Multichannel EEG Data Research Articles

Unsupervised EEG biosignal discrimination

This paper assesses the ability of unsupervised learning to discriminate positive and negative human emotions evoked while the person is exposed to images with high emotional content. The investigation is focused in two different settings – multi-channel EEG data from individual subjects (person data) and multiple subjects EEG data from individual channels (channel data). The person data is used for intra-subject clustering and the channel data is used for inter-subject clustering. Attribute selection procedure is first applied in order to select the most important data features. Secondly, K-means and fuzzy-C-means clustering techniques are comparatively applied in order to extract specific knowledge of the existing dependences and thus decode the two emotional states.

Multivariate Synchronization Analysis of Brain Electroencephalography Signals: A Review of Two Methods

Temporal synchronization of neuronal activity plays an important role in various brain functions such as binding, cognition, information processing, and computation. Patients suffering from disorders such as Alzheimer’s disease or schizophrenia show abnormality in the synchronization patterns. Electroencephalography (EEG) is a cheap, non-invasive, and easy-to-use method with fine temporal resolution. Modern multichannel EEG data are increasingly being used in brain studies. Traditional approaches for identifying synchronous activity in EEG are through univariate techniques such as power spectral density or bivariate techniques such as coherence. In this paper, we review two methods for synchronization analysis within multivariate time series. One method, denoted by multivariate state-space synchronization-estimator, calculates the generalized synchronization based on the shrinking of the embedding dimension in the state-space. The other method, denoted by multivariate phase synchronization-estimator, considers phase of the signals and calculates the mean coherency within multivariate phases. Their effectiveness is assessed on both simulated data and real EEGs.

Fast monitoring of epileptic seizures using recurrence time statistics of electroencephalography

Epilepsy is a relatively common brain disorder which may be very debilitating. Currently, determination of epileptic seizures often involves tedious, time-consuming visual inspection of electroencephalography (EEG) data by medical experts. To better monitor seizures and make medications more effective, we propose a recurrence time based approach to characterize brain electrical activity. Recurrence times have a number of distinguished properties that make it very effective for forewarning epileptic seizures as well as studying propagation of seizures: (1) recurrence times amount to periods of periodic signals, (2) recurrence times are closely related to information dimension, Lyapunov exponent, and Kolmogorov entropy of chaotic signals, (3) recurrence times embody Shannon and Renyi entropies of random fields, and (4) recurrence times can readily detect bifurcation-like transitions in dynamical systems. In particular, property (4) dictates that unlike many other non-linear methods, recurrence time method does not require the EEG data be chaotic and/or stationary. Moreover, the method only contains a few parameters that are largely signal-independent, and hence, is very easy to use. The method is also very fast—it is fast enough to on-line process multi-channel EEG data with a typical PC. Therefore, it has the potential to be an excellent candidate for real-time monitoring of epileptic seizures in a clinical setting.

Evolutionary Factor Analysis of Replicated Time Series

In this article, we develop a novel method that explains the dynamic structure of multi-channel electroencephalograms (EEGs) recorded from several trials in a motor-visual task experiment. Preliminary analyses of our data suggest two statistical challenges. First, the variance at each channel and cross-covariance between each pair of channels evolve over time. Moreover, the cross-covariance profiles display a common structure across all pairs, and these features consistently appear across all trials. In the light of these features, we develop a novel evolutionary factor model (EFM) for multi-channel EEG data that systematically integrates information across replicated trials and allows for smoothly time-varying factor loadings. The individual EEGs series share common features across trials, thus, suggesting the need to pool information across trials, which motivates the use of the EFM for replicated time series. We explain the common co-movements of EEG signals through the existence of a small number of common factors. These latent factors are primarily responsible for processing the visual-motor task which, through the loadings, drive the behavior of the signals observed at different channels. The estimation of the time-varying loadings is based on the spectral decomposition of the estimated time-varying covariance matrix.

EEGVIS: A MATLAB Toolbox for Browsing, Exploring, and Viewing Large Datasets

Recent advances in data monitoring and sensor technology have accelerated the acquisition of very large data sets. Streaming data sets from instrumentation such as multi-channel EEG recording usually must undergo substantial pre-processing and artifact removal. Even when using automated procedures, most scientists engage in laborious manual examination and processing to assure high quality data and to indentify interesting or problematic data segments. Researchers also do not have a convenient method of method of visually assessing the effects of applying any stage in a processing pipeline. EEGVIS is a MATLAB toolbox that allows users to quickly explore multi-channel EEG and other large array-based data sets using multi-scale drill-down techniques. Customizable summary views reveal potentially interesting sections of data, which users can explore further by clicking to examine using detailed viewing components. The viewer and a companion browser are built on our MoBBED framework, which has a library of modular viewing components that can be mixed and matched to best reveal structure. Users can easily create new viewers for their specific data without any programming during the exploration process. These viewers automatically support pan, zoom, resizing of individual components, and cursor exploration. The toolbox can be used directly in MATLAB at any stage in a processing pipeline, as a plug-in for EEGLAB, or as a standalone precompiled application without MATLAB running. EEGVIS and its supporting packages are freely available under the GNU general public license at http://visual.cs.utsa.edu/eegvis.

Employing spatially constrained ICA and wavelet denoising, for automatic removal of artifacts from multichannel EEG data

Detecting artifacts produced in electroencephalographic (EEG) data by muscle activity, eye blinks and electrical noise, etc., is an important problem in EEG signal processing research. These artifacts must be corrected before further analysis because it renders subsequent analysis very error-prone. One solution is to reject the data segment if artifact is present during the observation interval, however, the rejected data segment could contain important information masked by the artifact. The independent component analysis (ICA) can be an effective and applicable method for EEG denoising. The goal of this paper is to propose a framework, based on ICA and wavelet denoising (WD), to improve the pre-processing of EEG signals. In particular we employ concept of the spatially constrained ICA (SCICA) to extract artifact-only independent components (ICs) from the given EEG data, use WD to remove any cerebral activity from the extracted-artifacts ICs, and finally project back the artifacts to be subtracted from EEG signals to get clean EEG data. The main advantage of the proposed approach is faster computation, as it is not necessary to identify all ICs. Computer experiments are carried out, which demonstrate effectiveness of the proposed approach in removing focal artifacts that can be well separated by SCICA.

Multichannel feature selection using information maximization with application to multichannel EEG signals

An algorithm for feature selection based on information optimization is developed. This algorithm performs subspace mapping from multi-channel signals, where network modules (NM) are used to perform the mapping for each of the channels. The algorithm is based on maximizing the mutual information (MI) between input and output units of each NM, and between output units of different NMs. Such formulation leads to substantial redundancy reduction in output units, in addition to extraction of higher order features from input units that exhibit coherence across time and/or space useful in classification problems. A number of experiments were carried to validate the performance of the proposed algorithm with very promising results particularly in the case of multichannel EEG data analysis.

Extraction of single-trial cortical beta oscillatory activities in EEG signals using empirical mode decomposition

BackgroundBrain oscillatory activities are stochastic and non-linearly dynamic, due to their non-phase-locked nature and inter-trial variability. Non-phase-locked rhythmic signals can vary from trial-to-trial dependent upon variations in a subject's performance and state, which may be linked to fluctuations in expectation, attention, arousal, and task strategy. Therefore, a method that permits the extraction of the oscillatory signal on a single-trial basis is important for the study of subtle brain dynamics, which can be used as probes to study neurophysiology in normal brain and pathophysiology in the diseased.MethodsThis paper presents an empirical mode decomposition (EMD)-based spatiotemporal approach to extract neural oscillatory activities from multi-channel electroencephalograph (EEG) data. The efficacy of this approach manifests in extracting single-trial post-movement beta activities when performing a right index-finger lifting task. In each single trial, an EEG epoch recorded at the channel of interest (CI) was first separated into a number of intrinsic mode functions (IMFs). Sensorimotor-related oscillatory activities were reconstructed from sensorimotor-related IMFs chosen by a spatial map matching process. Post-movement beta activities were acquired by band-pass filtering the sensorimotor-related oscillatory activities within a trial-specific beta band. Signal envelopes of post-movement beta activities were detected using amplitude modulation (AM) method to obtain post-movement beta event-related synchronization (PM-bERS). The maximum amplitude in the PM-bERS within the post-movement period was subtracted by the mean amplitude of the reference period to find the single-trial beta rebound (BR).ResultsThe results showed single-trial BRs computed by the current method were significantly higher than those obtained from conventional average method (P < 0.01; matched-pair Wilcoxon test). The proposed method provides high signal-to-noise ratio (SNR) through an EMD-based decomposition and reconstruction process, which enables event-related oscillatory activities to be examined on a single-trial basis.ConclusionsThe EMD-based method is effective for artefact removal and extracting reliable neural features of non-phase-locked oscillatory activities in multi-channel EEG data. The high extraction rate of the proposed method enables the trial-by-trial variability of oscillatory activities can be examined, which provide a possibility for future profound study of subtle brain dynamics.

INCF Japan-Node and Platforms

Event Abstract Back to Event INCF Japan-Node and Platforms Usui Shiro1* 1 Neuroinformatics Japan Center, RIKEN BSI, Japan The INCF national node of Japan (J-Node) (http://www.neuroinf.jp/) is established at the Neuroinformatics Japan Center (NIJC), RIKEN Brain Science Institute (BSI). Based on the achievement of a Japanese pilot study on Neuroinformatics Research in Vision (1), we developed a base-platform XooNIps (http://xoonips.sourceforge.jp) and several neuroinformatics platforms (PFs). PF committee members collaborate to develop databases that are available for use online, and together with the J-Node committee, we promote domestic activities in neuroinformatics in Japan. PFs currently running under the J-Node are as follows: Visiome, Brain Machine Interface, Invertebrate Brain, Cerebellar Development Transcriptome, Comprehensive Brain Science Network, Cerebellar, Neuro-Imaging, Dynamic Brain, BSI-NI (under development) and Simulation (under development) (2). We here describe 2 platforms which are under development. The rest of PFs are opened at the J-Node portal. BSI-NI platform is a general term for several platforms which developed in BSI. RIKEN has been participating in the "Integrated Database Project" which MEXT launched from 2006 to develop and promote life science databases in Japan. To meet the same needs in the brain science, BSI established BSI-NI committee to promote neuroinformatics in April 2008. The following databases are under development to open. •BSI Microarray Database •Construction of 3-Dimensional brain atlas of novel experimental rodent "Degu" •Construction of 3-Dimensional brain atlas of novel experimental primate "Common Marmoset" •Multichannel EEG data for Brain Machine Interface (BMI) and/or Human Emotions (HE) Simulation platform (SimPF) provides a common environment for testing, evaluating and sharing computational models via web browser. Users can run a trial of computational models that are registered on PFs and Neuroinformatics databases; no need to install any software on their computers. A user is asked to upload a script of a model to SimPF from a web browser. Once uploaded, SimPF assigns a virtual machine (VM) for the user from SimPF clouds, and connects the VM automatically to the user's browser via VNC (Virtual Network Computing) protocol. We are also providing MPI simulation environment for various kind of neuron and local-circuit simulation. The system consists of portal hosts, ganglia server and execution hosts. Linux and open source software are used for every host and server. Anyone can easily access and use our cloud simulation environment from browser. Install and configuration methods are provided by the PF. Since the establishment of J-Node and PFs 5 years ago, top-page access statistics of unique users per day for each PF are shown in the Figure. The slopes at the initial phase are about 20 persons/day, which is mostly by the committee members to develop the PF. Once the URL is publicized at large, the slope becomes roughly 100 persons/day, rising by 5 times. This shows the importance of such PFs in neuroscience.

ERP denoising in multichannel EEG data using contrasts between signal and noise subspaces

In this paper, a new method intended for ERP denoising in multichannel EEG data is discussed. The denoising is done by separating ERP/noise subspaces in multidimensional EEG data by a linear transformation and the following dimension reduction by ignoring noise components during inverse transformation. The separation matrix is found based on the assumption that ERP sources are deterministic for all repetitions of the same type of stimulus within the experiment, while the other noise sources do not obey the determinancy property. A detailed derivation of the technique is given together with the analysis of the results of its application to a real high-density EEG data set. The interpretation of the results and the performance of the proposed method under conditions, when the basic assumptions are violated – e.g. the problem is underdetermined – are also discussed. Moreover, we study how the factors of the number of channels and trials used by the method influence the effectiveness of ERP/noise subspaces separation. In addition, we explore also the impact of different data resampling strategies on the performance of the considered algorithm. The results can help in determining the optimal parameters of the equipment/methods used to elicit and reliably estimate ERPs.

A P300-Based Brain-Robot Interface for Shaping Human-Robot Interaction

Brain-computer interfaces (BCI) based on the event-related potential (ERP) have been studied widely in the past decade. These BCIs exploit stimuli, called oddballs, which are presented on a computer screen in an arbitrary fashion to implement a binary selection mechanism. The potential has been linked to human surprise, meaning that potentials are triggered by unpredictable events. This hypothesis is the basis of the oddball paradigm. In this work, we go beyond the standard paradigm and exploit the in a more natural fashion for shaping human-robot interaction (HRI). In HRI a flawless behavior of the robot is essential to avoid confusion or anxiety of the human user when interacting with the robot. Detecting such reactions in the human user on the fly and providing instantaneous feedback to the robot is crucial. Ideally, the feedback system does not demand additional cognitive loads and operates automatically in the background. In other words, providing feedback from the human user to the robot should be an inherent feature of the human-machine interaction framework. Information extracted from the human EEG, in particular the P300, is a well-suited candidate for serving as input to this feedback loop. We propose to use as a means for human-robot interaction, in particular to spot the surprises of the human user during interaction to detect in time any mistakes in robot behavior the human user observes. In this way, the robot can notice its mistakes as early as possible and correct them accordingly. Our brain-robot interface implementing the proposed feedback system consists of the following core modules: (1) a P300 spotter that analyzes the incoming preprocessed data stream for identifying potentials on a single-trial basis and (2) a translation module that translates the detected P300s into appropriate feedback signals to the robot. The classification relies on a supervised machine learning algorithm that requires labeled training data. This data must be collected subject-wise to account for the high inter-subject variances typically found in EEG data. The off-line training needs to be carried out only once prior to using the interface. The trained classifier is then employed for on-line detection of signals. During the online operation, the incoming multi-channel EEG data is recorded and analyzed continuously. Each incoming new sample vector is added to a new window. Spectral, spatial and temporal features are extracted from the filtered windows. The resulting feature vectors are classified and a probability that the vector contains a is assigned. Eventually, a feedback signal to the robot is generated based on the classification result, either a class label or a probability between 0 and 1. The proposed framework was tested off-line in a scenario using Honda's humanoid robot ASIMO. This scenario is suited for eliciting events in a controlled experimental environment without neglecting the constraints of real robots. We recorded EEG data during interaction with ASIMO and applied our method off-line. In the future we plan to extend our system to a fully on-line operating framework.

Analysis of brain electrical topography by spatio-temporal wavelet decomposition

Currently, the Functional Magnetic Resonance Imaging (fMRI), Positron Emission Tomography (PET), and Electroencephalography (EEG) recordings are the major techniques of neuroimaging. The EEG with its highest temporal resolution is still a crucial measurement for localization of activities arising from the electrical behaviour of the brain. A scalp topographic map for an EEG may be a superposition of several simpler subtopographic maps, each resulting from an individual electrical source located at a certain depth. Furthermore, this source may have a temporal characteristic as an oscillation or a rhythm that extends in a certain time window which has been a basis of assumption for the time-frequency analysis methods. A method for the spatio-temporal wavelet decomposition of multichannel EEG data is proposed which facilitates the localization of electrical sources separate and/or overlapping on a continuum of time, frequency and space domains. The subtopographic maps asociated with each of these individual components are then used in the MUSIC source localization algorithm. The validations are performed on simulated EEG data. Spatio-temporal wavelet decomposition as a preprocessing method improves the source localization by simplifying the topographic data formed by the superposition of EEG generators, having possible combinations of temporal, frequency and/or spatial overlappings. Spatio-temporal analysis of EEG will help enhance the accuracy of dipole source reconstruction in neuroimaging.

Automatic Classification of Athletes With Residual Functional Deficits Following Concussion by Means of EEG Signal Using Support Vector Machine

There is a growing body of knowledge indicating long-lasting residual electroencephalography (EEG) abnormalities in concussed athletes that may persist up to 10-year postinjury. Most often, these abnormalities are initially overlooked using traditional concussion assessment tools. Accordingly, premature return to sport participation may lead to recurrent episodes of concussion, increasing the risk of recurrent concussions with more severe consequences. Sixty-one athletes at high risk for concussion (i.e., collegiate rugby and football players) were recruited and underwent EEG baseline assessment. Thirty of these athletes suffered from concussion and were retested at day 30 postinjury. A number of task-related EEG recordings were conducted. A novel classification algorithm, the support vector machine (SVM), was applied as a classifier to identify residual functional abnormalities in athletes suffering from concussion using a multichannel EEG data set. The total accuracy of the classifier using the 10 features was 77.1%. The classifier has a high sensitivity of 96.7% (linear SVM), 80.0% (nonlinear SVM), and a relatively lower but acceptable selectivity of 69.1% (linear SVM) and 75.0% (nonlinear SVM). The major findings of this report are as follows: 1) discriminative features were observed at theta, alpha, and beta frequency bands, 2) the minimal redundancy relevance method was identified as being superior to the univariate t -test method in selecting features for the model calculation, 3) the EEG features selected for the classification model are linked to temporal and occipital areas, and 4) postural parameters influence EEG data set and can be used as discriminative features for the classification model. Overall, this report provides sufficient evidence that 10 EEG features selected for final analysis and SVM may be potentially used in clinical practice for automatic classification of athletes with residual brain functional abnormalities following a concussion episode.

Design and Evaluation of Tiled Parallel Coordinate Visualization of Multichannel EEG Data

The field of visualization assists data interpretation in many areas, but does not manage all types of data equally well. This holds, in particular, for time-varying multichannel EEG data. No existing method can successfully visualize simultaneous information from all channels in use at all time steps. To address this problem, a new visualization method is presented based on the parallel coordinate method and making use of a tiled organization. This tiled organization employs a two-dimensional row-column representation, rather than a one-dimensional arrangement in columns as used for classical parallel coordinates. The usefulness of the new method, referred to as tiled parallel coordinates (TPC), is demonstrated by a particular type of EEG data. It can be applied to an arbitrary number of time steps, handling the maximum number of channels currently in use. An extensive user evaluation shows that, for a typical EEG assessment task, data evaluation by the TPC method is faster than by an existing clinical EEG visualization method, without loss of information. The generality of the TPC method makes it widely applicable to other time-varying multivariate data types.

Increased Omega Complexity and Decreased Microstate Duration in Nonmedicated Schizophrenic Patients

To explore brain functions in schizophrenic patients, the global analytic strategy of multichannel EEG was performed that combines measures of global complexity (Ω), total power (Σ) and generalized frequency (Φ), and EEG microstate analysis was applied to multichannel EEG data for 24 nonmedicated patients and 24 healthy subjects. The patients had higher Ω and Σ values, and lower Φ values compared with healthy subjects. Three topographical classes were obtained from all EEG data by EEG microstate analysis. The mean duration of one topographical class in the patients was shortened compared to healthy subjects. These results indicated looser cooperativity, or decreased connectivity of the active brain process and deviant brain information processing in schizophrenic patients.

Conventional and Wavelet Coherence Applied to Sensory–Evoked Electrical Brain Activity

The use of coherence is a well-established standard approach for the analysis of biomedical signals. Being entirely based on frequency analysis, i.e., on spectral properties of the signal, it is not possible to obtain any information about the temporal structure of coherence which is useful in the study of brain dynamics, for example. Extending the concept of coherence as a measure of linear dependence between realizations of a random process to the wavelet transform, this paper introduces a new approach to coherence analysis which allows to monitor time-dependent changes in the coherence between electroenecphalographic (EEG) channels. Specifically, we analyzed multichannel EEG data of 26 subjects obtained in an experiment on associative learning, and compare the results of Fourier coherence and wavelet coherence, showing that wavelet coherence detects features that were inaccessible by application of Fourier coherence.

Topographic Organization of Nonlinear Interdependence in Multichannel Human EEG

Thispaper investigates the spatial organization of nonlinear interactions between different brain regions in healthy human subjects. This is achieved by studying the topography of nonlinear interdependence in multichannel EEG data, acquired from 40 healthy human subjects at rest. An algorithm for the detection and quantification of nonlinear interdependence is applied to four pairs of bipolar electrode derivations to detect posterior and anterior interhemispheric and left and right intrahemispheric interdependences. Multivariate surrogate data sets are constructed to control for linear coherence and finite sample size. Nonlinear interdependence is shown to occur in a small but statistically robust number of epochs. The occurrence of nonlinear interdependence in any region is correlated with the concurrent presence of nonlinear interdependence in other regions at high levels of significance. The strength, direction and topography of the interdependences are also correlated. For example, posterior interhemispheric interdependence from right-to-left is strongly correlated with right intrahemispheric interdependence from back-to-front. There is a subtle change in these correlations when subjects open their eyes. These results suggest that nonlinear interdependence in the human brain has a specific topographic organization which reflects simple cognitive changes. It sometimes occurs as an isolated phenomenon between two brain regions, but often involves concurrent interdependences between multiple brain regions.

Effects of nootropic drugs for demented patients—a study using LORETA

To evaluate the efficacy of nootropic drugs on higher brain function in terms of time and space, electrical field distributions of the scalp map and low-resolution electromagnetic tomography (LORETA) were applied for evoked potentials (EPs) and spontaneous eyes-closed EEG. The studies were carried out on demented patients. We examined them before and after the administration of nicotine with a patch and nefiracetam, which is a pyrrolidine derivative agonist. We recorded event-related potentials (ERPs) with auditory “oddball” paradigm, auditory middle latency response (MLR) and spontaneous eyes-closed resting EEG. Multichannel EPs and EEG data were measured and averaged using a Biologic Brain Atlas. LORETA was used to compute the three-dimensional intracerebral distribution of electric activity of the EPs and the EEG frequency bands. Psychological examinations were also performed. After treatment with nefiracetam, the potential distribution of P3 differed clearly between before and after the administration. This change showed improvement towards normal values. For nicotine, significant effects were found in the MLR P1 component and in some EEG frequency bands. In addition, LORETA for EEG indicated inhibitory, normal and excitatory activity. These findings were supported by significant improvements of the performance test. We conclude that the spatial distribution of inhibitory, normal and excitatory activity, obtained from multichannel EPs and EEG data, allows the assessment of the complex effect of nootropic drugs.

Visualization of significant ERD/ERS patterns in multichannel EEG and ECoG data

Objectives: Analysis of event-related desynchronization (ERD) and event-related synchronization (ERS) often requires the investigation of diverse frequency bands. Such analysis can be difficult, especially when using multichannel data. Therefore, an effective method for the visualization of event-related changes in oscillatory brain activity is required.Methods: A bootstrap-based method is presented which gives time–frequency maps showing only significant changes of ERD or ERS in predetermined frequency bands.Results: Examples from an electroencephalographic study and an electrocorticographic study are shown. The results demonstrate how easily reactive channels and their spatio-temporal and frequency-specific characteristics can be identified by means of this method.Conclusions: The proposed method is a simple but effective way to visualize significant ERD/ERS patterns.

Analysis and visualization of single-trial event-related potentials.

In this study, a linear decomposition technique, independent component analysis (ICA), is applied to single-trial multichannel EEG data from event-related potential (ERP) experiments. Spatial filters derived by ICA blindly separate the input data into a sum of temporally independent and spatially fixed components arising from distinct or overlapping brain or extra-brain sources. Both the data and their decomposition are displayed using a new visualization tool, the "ERP image," that can clearly characterize single-trial variations in the amplitudes and latencies of evoked responses, particularly when sorted by a relevant behavioral or physiological variable. These tools were used to analyze data from a visual selective attention experiment on 28 control subjects plus 22 neurological patients whose EEG records were heavily contaminated with blink and other eye-movement artifacts. Results show that ICA can separate artifactual, stimulus-locked, response-locked, and non-event-related background EEG activities into separate components, a taxonomy not obtained from conventional signal averaging approaches. This method allows: (1) removal of pervasive artifacts of all types from single-trial EEG records, (2) identification and segregation of stimulus- and response-locked EEG components, (3) examination of differences in single-trial responses, and (4) separation of temporally distinct but spatially overlapping EEG oscillatory activities with distinct relationships to task events. The proposed methods also allow the interaction between ERPs and the ongoing EEG to be investigated directly. We studied the between-subject component stability of ICA decomposition of single-trial EEG epochs by clustering components with similar scalp maps and activation power spectra. Components accounting for blinks, eye movements, temporal muscle activity, event-related potentials, and event-modulated alpha activities were largely replicated across subjects. Applying ICA and ERP image visualization to the analysis of sets of single trials from event-related EEG (or MEG) experiments can increase the information available from ERP (or ERF) data.