Wearable devices can provide therapy in smaller, more frequent aliquots than traditional robotic rehabilitation therapies, since they have the potential to be administered outside of a clinical setting. Furthermore, wearable robotics have the potential to provide therapy while performing actual Activities of Daily Living (ADLs), which could in turn make therapy more effective [1] . However, in order to realize this vision, wearable devices must be equipped with user-driven controls that are both robust and intuitive.
A common approach to user-driven control is to measure mechanical or biological signals from the user in order to infer their intent. These signals are commonly used in a Supervised Learning approach: a regressor or a classifier is trained based on data with ground truth intent labels associated with it. Such data is typically collected by an experimenter in a dedicated training session. As an example, in our own previous work, we have introduced a wearable hand orthosis (Figure 1 ) for stroke subjects and used ipsilateral electromyography (EMG) as an input to determine the subject's intended hand motion [2] .
However, this approach is affected by challenges stemming from concept drift, i.e. the phenomenon where the measured biosignals change over time. Concept drift can occur between different sessions (intersession drift) or even gradually within a single session (intrasession drift). In healthy subjects and amputees, concept drift is caused by fatigue, and repositioning of the sensors, among other factors [3] . In stroke subjects, concept drift is additionally aggravated by abnormal muscle coactivation [4] and by the interaction of the hand and the robotic device ( Figure 1 ).
While we have found concept drift to be a significant problem for the stroke population, it is also rarely addressed Fig. 1 . Top: hand orthosis with multimodal sensing suite. Bottom: stroke subject performing an assisted grasp. Due to abnormal synergies, muscle activation signals change significantly compared to training data collected at rest, a type of concept drift that must be accounted for during intent inferral.
in the literature. Supervised learners compensate for concept drift by using a training set which incorporates data with as much signal variation as possible. In our own previous work cited above, we trained with data for many arm positions and orthosis states, which allowed our classifier to generalize to intrasession concept drift; we ignored intersession concept drift by retraining every session. However, such training comes at a high cost, since it is manually labeled, requiring the user to generate motions and labels specifically for training. This places a substantial burden on the user, especially in the case of stroke subjects, who fatigue quickly [5] .
Semi-supervised learning provides a potential solution to both intrasession and intersession concept drift, as it uses a small labeled dataset and then exploits additional unlabeled data to improve classifier performance. We hypothesize these controls will require less training data than supervised controls, while maintaining high accuracies.
The main contributions of this paper are as follows. We propose two semi-supervised learning algorithms to help our orthosis control adapt to concept drift. We propose a disagreement-based algorithm for intrasession drift (e.g. when the subject changes their arm position), and a Kmeans clustering algorithm for intersession drift where the data has shifted radically in the feature space (e.g. when the subject has doffed and donned the device). To our knowledge, we are the first to propose a semi-supervised control for a hand orthosis. We introduce a novel K-means semi-supervised algorithm, and also apply disagreement-based semi-supervision in the novel context of multimodal biosignals for intent inferral. We show that semi-supervised controls can reduce the burden placed on the subject during training for ipsilateral hand controls.
The preliminary data we collected with stroke patients shows that, while we do not always achieve the same accuracies as we could with a more extended or more frequent training procedure, semi-supervision can still reduce the training burden. Due to the Covid-19 pandemic, we were only able to collect a limited testing set with two stroke subjects, and perform offline analysis of this data covering both inter-and intrasession drift. We therefore consider this to be an exploratory study, one that nevertheless indicates that semi-supervised algorithms merit further investigation as controls for wearable orthoses.
In machine learning, there are three paradigms with which a classification algorithm can be trained: supervised learning, where all of the training points have a corresponding label, unsupervised learning, where none of the training points have a label, and semi-supervised learning, where a small subset of the training points have a corresponding label.
Traditionally, controls for prosthetics and orthotics have been supervised -trained on a relatively small test set and used during a longer session [6] , [7] , [8] . However, leveraging unlabeled data may make the control algorithm more robust to fatigue, different arm poses and abnormal muscle coactivation.
Semi-supervised learning has been shown to be an effective control paradigm for hand prosthetics. In this field, semisupervision uses the assumption that the user will perform gestures at a low frequency to correct the classifier [3] , [9] . Semi-supervised formulations have been described for EMG classifiers, updating based on confidence, or when there were rapid changes in the prediction stream [10] . Other semi-supervised paradigms for EMG include using a postprocessing neural network for prediction correction [11] , using all new data for updates [12] , reinforcement learning [13] , and cycle substitution paired with probability weighting [14] . He et al. showed updating when confidence was high improved classification of wrist movement [15] . Liu et al. found common characteristics among EMG classifiers to eliminate classifier retraining in later sessions [16] .
All of the above works are specific to EMG. Many of them leverage the low frequency nature of human hand motions in order to correct the classifiers [10] , [9] , [3] . The above works are designed for prosthetic controls and only tested on healthy subjects or amputees. Only three studies look at intersession accuracy [11] , [16] , [9] .
To our knowledge, semi-supervised learning has never been applied to a control for a hand orthosis. Concept drift for stroke subjects differs from amputees because of the abnormal coactivation in stroke subjects [4] . Prosthetic controls do not have to contend with this phenomenon.
There is a family of semi-supervision which we believe could also be applied to rehabilitation robotics. Disagree-ment based semi-supervised learning asks multiple learners to collaborate in order to exploit unlabeled data [17] . Disagreement semi-supervision uses confident learners to train less confident learners, and is well suited to ensemble learning [18] , [19] , [20] , [21] . To our knowledge, this type of semi-supervision has never been applied to an orthotic or prosthetic control.
To our knowledge, K-means has never been used to provide updates for a semi-supervised algorithm.
Our orthosis is an exotendon device consisting of a forearm splint and fingertip components. These two parts are connected through an exotendon network. The device is underactuated, moving all of the fingers at once. When the motor retracts the tendons, the subject's fingers extend. When the motor releases the tendons, the subject uses their own grip strength to close their hand. Figure 1 shows the exotendon device and the multimodal sensing suite, and additional details on the hardware can be found in our previous studies [22] . For the purposes of this work, we briefly review the sensing modalities mounted on our device: 1) Forearm EMG: EMG signals of the forearm from an 8 sensor armband (Myo from Thalmic Labs).
2) Motor Position: A motor encoder provides position feedback, allowing us to determine the state of the orthosis.
3) Finger Joint Angles: Some subjects retain partial voluntary movement of their fingers, so we measure finger joint angles. We place one inertial measurement unit (IMU) on the pointer, and one IMU on the back of the hand. The difference between the two IMUs measures the aggregate angle of the finger's joints. The derivative of the joint angle determines when the subject initiates voluntary motion or when the motor retracts or extends the exotendon network.
We measure the force between the device and the hand. This modality is provided by a force sensitive resistor (FSR) mounted inside the thumb fingertip component. We use the time derivative of the pressure.
To determine user's intent, we collect the raw EMG data (e 1 . . . e 8 ), motor position Γ, and time derivatives of the joint ∆j and pressure ∆p data at 100Hz. At time t, we standardize the sensor data, and collect it in a data vector x t :
We apply a median filter for each Φ i in Φ ens , and then average the filteredΦ values:
We note that generally Φ iT = 1. We compare each probability inΦ enŝ T to a threshold set by the experimenter L R , L O , L C , respectively. If none of the values exceed the threshold, the Intent t is set to the same value the previous time step Intent t−1 . Thresholds are set with subject feedback so the control is responsive, but there are no spurious errors during sustained hand commands.
If the control predicts the user intends to open, the device retracts the tendon, extending the fingers. If the user intends to close, the device extends the tendon, allowing the user to flex the fingers. If the predicted intention is to relax, we continue to send the previous motor command to the device.
Now that we have formulated our intent detection, we discuss how to use a semi-supervised learning algorithm to improve our classification accuracies.
Semi-supervised learning exploits unlabeled data to modify our intent detection classifier. We hypothesize it can make our intent detection robust to concept drift caused by fatigue, subject movement, and donning/doffing of the orthosis.
For any semi-supervised algorithm, we require an oracle. The oracle determines which new datapoints should be used to update the classifier and labels the data. The datapoints labeled by the oracle assembled into a training dataset X. Since we use an ensemble classifier, we generate a training dataset X i for every base learner i in the ensemble. When X contains a specified amount of data, we use use the training data and labels from the oracle to update the classifier.
We would like our semi-supervised learning algorithm to address two kinds of concept drift -intrasession and intersession concept drift. Intrasession concept drift tends to be a gradual shift in the data over time, whereas intersession concept drift is a sudden, often large, redistribution of the data in feature space (principally caused by donning and doffing the device). As such, the semi-supervised algorithms which work well for intrasession concept drift may not be appropriate for intersession concept drift, and visa versa.
We propose two semi-supervised algorithms: a disagreement semi-supervision, and a K-means semi-supervision.
The first semi-supervised learning algorithm we present uses a disagreement based oracle. When concept drift occurs gradually, as for intrasession testing, we hypothesize that can leverage disagreement between multiple learners. We assume that when concept drift begins, some of the base learners will be robust to the small changes in the data and will remain confident. Other learners which are not robust to the drift are corrected by the confident learners.
Our proposed disagreement based semi-supervision is enacted as follows: at time t, we calculate the entropy E of each base classifier i:
where k is the number of possible Intent classes for the classifier. We use entropy as a measure of the classifier's confidence. Lower entropy indicates higher confidence. Confident base learners are used to correct less confident predictors. We define confident predictors as base learners where E i < 0.2. Learners which are not confident have E i > 0.8. We select our confidence thresholds empirically.
If all confident classifiers agree on the subject's intent, i.e. if argmax(Φ i ) is the same for all confident predictors, for each unconfident predictor i, we add f i t to X i , along with the Intent label agreed upon by the confident predictors.
Once the combined number of training points across all X i s is a sufficiently large value (we chose 200 datapoints), the data and labels are used to update the classifier, all X i s are reset, and the supervision process restarts.
Oracles can also correct the classifier (before the base learners are updated). With disagreement semi-supervision, we only want confident predictors to contribute to the output of the ensemble. Only including confident predictors where E i < 0.2 is too restrictive, so we have an additional empirically selected threshold for the correction. We calculate the final probability for the ensemble as an average of all the probabilities from learners whose entropy is less than 0.6:
If there are no base learners where E i < 0.6 thenΦ enŝ T is calculated using all of the base learners in the ensemble.
We are the first to use disagreement semi-supervision for an assistive robot. We can successfully leverage this paradigm for a novel application because our orthosis includes a multimodal sensing suite with independent sensing modalities [23] . Disagreement semi-supervision works best if the base learners include multiple independent views [24] , or a large number of base learners [25] . Therefore, we use ensembles with at least five base learners whose features are sampled from all the sensors in the multimodal sensing suite.
The second semi-supervised algorithm we propose uses Kmeans clustering to label incoming data. With intersession concept drift, the data shifts in feature space. Thus, we cannot assume the majority of the base learners are correct. We therefore propose K-means semi-supervision to compensate for intersession concept drift. This is an unsupervised algorithm, so we do not require the classifier from the previous session to correctly classify any of the new data.
The algorithm for our K-means semi-supervision is as follows: we instruct the subject to perform all three intent motions at least once in the first 40 seconds of a new session. For each base learner i in the ensemble, we collect the first 40 seconds of sensor data X i = f i t , t ∈ [0s, 40s]. We then use K-means to cluster each X i dataset, specifying that it should look for three clusters, the number of Intent classes.
For each base learner i, K-means computes three cluster centers c i 1 , c i 2 , c i 3 and predicts which cluster each sample in X i belongs to.
We assume that each of the clusters found by K-means correspond to an Intent; however, we do not know which cluster corresponds to which Intent. To assign an intent to the clusters, we calculate the distance from each cluster center to each class mean in the base classifier i:
where j is the cluster and k is the Intent class. We take the minimum d j,k and assign cluster j to Intent k. We then take the next smallest dĵ ,k whereĵ andk do not belong to the cluster or Intent which have already been paired. Finally, the remaining cluster and Intent are paired together. Since the base learners have different features, the features f i t which come from a single time point may not be assigned the same Intent. Despite this, our experiments show that Kmeans semi-supervision can improve control performance.
K-means assigns each sample in X i to a cluster, which serves as the labels with which we can update our classifier. This algorithm only updates the base learners once.
Once the X i has a sufficient number of datapoints, we update our classifier. We use linear discriminant analysis classifiers (LDAs) as our base learners because they do not need past training data for updates. An LDA base learner i with k classes has k + 1 parameters: a mean vector for each class µ i k and a covariance matrix Σ i . To update our ensemble, we update each base learner i independently using the dataset X i collected for that LDA.
To update the parameters of an LDA base learner i, let z k be a sample from X i which is labeled as class k. The updated mean vector for class k µ k and the updated covariance matrix Σ for each LDA are calculated as follows:
where N i is the number of training data points for the base classifier i to date, and n i k is the number of training datapoints for the base classifier labeled as class k to date. 
Our experiments were performed with two chronic stroke survivors. Testing was approved by the Columbia University Institutional Review Board, and performed in a clinical setting under the supervision of an Occupational Therapist.
We hypothesize that semi-supervised controls will allow us to compensate for both intersession and intrasession concept drift while maintaining high accuracies.
Since this is a preliminary study to determine the feasibility of semi-supervised controls for orthoses, we perform offline analysis of sensor data. Due to COVID-19, we were unable to collect data for as many subjects or for as many sessions as we would have liked.
We have two data collection protocols: a complete protocol, and an abbreviated protocol. For the complete collection protocol: we collect data for all three intents under three conditions: 1) with the arm resting on a table and the orthosis motor off, 2) with the arm raised above the table and the orthosis motor off, and 3) with the arm raised above the table and the orthosis motor on, actively moving the hand. Specifically for the third case, Table I shows the commands given to the subject and the ground truth collected while the motor retracts and extends the tendons. In the abbreviated collection protocol, we only collect data from condition three in the extended protocol.
During data collection, the experimenter collects the true subject intent, or ground truth, while providing verbal commands to the subject.
In intersession experiments, we test if a classifier can be used at a later date without additional labeled training data.
We collect subject data on two occasions, with the first occurring approximately a year before the second. In the first session, we collect one dataset using the complete collection protocol. In the second session, we collect four sets of data using the same protocol -one trains a baseline control, and the other three are testing datasets. We train three classifiers:
• Supervised EMG, second session data: trained on labeled data from the second session. Such classifiers have high accuracy and are standard in the field, but have a high training cost. We consider this a baseline, as it makes the impractical assumption that users will provide training data each session. η = 1 and f 1 = (e 1 , ..., e 8 ). This classifier's parameters do not change. • Supervised EMG, first session data : trained on data from the first data collection session, assuming no labels are available on data from the second session. The ensemble parameters are η = 1 and f 1 = (e 1 , ..., e 8 ).
The parameters of this classifier do not change. • K-means Semi-Supervised EMG, first session data:
this is our approach introduced here, without requiring labels from the second session. Initially, this classifier is the same as the Supervised EMG trained on the first session data. As new unlabeled data arrives, it is labeled by a K-means oracle and used to update the classifier. We use each of the classifiers above to predict the subjects' Intent for the three testing datasets from the second session. We compare predicted Intent to the ground truth.
In our intrasession experiments, we test whether a classifier can be trained using less data and still achieve high accuracies during Intent detection. Here, all the data is collected during the same session. We collect one dataset using the abbreviated protocol. We collect four datasets using the entire protocol -one trains a baseline control, and the others are testing datasets. We train four classifiers:
• Supervised EMG, full training data: the only classifier trained on labeled data from the entire collection protocol. Classifiers trained under the same conditions as the test data have high accuracies. We consider this classifier as a baseline, as the assumption of labeled data from the entire protocol is impractical due to high burden on the patient. η = 1 and f 1 = (e 1 , ..., e 8 ).
Classifier parameters do not change after training. • Supervised EMG, partial training data: trained on the abbreviated protocol. η = 1 and f 1 = (e 1 , ..., e 8 ).
Classifier parameters do not change after training. • Supervised Multimodal, partial training data: trained on the abbreviated protocol. η is a random number between 5 and 10. The features for each base learner are selected randomly from x. The parameters of this classifier do not change. • Disagreement Semi-Supervised Multimodal, partial training data: this is our approach, only requiring labels on the abbreviated protocol. Initially, this classifier is the same as the supervised multimodal control with partial data. As new data arrives, it is labeled by a disagreement oracle and used to update the classifier. We use the above classifiers to predict the subjects' Intent for the three testing datasets collected with the entire protocol. We compare the predicted and ground truth Intents.
We select the multimodal features randomly, but, in our experience, this does not notably affect performance.
In each set of experiments, we report the results as an average across the three testing datasets. We report the motor command accuracy: the number of time points at which the Supervised EMG, second session data 83.6 ± 6.5 Supervised EMG, first session data 54.5 ± 1.7 K-means Semi-Supervised EMG, first session data 62.9 ± 6.8 command to the motor was correct, divided by the number of total time points. We report motor command accuracy instead of global accuracy (how often the classifier gets each class correct) because we care less about the correct Intent than about moving the orthosis as the subject intends. a) Intersession Experiments: Table II shows the average motor command accuracy across the three testing datasets for each subject. We italicize the output of the baseline classifier, and bold the best performing, non-baseline classifier. Figure 2a shows the classifiers' output for an example dataset where K-means semi-supervision improved the performance of a classifier trained during the first session.
For Subject 1, K-means semi-supervision lowered the accuracy by 4.2%. For Subject 2, K-means semi-supervision improved the accuracy of the EMG classifier by 8.4%. For both subjects, even when the K-means classifier improved performance of the supervised EMG classifier, it did not perform as well as the baseline classifier. b) Intrasession Experiments: Table III shows the average accuracy across the three testing datasets for each subject. Figure 2b shows the classifiers' output for an example dataset where disagreement semi-supervision improved the performance of a classifier trained on an abbreviated protocol beyond a baseline trained on the entire collection protocol.
For both subjects, the disagreement semi-supervision outperformed all other classifiers, including the baseline.
The intersession experiments show that K-means semisupervision improves classifier performance for one subject, but not for the other, when only using labeled data from the first session. Further testing is needed with more subjects to see whether we can predict when K-means semi-supervised learning will work and when it will not.
The intersession experiments also show that, although it can improve the performance of a supervised classifier trained on a previous session, K-means semi-supervision does not perform as well as a classifier trained on data from the same day as the testing data. This may be due to the fact that our K-means algorithm only updates the classifier once during the session. In future work, we would like to combine K-means with another supervision technique to continue updating the classifier throughout the session.
The intrasession experiments show that, for both subjects, our disagreement semi-supervision outperforms even the baseline classifier with full labeled training data, despite being trained on less data. This indicates that semi-supervised learning could make our control more robust to concept drift, while reducing the training burden.
We compare our semi-supervised multimodal classifier to our supervised multimodal classifier, both trained on partial data, to see if our advantage over the baseline comes from the semi-supervised nature of the control or from the multimodal ensemble. For both subjects, the semi-supervised learner outperforms the supervised classifier trained on similar data. We conclude that it is semi-supervision which improves performance, not the multimodal ensemble.
In the intrasession experiments, contrary to our expectations, the baseline classifier results in approximately the same accuracy as the supervised classifiers trained on partial data. We hypothesize that the advantage of the baseline classifier is less pronounced because we collect data during nonfunctional motions. In the future, we would like to evaluate our semi-supervised algorithms with functional movements.
Overall, our experiments show that semi-supervised learning has the potential to reduce the burden placed on users by controls that require an extensive labeled dataset to detect intent. Both of our proposed algorithms provide some improvement in accuracy when the classifier is trained on a more limited dataset or on data from a previous session. The K-means semi-supervised control worked better for Subject 2 than it did for Subject 1, which indicates that different methods could help some subjects more than others. The disagreement semi-supervision worked for both subjects, and even outperformed the baseline classifier.
In this paper, we propose two semi-supervised algorithms. We hypothesize that semi-supervision will help our controls adapt to concept drift, and could reduce the training burden placed upon the user for orthotic EMG-based controls.
To our knowledge, this is the first time a semi-supervised learning algorithm has been proposed for a hand orthosis. We intend this as an exploratory proof-of-concept study to evaluate semi-supervised learning as a potential avenue for orthotic controls. Due to COVID-19, we were unable to test with a larger number of subjects, or to use semi-supervision online to drive the orthosis for functional tasks, and thus consider this a preliminary study. Nevertheless, we believe our experiments on data from stroke subjects show that semisupervised learning is a promising avenue of exploration for orthotic hand controls. The results of the experiments also indicate areas of future research, emphasizing that these tests should be repeated in the context of functional movements.