Limb-position Robust Classification of Myoelectric Signals for Prosthesis Control using Sparse Representations

Abstract

The fundamental objective in non-invasive myoelectric prosthesis control is to determine the user’s intended movements from corresponding skin-surface recorded electromyographic (sEMG) activation signals as quickly and accurately as possible. Linear Discriminant Analysis (LDA) has emerged as the de facto standard for real-time movement classification due to its ease of use, calculation speed, and remarkable classification accuracy under controlled training conditions. However, performance of cluster-based methods like LDA for sEMG pattern recognition degrades significantly when real-world testing conditions do not resemble the trained conditions, limiting the utility of myoelectrically controlled prosthesis devices. We propose an enhanced classification method that is more robust to generic deviations from training conditions by constructing sparse representations of the input data dictionary comprised of sEMG time-frequency features. We apply our method in the context of upper-limb position changes to demonstrate pattern recognition robustness and improvement over LDA across discrete positions not explicitly trained. For single position training we report an accuracy improvement in untrained positions of 7.95%, p ≪ .001, in addition to significant accuracy improvements across all multi-position training conditions, p < .001.

I. Introduction

The movement classification performance of Linear Discriminant Analysis [1] using sEMG signals as input is sharply degraded when the user is exposed to real-world conditions that were not explicitly trained [2]. Electrode migration [3], [4], arm position [5]–[7], and load changes [8] are all factors which negatively affect the classification performance of LDA and other pattern recognition methods for prosthesis control [9]. LDA classifies by transforming the data to a lower dimensional subspace with the objective of minimizing the scattering of each class data cluster and maximizing the separation between clusters. However, all of the previously mentioned conditional effects can increase cluster size and diminish inter-cluster distances. Additionally, the input sEMG produced by a given movement during real-world use may deviate substantially from those produced under trained conditions [10], guaranteeing misclassification if it falls outside its respective class boundary. Going forward, we will refer to untrained conditions as asymmetric as they do not accurately reflect the conditions under which the classifier was trained.

To be considered robust in the context of myoelectric pattern recognition, a classifier must maintain a usable degree of discrimination when tested in asymmetric conditions to avoid class confusion and a consequent fall-off in accuracy. Algorithmic modifications like fault-detection [11] and confidence-based rejection [12] have been devised to probabilistically reduce decision errors. Training in more conditions can also improve general performance [9], a finding we reinforce herein, but this process could be continued beyond practical limits of regular user training. Furthermore, the training data becomes ever more crowded with each additional trained condition, diminishing the gains or tightening error margins from such an approach. For an amputee, these factors can render myoelectric prosthesis control unusable. The problem of condition-dependent data variation is not limited to myoelectric prosthesis control so it is practical to investigate methods which have proven successful in other application areas.

II. Sparse Representations

Facial recognition research has produced sparse representation classification (SRC) algorithms which quickly and accurately classify class-dense, feature-dense data that is 70% corrupted or 30% occluded [13]. Our decision to experiment with sparse representations for myoelectric pattern recognition originates from these error tolerance properties. We desire to avoid the daunting task of mitigating every conceivable data variation and training condition. Rather than create class boundaries through algorithm training, each class can simply be defined by the span of all its vector members, forming a single training data matrix $A_{m\times n}$ where m is the number of features and n is the size of the training data. New data samples y can be interpreted as a linear combination of the data Ax, where the specific weights x of each data sample are unknown. Furthermore, a sparsity constraint can be imposed on x by utilizing the ${\ell }_1$ basis pursuit solution

$$\mathbf{x}=\underset{\mathbf{x}}{\arg \min }{\Vert \mathbf{x}\Vert }_1\text{s.t.}\mathbf{Ax}=\mathbf{y}$$ (1)

This sparsity constraint helps ensure that the linear combination is composed of a minimal subset of the training data while reducing the influence of outliers. The ideal case for classification is to have this linear combination weighted heavily towards members of the correct class. Sparse representation classification [13] can be defined as follows: given a new test sample $y_{m\times 1}$ and a dataset matrix $A_{m\times n}$ which contains unit-normalized feature vectors of the training data sorted by movement class, $A=[A_1|A_2|\dots |A_C]$; find the ${\ell }_1$ solution (1) for x; construct matrices $A_{m\times n}^0$ for each of the i classes wherein only the vectors in $A_i$ are nonzero; and calculate the residual $r_i={\Vert {\mathbf{A}}_i^0\mathbf{x}-\mathbf{y}\Vert }_2$ for each class. The class of minimum residual is the chosen class.

The ${\ell }_1$ solution for x in (1) can be posed as the following convex optimization problem:

$$\widehat{\mathbf{x}}=\underset{\mathbf{x}}{\arg \min }\left\{\frac{1}{2}{\Vert \mathbf{Ax}-\mathbf{y}\Vert }_2^2+\lambda {\Vert \mathbf{x}\Vert }_1\right\}$$ (2)

where $\mathrm{\lambda }>0$ is an appropriately chosen regularization parameter influencing sparsity. Since the second term in (2) may not be continuously differentiable, a proximal gradient method can be used to approximate x. Given the need to classify intended movements near real-time, we use Fast Iterative-Shrinkage Thresholding (FISTA) with backtracking [14] to converge according to the update rule

$${\mathbf{x}}_{k+1}=S_{\lambda t}({\mathbf{x}}_k-2t_k{\mathbf{A}}^{\mathrm{\top }}({\mathbf{Ax}}_k-\mathbf{y}))$$ (3)

where t_k is the step-size at iteration k and $S_{\lambda t}{(\mathbf{v})}_i=(|v_i|-\lambda t)\cdot \text{sign}(v_i)$ is a shrinkage or soft-thresholding operator on each element in v. For the results herein, $\lambda =0.001$, and $t_k$ is determined iteratively using FISTA with t₀ = 1.

We define the SFT₁ method for myoelectric pattern recognition as the FISTA-based implementation of ${\ell }_1$-sparse classification described above with the discrete-time Fourier transform (FT) magnitude coefficients concatenated to each time-domain (TD) feature [15] vector. Preliminary investigations into the use of only the TD features yielded positive outcomes in terms of confusion robustness and overall accuracy, but algorithm performance improved using either the FT features or the concatenation of TD and Fourier coefficient features. The concatenated set was used to obtain our results.

III. Methods

This study was conducted in accordance with protocols approved by the Johns Hopkins University’s Institutional Review Board (IRB). Three able-bodied subjects participated in this experiment. The able-bodied subjects have no known neurological disorders and are ages 20-35.

A. Data Acquisition and Feature Extraction

Eight sEMG signals were continuously measured with differential electrode pairs placed equidistant around the circumference of the forearm muscle of greatest mass. Input data was amplified using 13E200 (Ottobock, Plymouth, MN) amplifiers and then sampled at 1024Hz using the NI USB-6009 (National Instruments, Austin, TX). Subsequent 20-500Hz digital bandpass and 60Hz digital notch filters were applied to the signals. TD features were extracted from a 200ms moving window (175ms overlap) resulting in a new feature vector every 25ms. The five TD features extracted from each signal were mean absolute value, waveform length, signal variance, slope sign change, and zero-crossings [15] for a total of 40 features. Furthermore, we use the magnitude of FT coefficients as a feature and found that a 256-length FT from each window of sEMG was optimal. Due to FT symmetry, half of the coefficients are redundant features and are discarded resulting in 128 features per signal.

B. Experiment Protocol and Analysis

For this study, we decided to focus on one asymmetric condition; specifically, the limb position effect. Untrained static positions can elicit sEMG patterns which are quite different from those in the training set, thereby hindering classifier performance. To explore pattern recognition performance with respect to limb position, a training method was devised allowing for simultaneous position and sEMG-based data acquisition. During a single trial, a computer prompt presented each subject with a random target position from 9 possible, representing one 23×23 cm physical location within the 69×69 cm activation space (Fig. 1). Once at the desired target position, 5 distinct movement cues were prompted in random order: rest (R), hand open (HO), hand close (HC), wrist pronate (WP), and wrist supinate (WS). Recording began 2 sec. after initial cue prompt and continued for 3 sec. while data was collected for each position and cue combination. The process was repeated for a random ordering of all 9 positions to complete a single trial. Each subject completed a total of 3 trials with no inter-trial resting period.

Fig. 1.

Training environment set-up. The subject is presented with a position indicator randomly chosen within a grid of 9 possible positions. Once the target position is acquired, the subject is presented with movement cues while sEMG data are collected.

All classification and analysis of our recorded data was performed offline using MATLAB 2014b (Mathworks, Inc., Natick, MA). The statistical significance p-values were obtained through two-sample T-testing of LDA performance against our method across the specified conditions.

IV. Results

The objective of our 9-position experiment was to quantify the comparative advantage, if any, of using sparse-based classification over LDA throughout a contiguous subset of static positions within the larger prosthesis activation space. Each position-specific asymmetric condition is constructed by regulating the number of positions used for training data while testing the resulting classifier in all 9 positions. For a desired quantity of trained positions, k, data from trials 1 and 2 in those positions were used for training and validated on data from trials 1, 2, and 3 in the remaining 9 – k positions. Performance in the k training positions was validated on the data from trial 3. This process was repeated for all possible k-of-9 position combinations, $\left(\begin{array}{c}9\\ k\end{array}\right)$, to obtain aggregate results across all subjects and position combinations.

To provide a better sense of the phenomena influencing the aggregate numbers, the per-position classifier accuracy confusion results of one subject’s single-position training are shown Fig. 2(a). In this case, the classifier is only trained with data from position 4 and tested in all 9 positions. Fig. 2(b) is the same analysis, but with position 9 used for training. The result from (a) is also shown in Fig. 2(c) emphasizing the comparison of per-position class confusion.

Fig. 2.

Position-variant performance fall-off from single-position training. (a) LDA (left) vs. SFT₁ (right) per-position accuracy when trained in side position 4 and tested in all positions, with underlying visualization of the per-position class confusion. (b) The same analysis but for corner position 9. (c) Classifier confusion example trained in side position 4 and tested in position 6. In all cases, SFT₁ demonstrated less asymmetric fall-off and class confusion than LDA within our 9-position experiment space. The confusion of SFT₁ was often limited to a single class. In the specific examples shown, both algorithms are supplied with the same train/test dataset for classification.

Our approach yielded significant p < .001 improvement across all conditions (Fig. 3) and lower variation with respect to positions used in the training set. In the case of single position training, the aggregated success rates of SFT1 and LDA are 89.77% and 81.82% (t₅₂ = 7.95 ± 0.05, p ≪ .001), respectively. In general, the accuracy improvement is increased when train and test conditions are more asymmetric. In symmetric conditions the improvement is minimal. On average, the total decision time including feature extraction for SFT₁ was 20.5 ms compared to 3.42 ms for LDA.

Fig. 3.

Classifier comparison from our limb-position experiment. Each combination of k positions were used for training and the classifiers were tested in all 9 positions. SFT₁ significantly outperforms LDA in untrained positions. Lower k-values correspond to greater train/test asymmetry.

V. Discussion

A major clinical hurdle for myoelectric pattern recognition control is the need to train in as many conditions as possible. Obviously, the many conditions a patient may encounter during real-world use cannot be enumerated nor trained for in a practical sense. Therefore, classification strategies which retain discrimination power despite asymmetric conditions like untrained limb positions are critical to improving the utility of myoelectric control.

The above results demonstrate that our sparse representation method significantly outperforms LDA in positions which were not explicitly trained, yielding a greater comparative advantage for more dissimilar train-test datasets and a lower performance variance with respect to which positions were trained. Illustrated in Fig. 2, SFT₁ possessed less confusion and asymmetric condition fall-off than LDA within our experiment position-space. It is also noteworthy that SFT₁ class confusion was typically limited to a single movement. Single-class fault detection may prove easier to mitigate from an engineering standpoint than the multi-class confusion of LDA.

The error-tolerant properties of sparse representation led to our decision to assess its potential use in myoelectric control, but additional factors warrant our optimism in such an approach. One benefit of sparse representations is that the training data need not cluster in a particular way, allowing interspersed samples to have membership in separate classes. The class dictionary itself can be sparsely defined (n′ < n), utilizing only members which maximally span each class. Furthermore, sparse classification methods can operate efficiently even with a large number of feature dimensions, allowing the inclusion of an arbitrary number of additional data sensors to aid movement discrimination. To establish a baseline and avoid competing influences, we demonstrate a bare-bones implementation of sparse classification above to obtain our results. However, the approach is extensible with modifications for residual-based fault detection and rejection [13] among others.

Though the limb position effect is but one asymmetric condition in myoelectric control, going forward we will explore our working theory that sparse classification methods better extrapolate beyond the boundaries of a generic trained condition space. Therefore, we will expand our experiment to test this theory in the offline context of static load variation and electrode migration, and online under dynamic movement conditions. To find an overall best method, we will incorporate any useful modifications such as confidence rejection mechanisms into our approach. Positive outcomes in this study comprising a population of amputee and able-bodied subjects could have broad implications for advancing the real-world utility of prosthesis control resulting in a reliable, condition-invariant myoelectric control paradigm.