Thesis Ph. Display Statistics. Search our collections Search this site:. ABC Copyright Conference Action for Health Cross Thematic Materials. Recent items Preventing youth substance misuse: Programs that work in schools. Treating substance misuse in young people. Helping children who have been maltreated. Preventing child maltreatment. Research process and sleep app design lessons learned from the reflective examination of a sleep study.
The difference between the o r i g i n a l measured s i g n a l and the estimated s i g n a l i s considered to be additive o u t l i e r content see Section 4.
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The o u t l i e r content i s then processed see Section 4. The objective of the cleaning process i s to provide an estimate of the o r i g i n a l s i g n a l without the AO content. Note that with the s c a l i n g given 4. Hampel's three part redescending p s i function  was used i n Equation 4. A GM1 estimate i s based on the estimated cleaned time ser i e s and a GM2 estimate i s a further i t e r a t i o n where the parameters from GM1 are used i n the cleaner to provide a t h e o r e t i c a l l y improved estimate of the cleaned time s e r i e s.
Through the simulation studies described i n Section 3. Each segment i s modeled at the order expected for i d l e task EEG and hence, reducing the a b i l i t y of the model to account for active task information i n the EEG see Section 4. The s i g n a l from each segment i s then cleaned using the estimated model parameters i n the cleaner described i n Section 4. The o u t l i e r s are then calculated by taking the diff e r e n c e between the o r i g i n a l and cleaned signals see Figure 4. This t e s t confirmed that the extraction process had some d i s t i n c t a b i l i t y to recover the o u t l i e r content from the simulated s i g n a l.
Patchy contamination was used since i t was expected that i n the case of r e a l EEG the additive event r e l a t e d p o t e n t i a l s would be correlated. As suggested by Martin and Zeh  , the correlated v a l u e s f o r v. This procedure r e s u l t s i n a correlated o u t l i e r series which has roughly the same variance as i n the independent case .
It was found i n t h i s a p p l i c a t i o n that the tuning parameters for the p s i function given i n Equation 4. Figures 4. OOO It i s clear from these examples that the process performs better with GM2 estimates than with GM estimates and much better than with LSQ estimates.
Since these t e s t s revealed three c l e a r l y discernable jumps i n performance i n using LSQ, GM, and GM2 parameter estimates, i t was decided that subsequent studies using o u t l i e r detection i n t h i s t h e s i s work would be r e s t r i c t e d to those three estimation methods. The o u t l i e r pattern i s then smoothed by convolving i t with a 16 point tapered smoothing window which i s based on a minimum-bias sp e c t r a l window suggested by Papoulis .
As w e l l , these studies were instrumental i n e s t a b l i s h i n g appropriate EEG segment lengths and a procedure for the s e l e c t i o n of the AR model order. Since the term S e f applies to the residuals which are i n theory white, the r e s u l t i n g power density function of the residuals should be f l a t and t h e r e f o r e S e f w i l l be a constant independent of frequency.
Id e a l l y , the value of t h i s constant noting that the mean of the residuals i s zero w i l l be proportional to the variance of the residuals [A6]. Hence, the f i n a l expression for the conventional AR spe c t r a l estimate i s obtained by r e p l a c i n g S f i n A. Single t r i a l AR sp e c t r a l estimates from adjacent one second segments demonstrated that considerable change i n si g n a l c h a r a c t e r i s t i c s could occur over t h i s span of two seconds.
An example of t h i s i s provided i n Figure A. I t contains four consecutive AR spe c t r a l p l o t s , each derived from a one second segment of 61 Figure 4. As was discussed i n Section 3.
This was an attempt to trade o f f the need for short segments because of the r e l a t i v e l y r a pid changing signal c h a r a c t e r i s t i c s with the desire to r a i s e the segment length above the lower bound for purposes of improving the parameter estimation e f f i c a c y. It was found that s e l e c t i n g the model order v i a conventional methods such as Akaike's Information C r i t e r i a AIC does not work well with these short segments .
Conclusions were s i m i l a r to Jansen  i n that the s e l e c t i o n of an appropriate model order requires some t r i a l and error and, i f possi b l e , some a - p r i o r i knowledge of expected r e s u l t s. I t was found useful to t r y a number of orders within a reasonable range for a sample rate of 64Hz, somewhere between 8 to 25 , following the trend of the estimate as the model order was increased. Features were i d e n t i f i e d that seemed reasonable based on both the a - p r i o r i knowledge of the condition under which the EEG was c o l l e c t e d and a conventional FFT based estimate.
The order was sequentially increased, expecting the features to become better defined, u n t i l spurious peaks began to occur. The appropriate model order was then selected to be two or three below that value. T y p i c a l l y , model orders were selected i n the range of 12 to 14 from subjects during the i d l e task and i n the range of 18 to 22 from subjects during the active task.
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The r e s i d u a l s i g n a l can be thought of as a whitened si g n a l because the information that can be represented by an AR model has been subtracted r e s u l t i n g i n a si g n a l with a much f l a t t e r spectrum. When the FFT i s applied to t h i s prewhitened signal the inherent drawback of leakage i s gre a t l y reduced. A p p l i c a t i o n of conventional leakage c o n t r o l , such as Blackman windowing, serves to further reduce t h i s problem.
The prewhitened AR estimation method, therefore, combines the spe c t r a l information from both the AR model and the re s i d u a l FFT spe c t r a l estimate. Some i n s i g h t into the a b i l i t y of the AR model to represent short segments of EEG was gained by pursuing studies using prewhitened AR spe c t r a l estimates. These studies demonstrated that when an appropriate model order was u t i l i z e d the conventional AR spe c t r a l estimates were reasonably good compared to the prewhitened AR estimate which makes use of information retained i n the residuals see Birch et a l.
This indicates that the AR model, although not perfect, does represent much of the information contained i n a short segment of EEG. An example of both a conventional and a prewhitened 12th order AR spe c t r a l estimate of i d l e task EEG i s given i n Figure 4. Figure A. Motor p o t e n t i a l a c t i v i t y i n the active case should occur, approximately, during the f i r s t three seconds of the epoch, noting that the actual thumb movement began one second into the epoch.
These pl o t s demonstrate that the conventional averaging technique reveals some d i s t i n c t motor a c t i v i t y i n the o r i g i n a l active case raised l e v e l of p o s i t i v i t y i n the averaged s i g n a l during the f i r s t three seconds with a peak at about two seconds. Results provided i n the following sections demonstrate that the information i n these o u t l i e r patterns i s r e l a t e d to the thumb movements. As w e l l , for comparison purposes, a p l o t of the conventional average for the active case i s also included i n t h i s f i g u r e.
The fact that the average active case patterns maintain a general shape s i m i l a r to the s i n g l e t r i a l patterns, strongly indicates that there i s information r e l a t e d to the thumb movement that i s consistent from t r i a l to t r i a l. The conventional average of active t r i a l s shows that with N's of 6 and 15 the motor p o t e n t i a l information i s quite l i m i t e d and the "smearing" e f f e c t of event r e l a t e d information that i s discussed above for the active case o u t l i e r patterns would also be occurring i n these conventional averages.
Hence, with the conventional averaging method, even with much greater N's as i n the case of the Grunewald study see Section A. A LSQ Active O u t l i e r Patterns Degrading with Higher Model Orders It would also be expected, based on the neurological premise, that the single t r i a l processing method would perform best when the AR model order was selected to best f i t the i d l e case. As the model order i s increased the AR model would be expected to gain some improved a b i l i t y to represent the motor r e l a t e d a c t i v i t y i n the active task EEG.
Hence, the performance of the sin g l e t r i a l method should begin to degrade since the cleaning process, which u t i l i z e s the higher order AR model, would lose some of i t s effectiveness i n 78 detecting motor r e l a t e d o u t l i e r s. A p a i r of averaged active o u t l i e r pattern p l o t s using LSQ parameters for model order 12 generally appropriate for the i d l e case and model order 22 generally appropriate for the active case are shown i n Figure 4.
These p l o t s demonstrate that the performance does degrade, i n terms of both the amplitude and the d e t a i l of features i n the averaged o u t l i e r pattern, when the model order i s better matched to the active case. The patterns, although unique from t r i a l to t r i a l , do seem to posses a generally consistent waveform which contains features that appear r e l a t e d to events i n the thumb movements. The features are described below and are shown i n Figure 4. Feature 1: Time from epoch onset to the point when the thumb movement f i r s t reaches the "on target" p o s i t i o n.
Feature 2: Time from epoch onset to the point when the thumb movement f i r s t leaves the "on target" p o s i t i o n.
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Feature A: Time from epoch onset to the f i r s t negative peak i n the o u t l i e r pattern a f t e r feature 3, that has a minimum of 5 units magnitude peak-to-trough d i f f e r e n c e. Feature 5: Time from epoch onset to the next p o s i t i v e peak i n the o u t l i e r pattern a f t e r feature A, that has a minimum of 20 units magnitude peak-to-trough diffe r e n c e on both sides of the peak.
There was an expectation r e s u l t i n g from the e a r l i e r conventional study by Grunewald and Grunewald-Zuberbier  and from observations taken from Figure A. The sample c o r r e l a t i o n c o e f f i c i e n t s between a l l of the features from Subject 1 were calculated and are summarized i n Table A.
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Hence, t h i s demonstrates that there i s a strong consistent r e l a t i o n s h i p between features i n the thumb movement and features i n the sing l e t r i a l o u t l i e r pattern. In p a r t i c u l a r , the r e l a t i o n s h i p between features i n the o u t l i e r pattern and i n the thumb movement was examined using the z-test for the difference between c o r r e l a t i o n s calculated on dependent samples see Steiger [5A].
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The r e s u l t s from these t e s t s are also summarized i n Table A. As expected, the c o r r e l a t i o n between feature 5 and feature 2 was larger than that between feature 5 and feature 1, but t h i s difference achieved only a marginal l e v e l of s i g n i f i c a n c e. These i n i t i a l i n v e s t i g a t i o n s , revealed that the use of dynamic time warping DTW provided the best quantitative measure of performance for the s i n g l e t r i a l processing method compared to the other previous a n a l y s i s.