Tirunagari, Daniel Abasolo, Aamo Iorliam, Anthony TS Ho, and Norman Poh University of Surrey, UK and QuintilesIMS, London IEEE International Conference on Computational Intelligence in Bioinformatics and Computational Biology (IEEE CIBCB 2017),

2 Motivation Alzheimer s disease (AD) is the most common type of dementia, affecting an estimated 850,000 people in the UK. Progressive neurological disease, affecting multiple brain functions, including memory. Necropsy can alone confirm the diagnosis of AD. However, typically diagnosed primarily on the basis of mental health tests [1] Electroencephalograms (EEGs), are an interesting alternative diagnostic tool because they are non-invasive and affordable. EEGs of AD patients dominate lower frequencies (in a spectrogram) are less complex contain more regular patterns compared to those of healthy subjects [2 3] 2/??

3 Our Proposal A pipeline for differentiating AD patients from the healthy ones based on their EEG signals. Our method Feature extraction inspired by Benford s law, i.e., First Digit Features (FDF) of temporal derivates of EEG signals Classification: support vector machines (SVMs) with a radial basis function (RBF) kernel The classification performance is evaluated by the half total error rate (HTER). 3/??

4 Benford s Law Benford s law describes the distribution of the first digit from a set of numbers. Define: x = D 1 (x ) D 1 (1.414) = 1 D 1 (0.482) = 4 D 1 (24.56) = 2 The law is expressed by: p(x) = log 10 (x + 1) log 10 (x) = log 10 ( x + 1 ) x (1) = log 10 (1 + 1 x ) where the leading digit x {1,..., 9} is the first digit of the number and p(x) refers to the probability distribution of x. 4/??

5 Probability distribution of Benford s law A typical distribution of digits according to Benford s law can be seen below Probability First Digit Figure: Probability distribution of Benford s law 5/??

6 Feature Extraction & Classification Details The first digit features (FDFs) from Benford s law are given as input to the SVMs, with a Radial Basis Function (RBF) kernel kernel scale σ = 1 box constraint value set to 1 Performance was evaluated using 10-fold cross validation, repeated 20 times, optimizing Half total error rate (HTER) 6/??

7 Evaluation Analysing the error based on FAR (False Acceptance Rate), False Rejection Rate (FRR), and Half Total Error Rate (HTER) 7/??

8 Dataset The database used in this pilot study included 11 patients with a diagnosis of probable (moderate) AD 5 men; 6 women; age: 72.5 ± 8.3 years 11 age-matched controls 7 men; 4 women; age: 72.8 ± 6.1 The international electrode system was used in a resting, awake state with eyes closed. 5-second artefact free epochs were selected from the 22 subjects The total number of artefact-free epochs available for analysis was from AD patients 4201 from control subjects On average, 28.0 ± 15.1 epochs were available from each electrode and each subject. 8/??

9 Experiments 1. Do EEG signals follow Benford s law? 2. Effect of time-derivatives of EEG signals. We investigate whether temporal derivative in EEG signals can improve the classification performance. 3. Importance of electrode. We investigate the performance obtained using each electrode, in terms of the HTER. 4. Cross subject evaluation. This ensures that each patient s data belongs to a single fold, thereby ensuring that we train on a set of subjects distinct from those used for testing. 9/??

10 1: Raw EEG signals Our results show that most of the raw EEG signals did not follow Benford s law for both AD patients and the controls as their deviation from the Benford s law is greater Probabilities Benford's law First digits Figure: First digit probabilities of electrode O1 on raw EEG signals. (Top) Alzheimer s patients and (bottom) control subjects. * in the Figure represents the true probabilities of first digits according to Benford s law. 10/??

11 2: Time-derivatives of EEG signals Most of the time-derivatives in EEG signals follow Benford s law as their deviation from the Benford s law is lower when compared to raw EEG signals EEG diff EEG Probabilities Benford's law Benford's Divergence First digits Figure: (Left) χ 2 divergence of first digit probabilities of all the electrodes from raw EEG signals as well as EEG with its time-derivatives. Greater divergence values indicate greater deviation from Benford s law. (Right) Lower outliers when compared to raw EEG signals, (*) indicate the true probabilities. Top: AD patients; bottom: control 11/??

12 3: Importance of electrodes Electrode C4 gave HTER of ± 0.03, which is the minimum when compared to other electrodes followed by O1 with HTER of ± Both electrodes showed consistently low HTER values mean WER 0.3 mean WER C3 C4 F3 F4 F7 F8 Fp1 Fp2 O1 O2 P3 P4 T3 T4 T5 T C3 C4 F3 F4 F7 F8 Fp1 Fp2 O1 O2 P3 P4 T3 T4 T5 T6 std WER std WER C3 C4 F3 F4 F7 F8 Fp1 Fp2 O1 O2 P3 P4 T3 T4 T5 T6 Electrodes (a) C3 C4 F3 F4 F7 F8 Fp1 Fp2 O1 O2 P3 P4 T3 T4 T5 T6 Electrodes Figure: Mean and standard deviations of the HTER over 20 runs of 10 fold cross validation. (a) raw EEG (b) time-derivatives. (b) 12/??

13 4: Subject-level cross-validation 13/??

14 4: Subject-level cross-validation results 14/??

15 4: Subject-level cross-validation results 2-3 subjects with AD are present in the test set. The results show an increase in the HTER across all electrodes. So, the classification model was positively biased when cross validation was not performed at the subject level. Despite an increase in the HTER is seen across all the electrodes, the results were consistent with the results at epoch level. Electrodes O1 and C4 still proved to be the best at discriminating between the AD patients and the controls. 15/??

16 Take away We presented a method for discriminating between AD and healthy patients based on their EEG signals using first digit features from Benford s law and SVMs with an RBF kernel. We found that in our evaluation with mean HTER, varying substantively between electrodes both in the epoch- and subject-level experiments. Electrodes O1, C4 and O2 showed high discriminating power across both experiments. With the relevance of this to a neurophysiological point of view, electrode O2 is one of the electrodes we tend to see differences between in both groups, but C4 is not usually flagged up with the non-linear methods [2 3]. 16/??

17 Acknowledgement ST and NP have benefited by the Medical Research Council project Modelling the Progression of Chronic Kidney Disease [grant number MR/M023281/1]. The project details can be found at 17/??

18 References 1. McKhann, Guy M., et al. The diagnosis of dementia due to Alzheimer s disease: Recommendations from the National Institute on Aging-Alzheimer s Association workgroups on diagnostic guidelines for Alzheimer s disease. Alzheimer s & dementia 7.3 (2011): Abasolo, Daniel, et al. Analysis of regularity in the EEG background activity of Alzheimer s disease patients with Approximate Entropy. Clinical Neurophysiology (2005): Abasolo, Daniel, et al. Analysis of EEG background activity in Alzheimer s disease patients with Lempel-Ziv complexity and central tendency measure. Medical engineering & physics 28.4 (2006): F. Benford, The law of anomalous numbers, Proceedings of the American Philosophical Society, vol. 78, pp , /??