Optimization-Based Data Mining Approaches in Neuroscience Research

1. Optimization-Based Data Mining Approaches in Neuroscience Research Panos M. Pardalos University of Florida

2. Introduction • Data Mining: “the practice of searching through large amounts of computerized data to find useful patterns or trends.” • Optimization: “An act, process, or methodology of making something (as a design, system, or decision) as fully perfect, functional, or effective as possible; specifically : the mathematical procedures (as finding the maximum of a function) involved in this.” Merriam Webster Dictionary

3. Introduction • The combination of data mining and optimization: • Find the “best” way to extract meaningful “patterns” from data. • Not always an easy task.

4. How difficult Optimization can be? • Given integers N1,N2,…,Nk and M find a subset of N1,N2,…,Nk such that their sum is equal to M. • Can you find a better algorithm than of O(2k). • Exponential complexity ?

5. Hard drive Cost • Approximately 1/10 cheaper every 5 years

6. Hard Drive Capacity • Approximately 10 times more every 5 years

7. Processing power • Number of transistors of a computer processor double every two years

8. References • Handbook of Massive Data Sets, co-editors: J. Abello, P.M. Pardalos, and M. Resende, Kluwer Academic Publishers, (2002).

9. Main problems in data mining • Data preprocessing • Dimensionality reduction • Feature selection • Regression • Clustering (Unsupervised learning) • Classification (Supervised Learning) • Semi-Supervised learning (between unsupervised and unsupervised) • Biclustering • Result Validation • Data Visualization/Representation • Biomedical Informatics is a challenging area with lots of these problems.

10. Agenda • Research Background • Epilepsy • Seizure Prediction • Sources of Data • Electroencephalogram (EEG) Time Series • Dimensionality Reduction • Chaos Theory • Feature Selection for Brain Monitoring • Time Series Classification of Neuro-Physiological States • Brain Clustering • Brain Network Models • Concluding Remarks

11. Facts About Epilepsy • At least 2 million Americans and other 40-50 million people worldwide (about 1% of population) suffer from Epilepsy. • Epilepsy is the second most common brain disorder (after stroke) that causes recurrent seizures. • Epileptic seizures occur when a massive group of neurons in the cerebral cortex suddenly begin to discharge in a highly organized rhythmic pattern.

12. Epileptic Seizures • Seizures usually occur spontaneously, in the absence of external triggers. • Seizures cause temporary disturbances of brain functions such as motor control, responsiveness and recall which typically last from seconds to a few minutes. • Seizures may be followed by a post-ictal period of confusion or impaired sensorial that can persist for several hours.

13. Normal Pre-Seizure Post-Seizure Seizure Onset 10-second EEGs: Seizure Evolution

14. Why do we care? • Based on 1995 estimates, epilepsy imposes an annual economic burden of $12.5 billion* in the U.S. in associated health care costs and losses in employment, wages, and productivity. • Cost per patient ranged from $4,272 for persons** with remission after initial diagnosis and treatment to $138,602 for persons** with intractable and frequent seizures.

15. Current Epilepsy Treatment • Pharmacological Therapy • Anti-Epileptic Drugs (AEDs) • Mainstay of epilepsy treatment • Approximately 25 to 30% remain unresponsive • Epilepsy Resective Surgery • Require long-term invasive EEG monitoring to locate a specific, localized part of the brain where the seizures are thought to originate • 50% of pre-surgical candidates do not undergo respective surgery • Multiple epileptogenic zones • Epileptogenic zone located in functional brain tissue • Only 50-60% of surgery cases result in seizure free

16. Current Epilepsy Treatment • Electrical Stimulation (Vagus nerve stimulator) • Parameters (amplitude and duration of stimulation) arbitrarily adjusted • As effective as one additional AED dose • Side Effects • Seizure Prediction? • Monitoring Unit? • Forecasting Impending Seizures? • Seizure Control? • Deep Brain Stimulator?

17. Electroencephalogram (EEG) • …is a traditional tool for evaluating the physiological state of the brain. • …offers excellent spatial and temporal resolution to characterize rapidly changing electrical activity of brain activation • …captures voltage potentials produced by brain cells while communicating. • In an EEG, electrodes are implanted in deep brain or placed on the scalp over multiple areas of the brain to detect and record patterns of electrical activity and check for abnormalities.

18. From Microscopic to Macroscopic Level (Electroencephalogram - EEG)

19. Electrode Montage and EEGs

20. Scalp EEG Data Acquisition

21. Open Problems • Is the seizure occurrence random? • If not, can seizures be predicted? • If yes, are there seizure pre-cursors (in EEGs) preceding seizures? • If yes, what data mining techniques can be used to indicate these pre-cursors? • Does normal brain activity during differ from abnormal brain activity?

22. Goals of Research • Test the hypothesis that seizures are not a random process. • Demonstrate that seizures could be predicted • Feature Selection to identify seizure pre-cursors (Statistical Process Control) • Demonstrate that normal and abnormal EEGs can be differentiated • Time Series Classification • Better understand the epileptogenic process – how seizures are initiated and propagated. • Brain Clustering • Develop a closed-loop seizure control device (Brain Pacemaker)

23. Dimensionality Reduction Chaos Theory

24. EEGs with the Curse of Dimensionality • The brain is a non-stationary system. • EEG time series is non-stationary. • With 200 Hz sampling, 1 hour of EEGs is comprised of 200*60*60*30 = 21,600,000 data points = 43.2MB (assume 16-bit ASCI format) • 1 day = 1.04GB • 1 week = 7.28GB • 20 patients ≈0.15TB → Terabytes → Gigabytes → Megabytes Kilobytes

25. Data Transformation Using Chaos Theory • Measure the brain dynamics from time series: • Stock Market • Currency Exchanges (e.g., Swedish Kroner) • Apply dynamical measures (based on chaos theory) to non-overlapping EEG epochs of 10.24 seconds = 2048 points. • Maximum Short-Term Lyapunov Exponent • measure the average uncertainty along the local eigenvectors and phase differences of an attractor in the phase space • measure the stability/chaoticity of EEG signals

26. Measure of Chaos

27. Pre-Seizure Seizure Onset Post-Seizure STLmax Profiles

28. Hidden Synchronization Patterns

29. Then, we calculate the average value, ,and the sample standard deviation, , of . How similar are they?Statistics to quantify the convergence of STLmax By paired-T statistic: Per electrode, for EEG signal epochs i and j, suppose their STLmax values in the epochs (of length 60 points, 10 minutes) are The T-index between EEG signal epochs i and j is defined as

30. Statistically Quantifying the Convergence

31. Convergence of STLmax

32. Not every electrode site shows the convergence. Feature Selection: Select the electrodes that are most likely to show the convergence preceding the next seizure. Why Feature Selection?

33. Feature Selection Quadratic Integer Programming with Quadratic Constraints

34. Optimization Problem • Optimization: • We apply optimization techniques to find a group of electrode sites such that … • They are the most converged (in STLmax) electrode sites during 10-min window before the seizure • They show the dynamical resetting (diverged in STLmax) during 10-min window after the seizure. • Such electrode sites are defined as “critical electrode sites”. • Hypothesis: • The critical electrode sites should be most likely to show the convergence in STLmax again before the next seizure.

35. Notation and Modeling • x is an n-dimensional column vector (decision variables), where each xi represents the electrode site i. • xi= 1 if electrode i is selected to be one of the critical electrode sites. • xi= 0 otherwise. • Qis an (nn) matrix, whose each element qijrepresents the T-index between electrode i andj during 10-minute window before a seizure. • bis an integer constant. (the number of critical electrode sites) • Dis an (nn) matrix, whose each element dijrepresents the T-index between electrode i andj during 10-minute window after a seizure. • α = 2.662*b*(b-1), an integer constant. 2.662 is the critical value of T-index, as previously defined, to reject H0: “`two brain sites acquire identical STLmax values within 10-minute window”

36. Multi-Quadratic Integer Programming • To select critical electrode sites, we formulated this problem as a multi-quadratic integer (0-1) programming (MQIP) problem with … • objective function to minimize the average T-index among electrode sites • a linear constraint to identify the number of critical electrode sites • a quadratic constraint to ensure that the selected electrode sites show the dynamical resetting

37. Conventional Linearization Approach for Multi-Quadratic 0-1 Problem

38. Theoretical Results:MILP formulation for MQIP problem • Consider the MQIP problem • We proved that the MQIP program is EQUIVALENT to a MILP problem with the SAME number of integer variables. Equivalent

39. Empirical Results:Performance on Larger Problems

40. Hypothesis Testing - Simulation • Hypothesis: • The critical electrode sites should be most likely to show the convergence in STLmax (drop in T-index below the critical value) again before the next seizure. • The critical electrode sites are electrode sites that • are the most converged (in STLmax ) electrode sites during 10-min window before the seizure • show the dynamical resetting (diverged in STLmax ) during 10-min window after the seizure • Simulation: • Based on 3 patients with 20 seizures, we compare the probability of showing the convergence in STLmax (drop in T-index below the critical value) before the next seizure between the electrode sites, which are • Critical electrode sites • Randomly selected (5,000 times)

41. Optimal VS Non-Optimal

42. Simulation - Results

43. Statistical Process Control:How to automate the system?

44. Automated Seizure Warning System ASWA Monitor the average T-index of the critical electrodes Continuously calculate STLmax from multi- channel EEG. Select critical electrode sites after every subsequent seizure EEG Signals Give a warning when T-index value drops below a critical value

45. Data Characteristics

46. Performance Evaluation for ASWS • To test this algorithm, a warning was considered to be true if a seizure occurred within 3 hours after the warning. • Sensitivity = • False Prediction Rate = average number of false warnings per hour

47. Training Results Performance characteristics of automated seizure warning algorithm with the best parameter-settings of training data set.

48. RECEIVER OPERATING CHARACTERISTICS (ROC) • ROC curve (receiver operating characteristic) is used to indicate an appropriate trade-off that one can achieve between: • the false positive rate (1-Specificity, plotted on X-axis) that needs to be minimized • the detection rate (Sensitivity, plotted on Y-axis) that needs to be maximized.

49. Test Results Performance characteristics of automated seizure warning algorithm with the best parameter settings on testing data set.

50. Validation of the ASWS algorithm • Temporal Properties • Surrogate Seizure Time Data Set • 100 Surrogate Data Sets • Spatial Properties • Non-Optimized ASWS – Selecting non-optimal electrode sites • 100 Randomly Selected Electrodes