Engineering Data Analysis & Modeling Practical Solutions to Practical Problems Dr. James McNames Biomedical Signal Processing Laboratory Electrical & Computer Engineering Portland State University

Course Overview Key question: How to extract useful information from data? Some theory Mostly methods & applications Problem oriented, not technology focused Project course

Talk Overview Problem definitions Applications Project ideas Course specifics

Problem Definitions Preprocessing (briefly) –Variable selection –Dimension reduction Decision theory (hypothesis testing) Density estimation Nonlinear optimization Pattern recognition/Classification (very briefly) Nonlinear modeling (univariate & multivariate)

Variable Selection Many algorithms fail if too many inputs Often fewer inputs are sufficient due to –Redundant inputs –Irrelevant inputs Goal: Find a subset of inputs that maximizes model accuracy Is Greenspan’s BP relevant?

Dimension Reduction Redundant inputs can also be combined into a smaller composite set –Improves accuracy –Reduces computation If done well, minimal information is lost Used for signal compression Principal component analysis is most common

Dimension Reduction Example 1

Dimension Reduction Example 2

Nonlinear Optimization Find the vector a such that E(a) is minimized Many algorithms have parameters that must be “fit” to the data Usually “fit” by minimizing error measure Sometimes subject to a constraint G(a) = 0 Unconstrained optimization more common Very widely used Many engineering applications

Pattern Recognition Closely related to nonlinear modeling Goal is to identify most likely category given an input vector Equivalent to drawing decision boundaries Following example –Crab data –Four categories –Two composite inputs

Crabs Data Set

Biomedical Application Goal: identify brain cell types from microrecordings Current research project 5 categories of cell types Created metrics to characterize signals Following scatterplot shows 2 of these metrics

Neurosurgery Example

Nonlinear Modeling Given many examples of observed variables, create a model that can predict the output No other assumed knowledge Observed variables –Quantitative –Measurable

Nonlinear Modeling Observed variables may not be causal Not all causal effects are observed Model will not be perfect How do you measure how good the model is?

Smoothing For single-input single-output (SISO) systems, can plot the data Problem is to estimate a curve that most accurately predicts future points Could draw a smooth curve by hand More difficult to implement automatically More than one curve may be reasonable

Smoothing Example

Multiple “Reasonable” Solutions

Nonlinear Modeling Many methods do not work well Usually is much more difficult –Noise –Multiple inputs –Time-varying system –Small data sets Still an active area of research Will discuss "tried and true” solutions

Overview of Course Introduction & review Linear models Univariate smoothing Optimization algorithms Nonlinear modeling Pattern recognition & classification

Application Areas Engineering –Controls (system identification) –Signal processing (estimation & prediction) –Communications (channel equalization) Statistics Mathematics Computer science Systems science

Application Examples Time series prediction –Aircraft carrier landing systems Spatial Wafer Patterns Fault Detection Machinery health monitoring Automated, objective credit rating Fraud detection

Time Series Prediction

Spatial Wafer Patterns

Wafer Components

Estimation (Regression) Results

Fault Detection in Semiconductor Manufacturing

Aircraft Carrier Landing System Can be very hard –Limited visibility –Rough seas –Night Predict location at touch down –Flight deck –Aircraft Is rocking of flight deck predictable?

Machinery Health Monitoring Cost of machinery failure can be very high Recent growth in real-time monitoring –Health and Usage Monitoring Systems (HUMS) –Condition Based Maintenance (CBM) Reduce costs Increase safety

Fraud Detection Credit card fraud cost $864 million in 1992 How quickly can fraud be detected? The companies have amassed large data bases What are the patterns of fraud? Active area of research

Past Projects Many past projects –See reports & slides on the web Many time series applications –Need not be time series related Many have resulted in conference and journal publications Expect improved quality this term

Project Ideas It is up to you to identify a project Preferred –Data readily available (no new instrumentation or study design) –Independent samples (not time series data) –Engineering related –High likelihood of success (no financial forecasting)

Course Logistics Project oriented –Project reports –Must meet IEEE journal requirements –May be encouraged to publish –Brief oral slide presentation at end of term Most projects are applied May also create new methods or compare existing methods

Prerequisites Helpful –Random processes (ECE 565) –Signal processing (ECE 566) –Proficient at MATLAB or similar Required –Calculus –Probability & statistics (STAT 451) –Linear algebra (MTH 343) –Proficiency at programming