Improving Template Based Spike Detection

Transcription

1 Improvig Template Based Spike Detectio Kirk Smith, Member - IEEE Portlad State Uiversity petra@ee.pdx.edu Abstract Template matchig algorithms like SSE, Covolutio ad Maximum Likelihood are well kow for their ability to detect spikes buried i oise. The key to a successful templatematchig algorithm is based o the selectio of a optimal template kerel. This paper focuses o showig the sesitivity the SSE ad covolutio methods of template matchig algorithms have to the width of the template kerel. The problem set used as a example is spike detectio of eural activity i ad ear the globus pallidus iterus area of the brai. Idex Terms Spike Sortig, Template Matchig, Biomedical Sigal Detectio, Template Width, Template Optimizatio. I. INTRODUCTION Template matchig techiques are well kow for the ability to discrimiate evets buried i oise. The template matchig techique relies o the use of a basis kerel that is compared to the sigal i questio. Usig oe of several trasforms (like SSE, covolutio ad maximum likelihood), the basis kerel is used to create a measure of error (or of differece) agaist the iput sigal. Because template-matchig fuctios use a basis kerel to trasform the sigal, the resultig measure of error is clearly sesitive to chages i the shape ad ature of the kerel. Thus may implemetatios of spike detectio usig template-matchig algorithms will try to optimize the shape of the kerel to match the uderlyig process. For example Dr. McNames suggests a three pass iterative refiemet for kerel selectio i Microelectrode Sigal Aalysis Techiques for Improved Localizatio []. However there is a reasoable amout of research to show that ot just the shape of the template is importat. The legth of the template ca have a sigificat effect o a template-matchig algorithm s performace. As oted i Detectio of Spotaeous Syaptic Evets Usig a Optimally Scaled Template [2] there ofte exists a expoetial relatio ship betwee the legth of the template ad the umber of false positives. This paper will exam how two differet kerel widths, both reasoable i size effect the ability of a SSE template matchig fuctio ad a covolutio template matchig fuctios ability to detect eural spikes. Work completed as part of a course project for Learig From Data at Portlad State Uiversity durig Witer term of Kirk Smith is a Masters studet with the Electrical ad Computer Egieerig Departmet, Portlad State Uiversity, Portlad, OR USA, ( petra@ee.pdx.edu). II. METHODOLOGY A. Creatio of Bechmark Data Set Actual microelectrode recordigs (MER) of extra-cellular euroal activity for the purpose of idetifyig structures ear the globus pallidus iterus (GPi) provided by Professor McNames were used as a bechmark for the spike detector. Of the 5 data sets provided, 6 sippets of data were chose (each sippet was approximately 30 secods i duratio), comprisig of sigle, multiple ad burst eural activity. Two differet people maually aotated each data set idepedetly. The results were merged together to form the expected detectio times. I areas where oe expert disagreed with the other, that locatio was flagged as a o-pealty detectio. If the detectio algorithm foud it, it was accepted as a true detect, however if the detectio algorithm failed to fid it, it was igored (ot pealized for missig it) ad was NOT couted as a missig evet. B. Template Matchig Overview Template matchig is the term give to the process of detectig a evet buried i a sigal by comparig it to a predefied template. The goal is to locate possible evets i the sigal that closely resemble the template. I practice there are three basic methods to determie how close ay give sectio of a sigal is to the template. They are Summed Squared Error (SSE), Covolutio (CONV), ad Maximum Likelihood (ML). Each method first estimates the template by detectig the most promiet spikes ad the averages the result to form a template kerel or basis spike. This kerel, ofte referred to as the template, is the shape that will be used by the rest of the algorithm to compare the sigal agaist (usig oe of the three previous metioed measures). A threshold is the applied to the output of the measured template fuctio, much like a ormal threshold detector, the result of which is used to idetify detectio evets. The key differece betwee a threshold detector ad a templatebased detector is over which fuctio the threshold is applied. With ormal threshold detectors, if the amplitude of the icomig data exceeds a threshold, a evet detectio is declared. With a template-based detector if the output of the template error measure crosses a threshold, a evet detectio is declared.

2 ) Summed Square Error Template Matchig Summed Squared Error (see equatio ) measures the squared differece betwee each poit i the template ad each correspodig poit i the sigal sectio beig compared. This method is good at detectig similar treds (sigal icreasig or decreasig i the same directio ad at the same rate), however it is sesitive to baselie (DC or very low frequecy) shifts. Thus it is commo to remove the mea from the template ad the sectio beig compared before performig the error measuremet. Figure shows a sectio of the C data set, ad the correspodig SSE fuctio of that data. Equatio : Sum of Squared Error Measure SSE () ( ) 2 i = X ( j + i) Template( j + i) Figure 2: Example of the covolutio fuctio (offset by 3 for view ability). Figure : Example of the SSE fuctio. 2) Covolutio Template Matchig Template Covolutio ca be thought of as a filter rather tha a error measure. It covolves (see equatio 2) the template with a sectio of the sigal. It seeks to amplify the areas of the sigal that are correlated to template. Because covolutio is a multiplicatio process i the frequecy domai, covolvig the template with the sigal ca be viewed multiplyig the frequecy compoets of the template with the correspodig frequecy compoets of the sigal. This has the effect of amplifyig oly those portios of the sigal that resemble the template. Figure 2 shows a sectio of the C data set, ad the correspodig covolutio fuctio of that data. Equatio 2: Covolutio Measure 3) Maximum Likelihood Template Matchig Maximum Likelihood refers to takig a sigal, ad measurig the probability it is of the same process as the template. This is achieved by buildig a estimated pdf fuctio for each poit i the template. The the algorithm measures the probability of each sigal usig the pdf at the correspodig locatio i the template (see equatio 3). The sum of the probabilities will thus be the largest at the poit that has the most likelihood (highest overall probability) of beig of the same process as the template. Because of the depedece o a pdf fuctio, this method is highly sesitive to errors i pdf estimatio. Because most oise is early ormal (see sectio IV.C), a ormal pdf with estimated mea ad variace ca be used i place of estimatig the true pdf. Figure 3 shows a sectio of the C data set, ad the correspodig maximum likelihood fuctio of that data. Equatio 3: Maximum likelihood measure ML () i = ( TemplatePdf ( j, X ( i + j)) ) Where j selects the pdf fuctio of j th locatio i the template. CONV () i = ( Template( j)* X ( i j) ) Figure 3: Example of maximum likelihood fuctio (output scaled dow by 50 for view ability). 2

3 C. Estimatio of Template Kerel To estimate the template kerel for each data set, a threshold was chose that would detect a large (~000) umber of spikes. A kerel width was the chose, ad each spike locatio was sampled so that the peak of the spike was located at the ceter of the template kerel. From this iitial collectio of spikes, two template kerels were created. The first template created was the stadard mea kerel. Each offset poit i the kerel was averaged to create the template value at that offset. This template geerated a averaged amplitude kerel. The secod kerel created was a ormalized mea kerel. Before the samples where averaged, each sample was ormalized by dividig by the differece i its peakto-peak value, thus ormalizig the peak-to-peak value of each sample. The average of each ormalized sample was the take to create a ew averaged kerel, which was the scaled by the largest peak-to-peak value that created it. This created a kerel that averaged the shape of the samples, rather tha the amplitudes (see Figure 4). Figure 5: The 96 samples that were used to create oe kerel. Fially for each kerel i each data set, two kerel widths were used. As see i Figure 6, a kerel with 00 poits ad a reduced kerel with 30 poits were used. Because both kerels where derived from the same iput set of spikes, they are idetical over the commo area (the 30 poits aroud the peak of the spike). Figure 4: Example stadard ad ormalized template kerel Closely comparig the two template kerels agaist Figure 5 shows that the ormalized kerel s shape is more represetative of the uderlyig process. The most otable differece i shape occurs i the idex rage of 60 to 90. The sharpess of the peaks ad valleys ad the distace away from baselie of those peaks ad valleys are the primary features used by template algorithms to distiguish a sigal evet from backgroud oise. Thus, improvig the kerel s represetatio of these key features should improve the template matchig fuctio s ability to properly detect a evet. Figure 6: Comparig template kerels of size 00 ad 30 D. Applicatio of Template Matchig For each data set a ormalized kerel was created with a width of 30 ad 00 poits. A Boolea lie search was the performed o the error measure fuctio to fid the optimal threshold for each kerel for each data set i the bechmark. The error measure chose was the total umber of true detectios (TD) mius the total umber of false detectios (FD) mius the total umber of missed evets (ME). For the SSE templates the lie search huted for the smallest value betwee 0 ad the mea of the output of the SSE fuctio that maximized the error measure. At each step of the lie search, the error measure was calculated, the results of which were used to choose which directio the Boolea search would go towards. 3

4 For the covolutio templates the lie search huted for the largest value betwee the mea of the covolutio fuctio ad the largest value of the covolutio fuctio. At each step of the lie search, the error measure was calculated, the results of which were used to choose which directio the Boolea search would go towards. E. Geeral Assumptios Made The oise itroduced to the processig beig measured is additive, o-correlated ad ormal i distributio (See sectio IV.C). It also assumed the local maximum/miimum of the error measure surface is also the global maximum/miimum (See sectio IV.B). III. RESULTS A. Liear Search of Threshold Error Figure 7 shows the results with threshold swept from 0 to 0.7, which is the value of the largest peak. B. Bechmark Data Results Table shows the results of usig the ormalized kerels with widths of 30 ad 00 o the bechmark data set. Algorithm Template Matchig SSE Kerel Width =30 Template Matchig SSE Kerel Width =00 Template Matchig Covolutio Kerel Width =30 Template Matchig Covolutio Kerel Width =00 True False Missed Detects Detects Evets Table : Bechmark test results comparig the kerel widths of 30 ad 00. C. Characterizatio of Noise i the Process Figure 9 shows the locatio of the histogram show i Figure 0. The mea was ad variace was over all the poits at idex 30 of this template. Figure 7: Overall plot of error space for stadard threshold detector. Figure 8 is the same plot, with focus o the peak of the error measure (the optimal threshold rage). Take otice of the global maximum plateau i the threshold rage of.3 to.36. Figure 9: Cross sectio at idex 30, used to create histogram. Figure 0: Histogram of oise at idex 30 of template. Figure 8: Plot of error space for threshold detector, focused o peak regio. 4

5 IV. DISCUSSION A. Impact of Kerel Width o Performace As metioed before the width of a kerel has a direct ifluece o its performace [2]. Both the SSE ad covolutio methods beefited from a smaller kerel. A approximate /3 reductio i kerel size lead to a /3 to /5 reductio i the umber of false detectios. I additio the /3 reductio i kerel size lead to at least /8 reductio i missed evets. This clearly shows the impact the size of kerel has o the algorithms performace. B. Error Surface of Normal Threshold Detector To verify the error surface was cocave dow, data set C was chose to perform a liear search of the error space usig a ormal threshold detector. As Figure 7 shows for thresholds above 0.05, the error surface is cocave dow. Error surfaces that have this property allow Boolea (ad other) liear search algorithms to settle o the global maximum, rather tha a local maximum. Thus assumig the template error surfaces model this same feature, we ca assume the threshold discovered usig a liear search is the globally optimal threshold. C. Characterizatio of Process Noise It was assumed the oise was from a ormal Gaussia distributio, with some particular mea ad variace. The histogram i Figure 0 shows the distributio of oise is very gaussia i shape. Furthermore this histogram was typical of all the templates i the areas where there is little or o slope. For areas of high slope i the template, the distributio was ot as clearly gaussia. Thus i areas where the uderlyig process appears to be dormat, the oise ca directly be measured ad estimated. method to further improve the sigal to oise ratio. The results of this combied approach should be compared to each approach idividually. C. Auto-Regressive Kerel Width Optimizer May techiques exists for idetify whether ay particular iput improves the overall accuracy of the estimator (or error measure i this case). It makes sice to try to apply a dimesioal reductio techique to choose the optimal size of the template kerel. VII. ACKNOWLEDGMENT The author would like to ackowledge Professor James McNames for the implemetatio of template base spike detector from which this work was derived, as well as providig the real world data from which the bechmark was created. VIII. REFERENCES [] Dr. James McNames, Microelectrode Sigal Aalysis Techiques for Improved Localizatio, Microelectrode Recordigs i Movemet Disorder Surgery, (submissio) Portlad State Uiversity mcames@ee.pdx.edu. [2] Detectio of Spotaeous Syaptic Evets Usig a Optimally Scaled Template V. CONCLUSION As the results clearly show, template-matchig algorithms are ot oly sesitive the shape ad amplitude of the kerel, but also to the size of the kerel. Thus whe implemetig ay of the template matchig algorithm a equal amout of time must be spet o optimizig both the width of the kerel, as well as the shape of the kerel. VI. FUTURE WORK A. Maximum Likelihood Detectors The prelimiary results of the maximum likelihood detector appear to geerate a very favorable measure of error (see Figure 3). More work will eed to be doe to idetify if ad where the oise takes o a o-gaussia behavior. Furthermore, the issue of pdf estimatio will also eed to be addressed. B. Combied SSE ad covolutio methods The output of the SSE template-matchig method geerates a very distictive shape. It may make sice to use this shape as a ew template, ad use the covolutio 5