MIXED EFFECTS MODELS FOR EEG EVOKED RESPONSE DETECTION Yonghong Huang, Deniz Erdogmus, Misha Pavel Oregon Health and Science University OGI School of Science & Engineering huang@csee.ogi.edu, derdogmus@ieee.org, pavel@bme.ogi.edu Santosh Mathan Honeywell Laboratories Human Centered Systems Group Santosh.Mathan@honeywell.com ABSTRACT Human brain signals associated with perceptual processes have been shown to be useful for visual target image search. For the purpose of online training, we develop a novel mixed ef- fects evoked response detector, which is capable of combin- ing individual random effects and population fixed effects, for the analysis of neural signatures associated with targets. To avoid numerical problems in high dimensional matrix compu- tations, we develop equivalent dimension reduced expressions for the mixed models. We construct the mixed effects evoked response model using principal component analysis to pro- vide bases for the population model and linear discriminant analysis (LDA) to provide bases for the individual models. In addition, the LDA is adopted for Elecroencephalography channel dimensionality reduction. Data collected at different time and experimental conditions from two subjects perform- ing image search tasks are utilized to assess the quality of the models. We also compare the proposed model with the sup- port vector machine (SVM). The results demonstrate that the mixed models approach the SVM and provide reliable infer- ence on cross session evaluation for the single-trial evoked response detection. 1. INTRODUCTION Human brain signals associated with perceptual processes have been shown to be useful for visual target image search. Ele- croencephalography (EEG) has been widely used for detect- ing cognitive disorders and other diseases. A brain’s electrical response present in EEG signals to a stimulus, related to as- pects of cognitive processing is referred to as an event-related potential (ERP) [1]. The ERPs associated with human per- ceptual judgments have been previously used for visual target image search [2, 3, 4]. The major task of an ERP-based image search systems is to detect the ERPs associated with the target stimuli. The conventional approach for studying the ERPs is trial averaging. However, this approach is not sufficiently ef- This work was supported by DARPA and NGA under contract HM1582- 05-C-0046 and by NSF under grants ECS-0524835, ECS-0622239, and IIS- 0713690. It has been approved for public release, distribution unlimited. ficient for fast brain interfaces that exploit the ERPs, therefore recent research focuses on single-trial ERP detection [5]. The main challenges of single-trial ERP detection are high dimensionality and scarcity of training data. The ideal sce- nario is to have enough training samples under controlled cir- cumstances. However, it is infeasible in real applications to have subjects perform a long training period with unchanging experimental conditions. When multiple EEG measurements are obtained from each individual at different times and pos- sibly under changing experimental conditions, we normally can not fully control the circumstances under which the mea- surements are taken. There are considerable variations among individuals in the number and timing of observations. There- fore we need to seek a model suitable for aggregated data to capture the population characteristics and also the individual features as well. A mixed effects model (MEM) [6] is a statistical hierar- chical model. It was first proposed for the analysis of longi- tudinal time-series data [7]. There are two sources of varia- tion in the MEM: between-individual variations and within- individual variation. By introducing multilevel random ef- fects, the MEM easily handles data with multiple sources of variation, such as EEG data. Specifically for designs of aggre- gating data across multiple subjects/sessions, we can easily use the population-averaged parameters to specify the com- mon EEG signal type (consistent pattern across subjects/sessions), and the subject-specific parameters to specify subject/session individuality (individual variety with the within- and between- subject/session variance). Therefore the MEM provides prin- cipled basis for combining historical and new data and is con- venient for online adaptation. To this end, we apply this statis- tical approach to the classification of single-trial multichannel EEG sequences. In this paper, we present a mixed-effects ERP detector that models single-trial ERP waveforms as varying individ- uals from a population; thus the classifier attempts to ex- plain fluctuations in the baseline ERP waveform via a hi- erarchical Bayesian topology. To avoid numerical problems in high dimensional matrix computations, we determine low- dimensional calculations utilizing low-rank matrix properties.