Logistic-weighted Regression Improves Decoding of Finger Flexion from Electrocorticographic Signals
One of the most important applications of brain computer interfaces (BCIs) is to assist people who have disrupted neuromuscular channels through which the brain communicates with and controls its external environment by reproducing their motor functions with a cursor or a robotic arm. Thanks to the progress of invasive recording techniques and decoding algorithms in the past ten years, many single neuron-based and electrocorticography (ECoG)-based studies have been able to decode continuous trajectories of limb movements. Unlike traditional BCIs which classify discrete brain states, these studies require prediction of continuous variables. In other words, they belong to regression problems rather than classification problems.
Nevertheless, the studies of limb movement translation are in fact not pure regression problems, because the limbs are not always under the motion state. Whether it is during an experiment or in the daily life, the resting state of the limbs is usually as long as their motion state, if not longer. In this case, the recorded movement data will exhibit a binary property, which was not made the best of in the previous studies.
In this paper, we propose a novel algorithm named logistic-weighted regression to synthesize the binary information and the continuous information of the movement data. The algorithm can significantly improve the decoding of finger flexion in the system described in the link below.
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Experimental setup of the BCI system predicting finger flexion
The BCI Competition IV dataset collected by Kubanek et al, 2009 is employed for this study. Three patients with intractable epilepsy had electrode array on the surface of the brain for the purpose of localization of seizure foci prior to surgical resection. Each subject had a 48- or 64-electrode array placed over the frontal-parietal-temporal region including parts of sensorimotor cortex. During the experiment, the patients were asked to move specific individual fingers in response to visual cues. The subjects typically flexed the indicated finger 3-5 times during a 1.5-3 s time period, and then rest for 2 s. The ECoG signals from the electrodes were amplified, band-pass filtered between 0.15 and 200 Hz, digitized at 1 kHz and recorded in a general purpose BCI2000 system. The flexion of each finger was measured and digitized in 12 bit and 25 Hz by a data glove (5DT Data Glove 5 Ultra, Fifth Dimension).
Diagram summarizing the principle of logistic-weighted Regression
The main characteristic of the finger flexion data is that it's approximately binary. Since the features extracted from the ECoG signals don't have a similar binary property, a traditional linear regression cannot fit the finger flexion data very well. As a result, the huge fluctuation of the target variable make the linear regression result full of oscillations.
On the other hand, since the finger flexion data is approximately binary, a threshold can be manually set to easily classify it into two states (motion and non-motion). Because the natural flexion or extension of fingers are limited to certain ranges due to the physical constraints of our hand, the threshold is usually very robust. After the classification the target variable becomes entirely binary, as a result of which a logistic regression can be used to estimate the probability that a time bin belongs to the motion state. The result of the logistic regression exhibits much more binary information than that of the linear regression, but it loses all the information within each state.
Therefore, a better strategy is to combine the two methods. In the algorithm called logistic-weighted regression, we weight the linear regression results with the logistic regression results on the basis of the Law of Total Expectation.
Correlation coefficients between real finger flexions and finger flexions predicted by linear regression, pace regression and logistic-weighted regression
To compare the algorithm with the existing methods, we also implemented linear regression and pace regression (part of the Java-based Weka package). The performances of these methods were evaluated based on the correlation between the real finger flexions within the testing set and the corresponding flexions predicted by different methods. As is shown in the table, the decoding performance of logistic-weighted regression is better than those of the other methods, whether it is for every single finger, every single subject or the overall average.
Real finger flexions and finger flexions predicted by linear regression, pace regression and logistic-weighted regression
In order to show the advantage of the algorithm in details, an excerpt of real finger flexions and predicted finger flexions within a testing set is shown above. It is obvious in the figure that, compared with the other two methods, logistic-weighted regression gives a much better estimate during the non-motion state of the finger without losing the sensitivity of detecting movements. This is because a logistic regression generates a small probability of movement when a finger is resting in reality, and by weighting the linear regression result with the probablity, the oscillations appearing in the non-motion phase of (A) and (B) are greatly suppressed.