Improved clustering of spike patterns through videosegmentation and motion analysis of micro

Electrocorticographic dataBugra Akyildiz∗, Yilin Song∗, Jonathan Viventi∗, Yao Wang∗

∗ Polytechnic Institute of New York University

Abstract—We have recently developed flexible, active, multi-plexed recording devices for high resolution recording over large,clinically relevant areas in the brain. While this technology hasenabled a much higher-resolution view of the electrical activityof the brain, the analytical methods to process, categorize andrespond to the huge volumes of seizure data produced by thesedevices have not yet been developed. This paper exams a seriesof new measurements of vivo animal seizure recording basedautomatic spike segmentation, feature extraction, unsupervisedclustering algorithm and quantitative evaluation for spike seg-mentation and clustering. We found significant improvement inspike classification accuracy by examining not only the patternof individual channel but also the spatial temporal patternvariation over all adjacent channels. In this paper, we first appliedadvanced video analysis techniques (particularly region andmotion analysis) for spike segmentation and feature extraction.Then we explored recent advances in machine learning fordiscovering useful features for clustering spike patterns andidentifying natural clusters. After comparison base on evaluationmatrices including Mutual Information Scores and intra clusterover inter cluster correlation, we found the best combinationof feature set and clustering algorithm to be applying DirichletMixture Model on raw video segmentation correlation matrix.The research is expected to yield new insights regarding howseizures initiate, progress and terminate, as well as subsequentlysignificant improvement in seizure detection and prediction.

I. INTRODUCTION

Currently many existing neurological data analysis rely onmanual inspection. With the new technology we and othersare developing to further enhance the spatial and temporalresolution, the data volume is infeasible for manual review.Further, manual inspection can miss subtle features that au-tomated machine learning techniques can detect. There is anurgent need for efficient and sensitive automated methods thatcan analyze huge volumes of data.

One major application of our high resolution device is torecord and examine brain signals in patients with epilepsy.Preliminary analysis of our high resolution data have discov-ered repetitive spatiotemporal microscale spike patterns thatinitiate and terminate seizures, not seen by standard electrodes.Understanding the ordering and relationships between thesepatterns is a key to develop better seizure detection andprediction techniques and ultimately better therapy.

In [2], one approach to recognize the pattern of epilepticseizure has been explored. In this early work, we identifiedspikes using a threshold-crossing based detector, extracted

Fig. 1: Photograph of a 360 channel, high density neural electrode array usedin a feline model of epilepsy. The electrode array is placed on the surface ofvisual cortex. The electrode size and spacing is 300 µm x 300 µm and 500µm, respectively.

delay and power features from the detected spikes, and thenperformed clustering, allowing a gap-statistic to determine thenumber of clusters in the data. This revealed the presence ofrepetitive, stereotyped spatial patterns.

But simple scheme like thresholding, will generate discon-nected parts or isolated scattered points even if the threshold ischosen properly. In this paper we treat the muti-channel signalas 3-D volume (successive 2D frames in time), and apply the3D region growing technique to detect spike region. Regiongrowing [6] is an effective technique to detect a connected(in 3D) region in which each pixel has an intensity that isnoticeably higher (or lower) than pixels outside the region.We have also proposed a labeling algorithms which allows allthe 3D segments have its unique identifier as their pixel value.

For each detected spike segment, we characterized itsspatial-temporal pattern using some features. These featureswill be used for spike pattern clustering, as well as spike clas-sification, and wavefront prediction. Intuitively, these featuresshould characterize how the spike wavefront moves and beable to discriminate different moving patterns. Furthermore,we would like to use as few features as possible to achievethe same discrimination power. Last but not least, featureextraction computation complexity should be adjusted to suitfor real time application.

The aim of this research task is to investigate whetherall possible spike patterns form some natural clusters, sothat patterns in each cluster can be approximated by themean pattern of that cluster. We explore serveral well-knowndeterministic model including K-means algorithm, mean-shiftalgorithm. In addition to a deterministic classification model,we also explored probabilistic model as Gaussian MixtureModel (GMM) [8] for representing the presence of clusterwithin an overall samples. However a major drawback of afinite mixture model as GMM is that it will almost alwaysuse all components as much as they can, and hence willproduce wildly different solutions for different numbers ofcomponents. Unlike finite models a Dirichlet Mixture Model[12] (DPM) solution wont change much with changes to theparameters, leading to more stability and less tuning. We willfurther demonstrate the difference between clustering methodin Section IV & V.

The rest of this paper is organized as follows: In SectionII, we present the algorithm we used for region growing &labeling. In Section III, several feature sets extracted fromsegmented regions are introduced. In Section IV, clusteringmodels and methods are introduced. In Section V, severalquantitative way to evaluate combinations of feature sets andclassification models is introduced, as well as their eachindividual performance. Section VI concludes the paper.

II. SPATIAL-TEMPORAL SEGMENTATION

In this paper, a spike segment refers to a consecutive setof frames (each consists of multi-channel signal at the sametime) in which one or several adjacent channels have highamplitudes. A simple scheme is by thresholding. This howeverwill generate disconnected parts or isolated scattered points ifthe threshold is not chosen properly. In our preliminary work[4] [5] , we detect spike segment by first detecting the timewhen a single channel has a negative large signal exceedinga threshold (-0.5 mV), and then including all frames that iswithin a certain time window from this point both in the past(60 ms) and future (100 ms). Because each spike may last forsomewhat different duration depending on its initial locationand its moving speed, this simple scheme sometimes includesmore than one spike or an incomplete spike in a detectedsegment. Given seizure video, we would like to develop anautomatic scheme to detect wave pattern related to seizureby not only taking consideration of the amplitude of localsignal but also the effect of its adjacent signal’s amplitude.Meanwhile we want to distinguish spike segments that are notspatially connected by giving them different labels.

A. 3D region growing

In this paper, we treated the multi-channel signal as a 3-D volume (successive 2D frames in time), and apply the3D region growing technique to detect the spike region. Thealgorithm of region growing first selects some pixels (calledseeds) that have intensity values above a preset threshold. Eachseed is an initial detected region. It then examines whetherany immediate neighbors of a previously detected region

boundary also have high intensity values, with a threshold thatis determined based on the mean and standard deviation of thepixels inside the region. This process continues until no morepixels can be included. We have applied this algorithm to ourECoG data.

The algorithm works as in algorithm 1:

Algorithm 1 Region growing1: n← 02: if {P~x > T, ~x1 ∈ Z+

18, ~x2 ∈ Z+20, ~x3 ∈ Z+

N} then3: −→x ∈ Sn

4: end if5: Pn ← E(PSn

)6: Dn ← E[(PSn − Pn)2]1/2

7: loop8: Sn+1 ← Sn

9: while ~x ∈ Sn do10: if P~x±~ei > Pn − α ∗Dn

subject to ~x± ~ei ∈ dom then11: ~x± ~ei ∈ Sn−112: end if13: end while14: n← n+ 115: Pn ← E(PSn

)16: Dn ← E[(PSn − Pn)2]1/2

17: if Sn = Sn−1 then18: break loop19: end if20: end loop

B. Labeling

After region growing, we get a binary representation ofthe raw signal with 1 representing foreground pixel relatedto seizure 0 representing background noise. In computervision, labeled regions are good intermediated representationfor regions that is helpful in further processing. There aremultiple ways to representing regions, a simple approach isassign a unique integer to pixels belonging to a region.

After doing labeling, with the dataset we previously col-lected we are able to isolate 1262 disconnected segments afterrunning region growing and labeling algorithm. However someof these segments only last up to 10ms, which not only havelittle benefit to study seizure pattern but also more prone tonoise. Therefore we further determine to set a time constraintfor the segmentations. By only selecting segments last longerthan 54 ms, 508 segments remained fit for further study. Fig.2 has shown two segments after region growing and labeling.

III. FEATURE EXTRACTION

For each detected spike segment, we would like to charac-terize its spatial-temporal pattern using some features. Thesefeatures will be used for spike pattern clustering, to be dis-cussed in Section V. Here we describe some of the features wehave tried out. Intuitively, these features should characterizehow the spike wavefront moves and be able to discriminate

(a) (b)

(c) (d)

Fig. 2: Examples of spike segmentation. Subfigure a,b are for a spike witha spiral motion: Subfigure a shows the segmented volume in blue overlaidwith the HR-ECoG signals captured at different times, with vertical axiscorresponding to frame number; Subfigure b shows the trajectory of thecentroid of the segmented region in successive frames, with the red dotindicating the beginning position; Subfigure c,d are for a spike with a verticalmotion.

different moving patterns. Furthermore, we would like to useas few features as possible to achieve the same discriminationcorrectness. Eventually, the goodness of a feature set can onlybe judged by the classification and prediction accuracy it leadsto. Therefore, feature extraction and evaluation is necessarilyintertwined with feature based clustering and classification,and these techniques need to be jointly optimized in aniterative/multipass process.

A. Wavefront Trajectory

One way to characterize the motion pattern of a spike isto describe the trajectory of its wavefront over the durationof the spike segment, which is simply obtained by connectingthe wavefront positions in successive frames. In Fig. 3 (c),we show trajectories representing the centroid of each clusterafter running DPM (to be discussed in Section IV). For a spikesegment consisting of N1N2N3 samples (from N3 frames ofN1 ∗ N2 channels), the trajectory can be captured by 2N3

features (including the wavefront 2D position at each frame).We further specified the area of detected region and the RMSsignal power at each frame, with additional 2N3 features.These features together succinctly capture how the wavefrontmoves in time and how do the total number of active channelsand their average energy change in time.

One problem with this representation is that N3, the numberof frames in each spike segment, and consequently the numberof features for each segment is not a constant, which canlead to difficulty in feature-based clustering and classification.To get around this problem, we first pre-cluster the trajectorybase on the length of the spike segments. For each segmentswithin each cluster, resample each one to maintain the samefeature dimension. An alternative approach is to calculatethe correlation with each pair of trajectory, with shiftingthe shorter trajectory measuring the maximum correlation forthe overlapping region with the longer one. Without losinggenerality, assume trajectories X ∈ R2n, Y ∈ R2m, n ≥ mCorrelation of X, Y is measured under following term:

minimizei

Cov(X(i:i+m), Y )

subject to i ∈ Z+n−m

For each of the 508 segments, we measure the correlationwith all the segments including itself and use this new trajec-tory correlation map as a new feature for further clustering.

B. Delay and Energy Map

Another way to characterize the spike motion is by com-puting the delays of individual channels with respect to a ref-erence channel. In our prior work [2] , for each spike segmentwe compute a delay map, both have the same dimension asthe 2D sensor array, and each element indicates the delay ofthe signal at that sensor with respect to the average of thesignals or the strongest channel from all sensors over the timeduration of the spike segment. As can be seen in Fig.3 (a), sucha delay map is an effective and efficient way to characterizethe spike motion. Unlike the trajectory representation whichonly characterizes the motion of the spike wavefront, the delaymaps provide additional region shape information, by usingN1∗N2 features. Furthermore, a summation of absolute signalvalue is calculated as energy map (Fig.3 b).

C. Segmented video signal correlation Map

The features listed above all serves the same purpose ofdimension reduction which is necessary for real time classi-fication. They are all partial representation of the true signal,by running whatever clustering algorithm on those featurewould not give us a quantitative evaluation of correctness. Toevaluate the correctness of classification we have to look backto the segmented region to evaluate the similarity betweeneach two pairs. To tackle different length of segmentationsand segmentations existing within the same time period butnot spatially connected, we introduce MX , which serversas a binary mask for the each specific segmentations X .Without losing generality, assume raw video signal X ∈RN1∗N2∗n, Y ∈ RN1∗N2∗m, n ≥ m Correlation between tworegion are calculated as such:

1 2 3

4 5 6

7 8 9

(a) delay map

1 2 3

4 5 6

7 8 9

(b) energy map

0 10 200

5

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(c) trajectory

50 100 150 200 250 300 350 400 450 500

50

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−0.2

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(d) correlation map

Fig. 3: Examples of extracted features. Subfigure a,b,c are delay, energy,trajectory representation of 9 spike segments closest to the cluster centroidafter running DPM.1) In a,b, blue indicates signal started earlier while red indicates late. Whiteregion in 7-9 shows it’s not included in the spike.2) In c, spike starting point is marked with blue, whereas ending point ismarked with red. Each black dot represents the energy weighted centroid ofone specific frame.3) Subfigure d is the correlation map of all 508 segments. A similar coloumnvector indicates two segmentation belonging to the same cluster. For examplesimilar column vectors between 150 to 220 could be interpreted as they forma natural cluster.

minimizei

Cov(X(,i:i+m), Y )

subject to i ∈ Z+n−m

X = reshape(Mx ·X,N1 ∗N2, n)

Y = reshape(My · Y,N1 ∗N2,m)

Correlation of each pair of the raw video segments arecalculated to form a raw signal correlation map. The raw signalcorrelation map would also serve as a quantitative referencefor feature and clustering algorithm selection.

IV. UNSUPERVISED CLUSTERING OF INDIVIDUAL SPIKEPATTERN

Before running any clustering algorithm, we pre-processedthe data to normalize its mean and variance to maintain consis-tancy across features. For each feature set discussed earlier orseveral sets combined, we tried to reduce the feature dimension

in an unsupervised way to remove the intrinsic redundancywithin the raw features by using principle component analysis(PCA). PCA is a mathematical procedure that uses orthogonaltransformation to convert a set of observations of possiblycorrelated variables into a set of values of linearly uncorrelatedvariables. Thus by appling an orthogonal transform, originalx(i) ∈ Rn feature renders a new vector y(i) ∈ Rk with a lowerdimension k, uncorrelated representation of x(i). We iterativelyinclude transformed feature space with largest variance until> 99% of data variance was retained.

A. Deterministic Model

1) K-means algorithm: K-means[7] is one of the simplestand most frequently unsupervised learning algorithm which ismainly used for clustering purpose. It is used for partitioningN-dimensional observations into K disjoint observations byminimizing sum of least square criterion.

2) Mean Shift Algorithm: Mean Shift is an adaptivenonparametric iterative unsupervised learning algorithm [13],which unlike K-Means clustering algorithm does not requirea prior knowledge of how many clusters are present in theobservation space. It seeks mode to estimate clusters in the ob-servation space. As K-means algorithm, Mean Sift Algorithmuses an iterative procedure to find the clusters in observationspace, the different is Mean Shift removes one cluster once itconverged to the center of the mass and run for another clusteruntil all the samples have labels.

B. Mixture model

In contrast to fitting a deterministic model for each ofthe feature set as k-means, an alternative one is mixturemodel approach. A mixture model is a mixture distributionover probability distribution of observations in the observationspace [3]. A finite mixture model can be formulated as such:

p(x|φ, π) =

K∑k=1

(πkp(x|φk))

where π = (π1, . . . , πk), φ = (φ1, . . . , φk) are the param-eters. One of the most common mixture model is GaussianMixture Model (GMM) where the φk = (µk,

∑k) and con-

ditional density p(x|φk) is a Gaussian density with mean µk

and covariance matrix∑

k. Another mixture model is DirichletProcess Mixture Model(DPM). The Dirichlet process is aprior probability distribution on clusterings with an infinite,unbounded, number of partitions.

1) Gaussian Mixture Model: A gaussian mixture modelis a probabilistic model that assumes all the data points aregenerated from a mixture of a finite number of gaussiandistribution with unknown mean µk, covariance matrix

∑k

and mixing coefficients πk. Estimating µk and covariancematrix

∑k is to find maximum likelihood solutions for given

dataset provided number of cluster k. An elegant and powerfultool is call expectation-maximization [10] algorithm or EMalgorithm. It is the fastest algorithm for learning mixturemodels and as the algorithm maximizes only the likelihood it

✓?kzi

xi

⇡?

↵0 H

i#=#1,…,n

k#=#1,2,...

Fig. 4: Dirichlet Process Mixture Model

will not bias the means towards zero or bias the cluster sizesto have specific structures that might or might not apply. Thatbeing said estimating number of cluster k is crucial for thisalgorithm as it will always use all the component it has accessto. The Bayesian information criterion [11] (BIC) criterioncan be used to select the number or components in a GMMin an efficient way. In theory, it recover the true number ofcomponents only in the asymptotic regime (i.e. if much datais available).

2) Dirichlet Process Mixture: An alternative approach toGMM is DPM, which has a variant of Gaussian mixturemodel with a variable number of clusters using the DirichletProcess. A Dirichlet Process is a process that is a probabilitydistribution over probability measures, which are randomdistributions[12]. Unlike finite models, which will almostalways use all components as much as they can, and hencewill produce wildly different solutions for different numbersof components, the Dirichlet process solution won’t changemuch with changes to the parameters, leading to more stabilityand less tuning. The general struction of DPM is illustrated inFig.4. With its parameter listed as following:

π?|α ∼ GEM(α)

θ?k|H ∼ Hzi|π? ∼ Discrete(π?)

xi|zi, θ?zi ∼ F(θ?zi)

α is the concentration parameter that determines the likeli-hood of assigning a new cluster, and it is the only parameter inthe algorithm. Distribution of πk follows the Griffiths-Engen-McCloskey(GEM) distribution. H is the base distribution. Toavoid sigularity of covarince matrix induced by insufficientlymany points per mixture, H is selected to be gaussian distri-bution with diagnoal covarince matrix.

V. EVALUATION MATRIC AND RESULTS

To evaluate all the feature sets and clustering method, wedevelop two kind of senarios. One is proved with ground truth,the other is without ground truth.

manual label Delay & Energy Correlation Map Trajectory0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

kmeans

meanshift

manual

dirichlet mixture

gaussian mixture

Fig. 5: Mutual Information Score of feature comparison and clustering methodcomparison. DPM outperforms other clustering method and correlation mapis the best feature set. Inspect of rescaling the plots, Manual label actuallyhave the score of 1.

A. Mutual Information Score

We look at raw video signal and manually label eachsegmantation as ground truth. And use Mutual InformationScore as evaluation of similarity between ground truth andtarget cluster. Mutual Information of two random variables isa quantity that measures the mutual dependence of two randomvariables by taking account of their common information.Assume two label assignments, U and V there entropy is theamount of uncertainty for a partition set, defined by:

H(U) =

|U |∑i=1

P (i)log(P (i))

H(V ) =

|V |∑j=1

P ′(j)log(P ′(j))

where P (i) = |Ui|/N is the probability that an objectpicked at random from U falls into class Ui, similarly P (j) =|Vj |/N is the probability that an object picked at random fromV falls into class Vj And mutual information between U andV is calculated by:

MI(U, V ) =

|U |∑i=1

|V |∑j=1

P (i, j)log(P (i, j)

P (i)P ′(j))

where P (i, j) = |Ui ∩ Vj |/N is the probability that anobject picked at random falls in both classes Ui and Vj . Thenormalized mutual information is defined as:

NMI(U, V ) =MI(U, V )√H(U)H(V )

As we can see from Fig.5, the descending order in terms ofperformance is correlation map, delay & energy map, trajec-tory. And the clustering method in a performance descendingorder is: DPM, GMM, K-means, Mean shift.

manual label Delay & Energy Correlation Map Trajectory1.4

1.6

1.8

2

2.2

2.4

kmeans

meanshift

manual

dirichlet mixture

gaussian mixture

Fig. 6: Intra cluster over inter cluster correlation. Similar in Fig.5, intra overinter score renders a similar result in terms of best feature set and bestclustering algorithm. And it also shows the human labeling is also reasonablyhigh to be considered as a ground truth in the previous section.

B. Intra over Inter cluster corrlation score

Unfortunately, in the field of seizure prediction, HR-ECoGhas not yet been used as a standard procedure. Hence wedon’t have an expert in the field to claim the label is correct,to demonstrate DPM and Correlation Map is still the bestapproach we use intra cluster over inter cluster raw videocorrelation as evaluation metric. Heuristically, a high intraover inter score indicates high consistancy within cluster anddifferent result across clusters. The defision of intra, intercluster correlation is denoted as:

intra =

∑i∈Z+

K

∑a,b∈Mi

a6=b

Cov(M ia,M

ib)

∑i∈Z+

K

(Ni

2

)−Ni

inter =

∑i,j∈Z+

Ki 6=j

∑a∈Mi

b∈Mj

Cov(M ia,M

jb )

∑i,j∈Z+

K

Ni ∗Nj

As can be seen in Fig.6, the results of best clusteringalgorithm and feature sets are the same.

VI. CONCLUSION

HR-ECoG has tremendous potential for many researchand clinical application. In this paper, we have combinedexciting new ideas in video analysis and machine learningwith traditional signal processing method to look as thesenew datasets in novel ways. We have developed efficientmethods for identifying and localizing the spatial and temporalextent of interictal and ictal spikes and detecting the spikewavefront, through advanced region and motion analysis. Thisnew robust approach overcomes falsely connected and speratedspike segmentaion in simple scheme like thresholding and fix-window detection.

We also come up with multiple feature sets to represent theraw spike segmentation, in terms of offline clustering perfor-

mance the best feature sets would be correlation map betweendifferent spikes. However in real time application, when anew spike segmentation comes in, we want to classify it intoone existing cluster by computing the correlation betweenthe cluster centroid. Assume each segmentation have similarlength, the complexity for correlation map is ∼ O(kn1n2n3) kbeing number of current clusters centroids. Whereas for delaymap, correlation for each n1n2 channels is O(n3). Then usethis n1n2 delay vector to compute euclidean distance witheach cluster centroids whose complexity would be relativelytrivial. And the total classification complexity for delay mapwould be O(n1n2n3), which is an enormous reduction ofcorrelation map if the cluster number is high. And trajectorywould serve as a within spike wavefront predition method.Hence at this point it’s too early to tell which feature set isbest for classification and prediction but all feature sets wouldhave different roles in future seizure prediction.

In terms of clustering method, DPM is undoubtably the bestclustering algorithm in terms of correctness. It’s robust forparameter tuning and only need an upper bound for numberof clusters. Although the extra parameterization necessary forvariational inference will make inference slower, the clusteringalgorithm is running offline so this drawback is relativelytrivial.

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