A robust feature adaptation approach against variation of muscle contraction forces for myoelectric pattern recognition-based gesture characterization

doi:10.1016/j.bspc.2024.106446

Biomedical Signal Processing and Control
生物医学信号处理与控制

Volume 95, Part A, September 2024, 106446
卷 95，A 部，2024 年 9 月，106446

https://doi.org/10.1016/j.bspc.2024.106446 Get rights and content 获取权利和内容

Highlights 亮点

•
Development of a novel non-Euclidean space based descriptor for EMG characterization.
开发一种基于新型非欧几里得空间的描述符用于肌电图特征化。
•
Extensive validation of the approach in the presence of Muscle contraction force variation.
在肌肉收缩力变化的情况下，对该方法进行了广泛的验证。
•
Experimental results revealed the efficacy of the proposed method in aiding smooth deployment EMG-based controlled Prostheses.
实验结果揭示了所提方法在帮助平滑部署基于肌电图的控制假肢方面的有效性。
•
The proposed could potentially spur positive advancements in research and development in the field of intelligent myo-control systems.
所提议的可能会推动智能肌肉控制系统领域的研究和开发的积极进展。

Abstract 摘要

The lack of a robust scheme that can withstand the muscle contraction force variations (MCFV) in pattern recognition (PR)-based myoelectric prosthesis is a major challenge that prevents it from being fully realized in clinical settings. To overcome this issue, a novel feature adaptation scheme which partially leverages the non-Euclidean space concept based on Riemann manifold was proposed in this study. The scheme is comprised of three logically connected stages. The first stage leverages the symmetric positive definite (SPD) matrices as features. The second stage reduces the discrepancy between SPDs of different force levels by projecting all the SPDs towards a Riemann mean, while the third stage reinforces the robustness against MCFV by projecting the features toward a common distribution drawn from the training set. While considering the three force levels, the scheme was validated on in-house and public datasets obtained from amputees who performed different wrist and finger movements. The results of the evaluation revealed that the suggested method could greatly address the issue of MCFV with an increment in movement decoding greater than 15.02% accuracy and 16.50% F1-score against other state-of-the-art techniques. Additional investigation on the suitable force level that could be a benchmark for training showed that the moderate force level would give an optimal performance compared to low, or high force level in the presence of MCFV. The findings of the study revealed that the suggested control scheme could be used to adapt to MCFV, which could improve the overall robustness of myoelectric systems in both commercial and clinical applications.
在基于模式识别（PR）的肌电假肢中，缺乏一种能够承受肌肉收缩力变化（MCFV）的稳健方案是一个主要挑战，这阻碍了其在临床环境中的全面实现。为了解决这个问题，本研究提出了一种新颖的特征适应方案，该方案部分利用基于黎曼流形的非欧几里得空间概念。该方案由三个逻辑上相连的阶段组成。第一阶段利用对称正定（SPD）矩阵作为特征。第二阶段通过将所有 SPD 投影到黎曼均值，减少不同力水平之间的差异，而第三阶段通过将特征投影到从训练集中提取的共同分布，增强对 MCFV 的鲁棒性。在考虑三个力水平的情况下，该方案在来自进行不同手腕和手指运动的截肢者的内部和公共数据集上进行了验证。评估结果显示，所建议的方法能够大大解决 MCFV 问题，运动解码的准确率提高超过 15.02%和 16。与其他最先进技术相比，F1-score 达到 50%。对适合的力水平进行的额外研究表明，在存在 MCFV 的情况下，中等力水平相比低或高力水平能够提供最佳性能。研究结果显示，建议的控制方案可以用于适应 MCFV，这可以提高肌电系统在商业和临床应用中的整体鲁棒性。

Keywords 关键词

Upper limb prostheses

Electromyogram EMG

Riemann manifold

Symmetric positive definite (SPD) matrices

上肢假肢肌电图 EMG 黎曼流形对称正定 (SPD) 矩阵

1. Introduction 1. 引言

For many years, pattern recognition (PR) techniques have been used to control the electromyogram (EMG) based prostheses. These techniques are aimed at restoring the lost limb functions of amputees. The popularity of this method can be attributed to its non-invasive nature, as well as the ability to provide numerous motor-related data [1], [2], [3]. Although several studies have been done in an attempt to realize clinically relevant EMG-PR driven control schemes, such schemes are characterized by satisfactory performance when implemented in controlled lab circumstances [4], [5], but when deployed in practical conditions they face substantial performance degradation due to a number of confounding factors that rarely come into play in laboratory environments. Such factors include unavoidable shift of electrodes, alteration of muscle contraction forces, and the movement of subjects while eliciting targeted limb movements [6], [7]. Due to these confounding factors and others, only a handful of companies have managed to deploy EMG-PR based prosthetic control schemes [7], [8]. In essence, the technological advancements that have occurred within the PR-driven prosthesis sector are still in their early stages. This has prompted us to focus on the core issue of variability in the muscle contraction force and resolving it through the feature adaptive scheme which in-turn makes the features more invariant.
多年来，模式识别（PR）技术一直被用于控制基于肌电图（EMG）的假肢。这些技术旨在恢复截肢者失去的肢体功能。这种方法的普及可以归因于其非侵入性特征，以及能够提供大量与运动相关的数据[1]，[2]，[3]。尽管已经进行了一些研究，试图实现临床相关的 EMG-PR 驱动控制方案，但这些方案在受控实验室环境中实施时表现令人满意[4]，[5]，但在实际条件下部署时，由于许多在实验室环境中很少出现的混杂因素，它们面临显著的性能下降。这些因素包括电极不可避免的位移、肌肉收缩力的变化，以及在引发目标肢体运动时受试者的移动[6]，[7]。由于这些混杂因素及其他因素，只有少数公司成功部署了基于 EMG-PR 的假肢控制方案[7]，[8]。本质上，PR 驱动的假肢领域内发生的技术进步仍处于早期阶段。这促使我们关注肌肉收缩力变异性的核心问题，并通过特征自适应方案来解决，从而使特征更加不变。

Several research works have been carried out to explore the effects of muscle contraction force variation (MCFV). For instance, the study carried out by Dennis et al. verified that the decoding results of the time domain descriptors was significantly affected by the variation of muscle contraction forces [7]. Similarly, Scheme et al. demonstrated that around 32 % of motor intent classification performance was decreased if a force variation ranged from 20 % to 80 % [2]. Likewise, Nazarpour et al. revealed that the decrease in motion intent decoding caused by MCFV could be attributed to change in the probability density function and time–frequency properties of EMG signals related to specific limb movements [9]. In an effort to explore the effects of MCFV on decoding performance of EMG pattern recognition systems, Mojisola et al. carried out a systematic study and proposed the invariant time domain features that demonstrated invariance to force changes [10]. Besides, Scheme et al. in his respective studies, demonstrated that the decoding performance could be enhanced when training a corresponding classifier with the EMG data obtained from dissimilar force levels [2], [11]. Similarly, Li et al. presented a parallel classification technique that involved the use of parallel classifiers at varying forces levels [12]. Despite the improvement obtained from these techniques, the laborious process of acquiring data from different force levels to train classifiers can be a major challenge when it comes to developing clinical prostheses. Therefore, in this research we propose a robust feature extraction and adaptation scheme to resolve the effect of variation of muscle contraction forces using Riemann manifold metrics and probability density distribution adaptation. The proposed method utilizes data from one force level only during training (and testing on other force levels) thus representing a practical case where data from one force level is always needed for training the prosthesis.
多项研究工作已开展以探讨肌肉收缩力变化（MCFV）的影响。例如，Dennis 等人的研究验证了时域描述符的解码结果受到肌肉收缩力变化的显著影响[7]。类似地，Scheme 等人展示了当力的变化范围在 20%到 80%之间时，运动意图分类性能下降了约 32%[2]。同样，Nazarpour 等人揭示了 MCFV 导致的运动意图解码下降可以归因于与特定肢体运动相关的 EMG 信号的概率密度函数和时频特性的变化[9]。为了探讨 MCFV 对 EMG 模式识别系统解码性能的影响，Mojisola 等人进行了系统研究，并提出了对力变化不变的时域特征[10]。此外，Scheme 等人在其各自的研究中展示了当使用来自不同力水平的 EMG 数据训练相应分类器时，解码性能可以得到提升[2]，[11]。同样，Li 等人提出了一种并行分类技术，该技术涉及在不同力量水平下使用并行分类器[12]。尽管这些技术带来了改进，但从不同力量水平获取数据以训练分类器的繁琐过程在开发临床假肢时可能是一个主要挑战。因此，在本研究中，我们提出了一种稳健的特征提取和适应方案，以解决肌肉收缩力量变化的影响，使用黎曼流形度量和概率密度分布适应。所提出的方法在训练期间仅利用一个力量水平的数据（并在其他力量水平上进行测试），因此代表了一个实际案例，其中始终需要来自一个力量水平的数据来训练假肢。

Numerous signal transformation techniques have been proposed, including the Fourier transform [13], the Wavelet transform [14], [15], the S-transform [16], and the synchrosqueezing transform [13], with the objective of attaining an enhanced representation capable of discerning distinct classes. These methods operate in the euclidean space. However, certain types of data, such as EMG, EEG and speech signals are high-dimensional, exist in a nonstationary state, and do not conform to a Euclidean space [17], [18], [19], [20], [21]. Consequently, applying analysis techniques that rely directly on Euclidean distances (space) to such data often results in inadequate results. By considering non-Euclidean based techniques (space) such as Riemannian geometry, it becomes possible to extract and utilize the inherent structure of the data. This approach enables meaningful comparisons between data points in high-dimensional spaces, thereby facilitating more effective analysis and utilization of the data. Specifically in this study, our main focus is on the Riemannian geometry of covariance matrices (CMs), which fall under the category of Symmetric Positive-Definite (SPD) matrices [22], [23]. The utilization of CMs as features for high-dimensional data, while leveraging their intrinsic Riemannian geometry, has shown considerable effectiveness in diverse tasks, especially in the domains of EEG (electroencephalography) and image processing [24], [25]. However, when dealing with data that originates from diverse domains, such as data collected from different acquisition systems, different sessions, or different force levels, the covariance matrices may exhibit highly distinct structures. This discrepancy in structures can lead to poor performance when using covariance matrices as features [17]. To remedy this, we proposed a feature adaptation scheme which is based on Riemann geodesic distance and probability distribution parameters. Specifically, our contributions can be summarized as follows:(1) For the first time we have attempted to leverage the Riemann manifold metric and geodesic distance in decoding multiple classes of targeted limb movement of EMG based prostheses and minimize the discrepancy (which is caused by variation of muscle contraction forces) between the training and test set feature space obtained from different muscle contraction forces. (2) We attempted to minimize the alterations in probability density function between the training and testing datasets/features (which are acquired from dissimilar force levels) by pooling all the test features towards the distribution density function of the training set.
许多信号变换技术已被提出，包括傅里叶变换 [13]、小波变换 [14]、S 变换 [16] 和同步挤压变换 [13]，其目的是获得一种增强的表示，能够区分不同的类别。这些方法在欧几里得空间中操作。然而，某些类型的数据，如肌电图（EMG）、脑电图（EEG）和语音信号是高维的，处于非平稳状态，并且不符合欧几里得空间 [17]、[18]、[19]、[20]、[21]。因此，直接依赖欧几里得距离（空间）的分析技术应用于这些数据时，往往会导致结果不佳。通过考虑基于非欧几里得的技术（空间），如黎曼几何，可以提取和利用数据的内在结构。这种方法使得在高维空间中对数据点进行有意义的比较成为可能，从而促进数据的更有效分析和利用。具体来说，在本研究中，我们的主要关注点是协方差矩阵（CMs）的黎曼几何，这些矩阵属于对称正定（SPD）矩阵的范畴 [22]、[23]。利用 CM 作为高维数据的特征，同时利用其内在的黎曼几何，在各种任务中显示出相当大的有效性，特别是在脑电图（EEG）和图像处理领域。然而，当处理来自不同领域的数据时，例如从不同采集系统、不同会话或不同力量水平收集的数据，协方差矩阵可能会表现出高度不同的结构。这种结构上的差异可能导致使用协方差矩阵作为特征时性能不佳。为了解决这个问题，我们提出了一种基于黎曼测地距离和概率分布参数的特征适应方案。具体而言，我们的贡献可以总结如下：（1）我们首次尝试利用黎曼流形度量和测地距离来解码基于肌电图（EMG）的假肢的多类目标肢体运动，并最小化由肌肉收缩力量变化引起的训练集和测试集特征空间之间的差异。我们试图通过将所有测试特征汇聚到训练集的分布密度函数上，来最小化训练和测试数据集/特征之间的概率密度函数的变化（这些特征来自不同的力水平）。

2. Materials and methods 2. 材料和方法

2.1. Data collection 2.1. 数据收集

In order to evaluate the efficacy of the proposed approach, we performed experimental analysis on non-invasively acquired EMG signals obtained from both the in-house and public databases.
为了评估所提方法的有效性，我们对从内部和公共数据库获得的非侵入性肌电信号进行了实验分析。

Public dataset: This is a publicly available dataset [1] and can be accessed from the URL: https://www.rami-khushaba.com/biosignals-repository. The electromyogram recordings were collected via standard experimental procedure from nine transradial amputees. In the data collection phase, each participant was equipped with a set of eight pairs of Ag/AgCl electrodes (manufactured by a Germany company, Tyco healthcare). The electrodes were positioned round the stump area and the EMG data were acquired at a sampling frequency of 2000 Hz. Additionally, a LABVIEW-based virtual instrument (VI) was employed to facilitate both signal acquisition and assisting the subjects in generating the desired force level. The experiments incorporated six distinct grip and finger movements, namely spherical grip (SG), thumb flexion (TF), tripod grip (TG), index flexion (IF), fine pinch (FP), and hook grip (HG). The amputees executed each of these movements at three varying force levels: high, moderate, and low. Besides, five trials were recorded for every force level, and each trial consisted of a holding phase lasting between 8 and 12 sec. For more details about the dataset and experimental protocol, refer to [1].
公共数据集：这是一个公开可用的数据集[1]，可以通过以下网址访问：https://www.rami-khushaba.com/biosignals-repository。肌电图记录是通过标准实验程序从九名前臂截肢者收集的。在数据收集阶段，每位参与者配备了一套八对 Ag/AgCl 电极（由德国公司 Tyco healthcare 制造）。电极被放置在残肢区域周围，EMG 数据以 2000 Hz 的采样频率获取。此外，使用基于 LABVIEW 的虚拟仪器（VI）来促进信号采集，并协助受试者产生所需的力量水平。实验包含六种不同的握持和手指运动，即球形握持（SG）、拇指屈曲（TF）、三脚架握持（TG）、食指屈曲（IF）、精细捏合（FP）和钩形握持（HG）。截肢者在三个不同的力量水平下执行每种运动：高、中和低。此外，每个力量水平记录了五次试验，每次试验包括一个持续 8 到 12 秒的保持阶段。有关数据集和实验方案的更多细节，请参阅[1]。

In-house dataset: The experiments were carried out on two individuals with transradial amputation, whose residual arm lengths varied from 7.1 cm to 7.4 cm, respectively. Before data acquisition, the subjects were informed about the study's objectives and the protocol for the data acquisition. They were then asked to sign the consent form, which indicated their willingness to participate in the experiment and allowed the publication of their data. Subsequently, the research protocol obtained approval from the Institutional Review Board at the Shenzhen Institute of Advanced Technology.
内部数据集：实验在两名桡骨截肢者身上进行，他们的残余手臂长度分别为 7.1 厘米和 7.4 厘米。在数据采集之前，受试者被告知研究的目的和数据采集的协议。然后，他们被要求签署知情同意书，表明他们愿意参与实验并允许发布他们的数据。随后，研究协议获得了深圳先进技术研究院伦理审查委员会的批准。

For data acquisition, a commercial EMG data collection system (from Delsys Inc) was employed for recording signals from the residual arm of the participants using six wireless bipolar sensors. Specifically, four sensors were strategically positioned around the lower arm while remaining two sensors were placed on the flexor and extensor muscles, as depicted on Fig. 1 (a). The study encompassed seven different movement classes (indicated in Fig. 1 (b)), namely wrist pronation (WP), hand open (HO), wrist flexion (WF), wrist extension (WE), hand close (HC), wrist supination (WS), and no-movement (NM). In order to examine the impact of variation of muscle contraction force, participants were instructed to perform the aforementioned motion intents at three distinct levels of muscle contraction forces at (measured in terms of Maximum Voluntary Contractions (MVCs)): 20 % MVC, 50 % MVC, and 80 % MVC. The selection of these specific muscle contraction levels was based on recommendations from previous studies [1], [10], [26], so as to ensure a standardized and benchmark experimental procedure.
为了数据采集，采用了一套商业化的肌电图（EMG）数据采集系统（来自 Delsys Inc），使用六个无线双极传感器记录参与者残余手臂的信号。具体而言，四个传感器被战略性地放置在下臂周围，而另外两个传感器则放置在屈肌和伸肌上，如图 1（a）所示。本研究涵盖了七种不同的运动类别（如图 1（b）所示），即腕部内旋（WP）、手部打开（HO）、腕部屈曲（WF）、腕部伸展（WE）、手部闭合（HC）、腕部外旋（WS）和无运动（NM）。为了检验肌肉收缩力变化的影响，参与者被指示在三种不同的肌肉收缩力水平下执行上述运动意图（以最大自愿收缩（MVC）为单位测量）：20% MVC、50% MVC 和 80% MVC。这些特定肌肉收缩水平的选择基于之前研究的建议[1]，[10]，[26]，以确保实验程序的标准化和基准化。

i)
Low muscle contraction force level: During this particular session, subjects were instructed to generate a force equivalent to about 20 % of the MVC in order to perform the specified limb movements. A visual feedback system was then implemented to make sure that the force applied correctly matched the target force level. This system provided participants with real-time visual representations of their muscle contraction levels, which were derived from the amplitude of the electromyogram recordings.
低肌肉收缩力水平：在这一特定的实验中，受试者被指示产生相当于最大自愿收缩（MVC）约 20%的力量，以执行指定的肢体运动。随后实施了一个视觉反馈系统，以确保施加的力量正确匹配目标力量水平。该系统为参与者提供了实时的肌肉收缩水平的视觉表示，这些表示是根据肌电图记录的幅度得出的。
ii)
Moderate muscle contraction force level: During this session, subjects were instructed to execute each class of movement by using a medium force level of the muscle contraction, which was about 50 % MVC.
适度的肌肉收缩力水平：在本次实验中，受试者被指示以中等的肌肉收缩力水平执行每类运动，约为 50% MVC。

iii) High force level contraction force level: In this particular session, the subjects were instructed to execute the various types of movements using a high force level of about 80 % MVC. Fig. 2 conceptualizes the experimental protocol at different force levels.
iii) 高强度收缩力水平：在这一特定实验中，受试者被指示以约 80%的最大自愿收缩（MVC）执行各种类型的运动。图 2 概念化了不同力水平下的实验协议。

During the experiments, each subject performed five trials for all seven specific movements. Each trial had a duration of approximately 5 to 6 s. Between the various trials, a 5-second break was implemented to prevent mental fatigue and muscle distress. Before shifting to a new session, the subjects were provided with a break of around 5 to 8 min. The EMG recordings were sampled at the frequency of 1024 Hz. To eliminate the effects of power line interference, a notch filter of frequency 50 Hz was used. Besides, a 5th order Butterworth filter of 20 Hz to 500 Hz frequency range was applied to refine the signal recordings.
在实验过程中，每个受试者对所有七种特定动作进行了五次试验。每次试验的持续时间约为 5 到 6 秒。在各次试验之间，实施了 5 秒的休息，以防止心理疲劳和肌肉不适。在转到新一轮之前，受试者获得了大约 5 到 8 分钟的休息。肌电图（EMG）记录的采样频率为 1024 Hz。为了消除电源线干扰的影响，使用了 50 Hz 的陷波滤波器。此外，还应用了 20 Hz 到 500 Hz 频率范围的 5 阶巴特沃斯滤波器来精炼信号记录。

2.2. Methods 2.2. 方法

In this study, a robust feature extraction and adaptation scheme were proposed to accurately characterize EMG signals even when MCFV is present. We denoted this scheme/features as Non-Euclidean Riemannian-based Descriptor (NERD). Before extracting the features, a sliding window technique was applied to both the in-house and public datasets with window size of 150 ms and overlap of 50 ms as recommended from previous works [27]. The key steps of the proposed scheme (NERD) are outlined in the following subsections with the visual guide in the flow-chart in Fig. 3.
在本研究中，提出了一种稳健的特征提取和适应方案，以准确表征即使在存在 MCFV 的情况下的 EMG 信号。我们将该方案/特征称为非欧几里得黎曼基础描述符（NERD）。在提取特征之前，采用滑动窗口技术对内部和公共数据集进行了处理，窗口大小为 150 毫秒，重叠为 50 毫秒，符合之前工作的建议[27]。所提方案（NERD）的关键步骤在以下小节中概述，并在图 3 的流程图中提供了视觉指导。

(i)
Symmetric positive definite (SPD) matrices construction:
对称正定（SPD）矩阵构造：

Let

X \in X^{nxNs}

denotes an EMG signal with

n

representing the quantity of channels, and Ns the amount of discrete time points. The sample covariance matrix (SCM), denoted as

S \in R^{nxn}

can be estimated using Eq. (1). It is important to note that there are various estimators available to estimate the SCM, including the Ledoit Wolf, Schaefer Strimmer, Oracle approximating shrunk (OAS), among others [28], [29]. In this study, we utilized the “OAS” which is a regularized estimator, as it demonstrated superior performance compared to other estimators.(1)

S = \frac{X X^{T}}{trace (X X^{T})}

让

X \in X^{nxNs}

表示一个 EMG 信号，

n

表示通道数量，Ns 为离散时间点的数量。样本协方差矩阵（SCM），记作

S \in R^{nxn}

，可以使用公式（1）进行估计。需要注意的是，有多种估计量可用于估计 SCM，包括 Ledoit Wolf、Schaefer Strimmer、Oracle 近似收缩（OAS）等[28]，[29]。在本研究中，我们使用了“OAS”，这是一种正则化估计量，因为它相比其他估计量表现出更优越的性能。 (1)

S = \frac{X X^{T}}{trace (X X^{T})}

These covariance matrices are classified as belonging to the symmetric positive definite (SPD) space [22]. Let a set of

nxn

SPD matrices be denoted as

S (n)

.
这些协方差矩阵被归类为对称正定（SPD）空间 [22]。设一组

nxn

SPD 矩阵记为

S (n)

。

Riemannian Manifold: According to Wang et al. [30], the Riemannian manifold is characterized as a smooth manifold where the tangent space forms an infinite-dimensional Euclidean space.
黎曼流形：根据 Wang 等人[30]的说法，黎曼流形被描述为一个光滑流形，其中切空间形成一个无限维的欧几里得空间。

The characterization of the space of SPD as Riemannian manifolds has facilitated the application of Riemann-based operations on covariance matrices. Since the covariance matrices possess all the essential properties of SPD matrices [22], [23]. Below are important definitions in the Riemann manifold that were used to develop part of the novel feature adaption scheme proposed in this study.
SPD 空间作为黎曼流形的特征化促进了基于黎曼的操作在协方差矩阵上的应用。由于协方差矩阵具有 SPD 矩阵的所有基本属性[22]，[23]。以下是黎曼流形中的重要定义，这些定义用于开发本研究中提出的新特征适应方案的一部分。

Geodesic distance (

δ_{γ})

: It is the shortest path (in the differential Riemann manifold) between two SPDs as conceptualized in Fig. 4. The distance between two SPDs (

S_{1}

and

S_{r}

) is given in Eq. (2).(2)

δ_{γ} {(S}_{1} {, S}_{r}) = \int_{0}^{1} γ (S_{1} {, S}_{r}, t) d t = ‖ L o g (S_{1}^{- \frac{1}{2}} S_{r} S_{1}^{- \frac{1}{2}}) ‖ F

测地距离 (

δ_{γ})

：它是两个 SPD 之间的最短路径（在微分黎曼流形中），如图 4 所示。两个 SPD（

S_{1}

和

S_{r}

）之间的距离在公式(2)中给出。 (2)

δ_{γ} {(S}_{1} {, S}_{r}) = \int_{0}^{1} γ (S_{1} {, S}_{r}, t) d t = ‖ L o g (S_{1}^{- \frac{1}{2}} S_{r} S_{1}^{- \frac{1}{2}}) ‖ F

In the Eq. (2), the

Log (.)

represents the logarithmic matrix and

‖ . ‖ F

is the frobenius norm. The Riemann distance, denoted as

δ_{γ} (\dots)

exhibits the property of affine invariance [31] and is widely recognized as the Affine Invariant Riemann Metric (AIRM) distance. According to Moakher et al [32], using Eq. (2), an estimation of the geodesic distance between symmetric positive definite matrices

S_{1}

and

S_{r}

on the Riemann space can be obtained as in Eq. (3):(3)

γ (S_{1}, S_{r}, t) = S_{1}^{\frac{1}{2}} {(S_{1}^{- \frac{1}{2}} S_{r} S_{1}^{- \frac{1}{2}})}^{t} S_{1}^{\frac{1}{2}} t \in (0, 1)

在公式(2)中，

Log (.)

表示对数矩阵，

‖ . ‖ F

是弗罗贝尼乌斯范数。黎曼距离，记作

δ_{γ} (\dots)

，具有仿射不变性[31]，并被广泛认可为仿射不变黎曼度量（AIRM）距离。根据 Moakher 等人[32]的研究，使用公式(2)，可以在黎曼空间中获得对称正定矩阵

S_{1}

和

S_{r}

之间的测地距离估计，如公式(3)所示： (3)

γ (S_{1}, S_{r}, t) = S_{1}^{\frac{1}{2}} {(S_{1}^{- \frac{1}{2}} S_{r} S_{1}^{- \frac{1}{2}})}^{t} S_{1}^{\frac{1}{2}} t \in (0, 1)

It should be noted that

t

is a hyper-parameter to be tuned and in this study we used

t

= 0.5 due to its consistent and high results compared to other values which were examined in the preliminary tests. The preliminary analysis was conducted by using moderate force for training and testing with different force levels, moderate, low, and high at different values of

t

(on Random Forest classifier) as indicated in Table 1.
需要注意的是，

t

是一个需要调整的超参数，在本研究中我们使用了

t

= 0.5，因为与初步测试中检查的其他值相比，它的结果一致且较高。初步分析是通过使用中等力度进行训练和测试，采用不同的力度水平（中等、低和高）以及不同的

t

值（在随机森林分类器上）进行的，如表 1 所示。

Table 1. Classification accuracy of NERD at different values of t on Random Forest classifier: Moderate: indicate that the moderate force level was used for testing, Low: the low force level was used for testing, and High: means the high force level was used for testing.
表 1. NERD 在随机森林分类器上不同 t 值的分类准确率：中等：表示使用了中等力度水平进行测试，低：表示使用了低力度水平进行测试，高：表示使用了高力度水平进行测试。

t values t 值	0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	10.0
Moderate 适度	47.71	87.47	87.54	87.57	87.51	87.70	87.62	87.62	87.54	87.67	87.51
Low 低	38.94	66.82	66.65	66.85	66.89	67.62	67.31	67.44	67.21	67.35	67.22
High 高	42.66	67.56	67.90	67.77	67.91	68.09	67.97	67.88	67.64	67.64	67.36

Tangent space (

T_{S})

: With reference to the Fig. 4, the tangent space at S, is defined by the collection (set) of tangent vectors denoted as

P_{i}

. Within this space, the metric exhibits a flat structure, which permits the utilization of arithmetic mean and various conventional mathematical techniques. Given a point

S \in S (n)

in a Riemann space, it is possible for every point

S_{i} \in S (n)

to find a tangent vector

P_{i} \in P (n)

such that

P_{i} = γ

(0). Where,

γ (t)

is the geodesic distance between

S

and

S_{i}

. The Riemannian

Log

map operator

{Log}_{s} : S (n) \to P (n)

enables the mapping

{Log}_{s} : (S_{i}) = P_{i}

(from the Riemann manifold to the tangent space), while the

Exp

map operator

{Exp}_{s} : (P_{i}) = S_{i}

enables a bijective mapping back to the original space of symmetric positive definite matrices

S (n)

. Using the AIRM [33] the two operations (

Log

and

Exp

) can be expressed as;(4)

{Exp}_{s} (P_{i}) = S^{\frac{1}{2}} E x p {(S}^{- \frac{1}{2}} P_{i} S^{- \frac{1}{2}}) S^{\frac{1}{2}}

(5)

{Log}_{S} (S_{i}) = S^{\frac{1}{2}} L o g {(S}^{- \frac{1}{2}} S_{i} S^{- \frac{1}{2}}) S^{\frac{1}{2}}

切空间 (

T_{S})

：参考图 4，点 S 的切空间由切向量的集合（集合）定义，记作

P_{i}

。在这个空间内，度量呈现平坦结构，这允许使用算术平均数和各种传统数学技术。在黎曼空间中给定一个点

S \in S (n)

，对于每个点

S_{i} \in S (n)

，可以找到一个切向量

P_{i} \in P (n)

，使得

P_{i} = γ

(0)。其中，

γ (t)

是

S

和

S_{i}

之间的测地距离。黎曼

Log

映射算子

{Log}_{s} : S (n) \to P (n)

使得从黎曼流形到切空间的映射

{Log}_{s} : (S_{i}) = P_{i}

成为可能，而

Exp

映射算子

{Exp}_{s} : (P_{i}) = S_{i}

则使得可以双射映射回对称正定矩阵的原始空间

S (n)

。使用 AIRM [33]，这两个操作（

Log

和

Exp

）可以表示为； (4)

{Exp}_{s} (P_{i}) = S^{\frac{1}{2}} E x p {(S}^{- \frac{1}{2}} P_{i} S^{- \frac{1}{2}}) S^{\frac{1}{2}}

(5)

{Log}_{S} (S_{i}) = S^{\frac{1}{2}} L o g {(S}^{- \frac{1}{2}} S_{i} S^{- \frac{1}{2}}) S^{\frac{1}{2}}

Note: The projection of SPD matrix from the Riemann space to the tangent manifold, and the inverse operation, can be achieved using Eqs. (4), (5). Fig. 4 conceptualizes the two operations. For example, based on the concept presented in Eq. (5), the logarithmic mapping of the SPD matrix

S_{1}

to the tangent space of

S_{r}

, considering the shortest geodesic distance

δ_{γ}

, can be approximated as follows:(6)

{S = S}_{r}^{\frac{1}{2}} L o g (S_{r}^{- \frac{1}{2}} S_{1} S_{r}^{- \frac{1}{2}}) S_{r}^{\frac{1}{2}}

注意：SPD 矩阵从黎曼空间投影到切丛的操作及其逆操作，可以使用公式（4）、（5）实现。图 4 概念化了这两种操作。例如，基于公式（5）中提出的概念，SPD 矩阵

S_{1}

到

S_{r}

的切空间的对数映射，考虑最短测地距离

δ_{γ}

，可以近似为如下： (6)

{S = S}_{r}^{\frac{1}{2}} L o g (S_{r}^{- \frac{1}{2}} S_{1} S_{r}^{- \frac{1}{2}}) S_{r}^{\frac{1}{2}}

From the Eqs. (5), (6), the

S_{i}

and

S_{r}

can be considered as reference points of projection. Thus, projecting the SPD (

S_{1}

) to tangent space, it is important to have the reference point

S_{r}

.
根据方程(5)、(6)，

S_{i}

和

S_{r}

可以视为投影的参考点。因此，将 SPD（

S_{1}

）投影到切空间时，参考点

S_{r}

是非常重要的。

Geometric mean: Inspired by Barachant et al. [33], the calculation of the mean of a set of m symmetric positive definite matrices can be achieved by utilizing the principles of the tangent space. Initially, the entire dataset of SPD matrices is projected onto the Euclidean (tangent) space using the Riemann Log map (as described in Eq. (5). In this tangent (Euclidean) space, the arithmetic mean can be easily computed. Subsequently, the resultant arithmetic mean is converted back into the SPD space using the Riemannian exponential mapping (as defined in Eq. (4). After a few iterations, the resultant geometric mean of the matrices (SPDs) is obtained. The process is expressed in Algorithm 1. Where,

S (n)

represents the set of all

nxn

SPD matrices,

m

denotes the amount of samples, and

t

is the number of iterations.

*Algorithm 1:* Geometric Mean of m SCM matrices
*Input:* m SCMs { $S_{1}, S_{2}, S_{3} \dots \dots S_{m}$ ) and tolerance > 0
*Output*: The estimated geometric mean ( $S_{r}$ )
*Initialize:* $S_{r}^{(t)}$ = $\frac{1}{m} \sum_{i = 1}^{m} {(S}_{i}), t = 1$
*While*
$\bar{S} = \frac{1}{m} \sum_{i = 1}^{m} {Log}_{S_{r}^{(t)}} {(S}_{i})$
$S_{r}^{(t + 1)} = {Exp}_{S_{r}^{(t)}} (\bar{S})$
$t = t + 1$
*Until* $‖ S_{r}^{(t + 1)} ‖ F$ <∈
*Return* $S_{r}^{(t + 1)}$

几何平均数：受 Barachant 等人[33]的启发，一组 m 个对称正定矩阵的平均值的计算可以通过利用切空间的原理来实现。最初，整个 SPD 矩阵的数据集通过 Riemann Log 映射投影到欧几里得（切）空间中（如公式（5）所述）。在这个切（欧几里得）空间中，算术平均数可以很容易地计算出来。随后，得到的算术平均数通过 Riemannian 指数映射转换回 SPD 空间（如公式（4）所定义）。经过几次迭代，得到矩阵（SPDs）的几何平均数。该过程在算法 1 中表示。其中，

S (n)

表示所有

nxn

SPD 矩阵的集合，

m

表示样本的数量，

t

是迭代的次数。

*Algorithm 1:* Geometric Mean of m SCM matrices
*Input:* m SCMs { $S_{1}, S_{2}, S_{3} \dots \dots S_{m}$ ) and tolerance > 0
*Output*: The estimated geometric mean ( $S_{r}$ )
*Initialize:* $S_{r}^{(t)}$ = $\frac{1}{m} \sum_{i = 1}^{m} {(S}_{i}), t = 1$
*While*
$\bar{S} = \frac{1}{m} \sum_{i = 1}^{m} {Log}_{S_{r}^{(t)}} {(S}_{i})$
$S_{r}^{(t + 1)} = {Exp}_{S_{r}^{(t)}} (\bar{S})$
$t = t + 1$
*Until* $‖ S_{r}^{(t + 1)} ‖ F$ <∈
*Return* $S_{r}^{(t + 1)}$

(ii)
Feature adaptation (FA) 特征适应 (FA)

To be more precise, in the process of feature adaptation all the high dimension EMG signals (of size Channels*Samples) in training set and testing set (from different force levels) were transformed to covariance matrices using Eq. (1). It should be noted that, these matrices were considered to belong in Riemann manifold. Therefore, to reduce the discrepancy between the training and testing matrices, every covariance matrix was projected into the tangent space using a common reference point

S_{r}

as expressed in Eq. (6), In our case,

S_{r}

represents the geometric mean (as outlined in Algorithm 1) of all covariance matrices in the training set. As per Fig. 3 we denoted the output of this stage for the training and test sets to be

S_{train}

and

S_{test}

respectively.
为了更精确地说，在特征适应的过程中，训练集和测试集中的所有高维 EMG 信号（大小为通道*样本）都使用公式（1）转换为协方差矩阵。需要注意的是，这些矩阵被认为属于黎曼流形。因此，为了减少训练矩阵和测试矩阵之间的差异，每个协方差矩阵都使用共同参考点

S_{r}

投影到切空间中，如公式（6）所示。在我们的案例中，

S_{r}

表示训练集中所有协方差矩阵的几何平均值（如算法 1 所述）。根据图 3，我们将这一阶段的输出分别标记为训练集和测试集的

S_{train}

和

S_{test}

。

(iii)
Distribution adaptation (DA)
分布适应（DA）

In this stage we project the features to follow the distribution of the baseline data (training set), were all the matrices from the test set

S_{test}

and training set

S_{train}

are projected to a common distribution using the arithmetic mean

U

and standard deviation

D

as outlined in Eq. (7).(7)

Z_{test} = \frac{S_{test} - U}{D} a n d Z_{train} = \frac{S_{train} - U}{D}

(8)

w h e r e, U = \frac{1}{m} \sum_{i = 1}^{m} ({S (i)}_{train})

and(9)

D = \sqrt{\frac{{(\sum_{i = 1}^{m} ({S (i)}_{train} - U))}^{2}}{m}}

在这个阶段，我们将特征投影到基线数据（训练集）的分布上，测试集

S_{test}

和训练集

S_{train}

中的所有矩阵都使用算术平均

U

和标准差

D

投影到一个共同的分布，如公式（7）所述。 (7)

Z_{test} = \frac{S_{test} - U}{D} a n d Z_{train} = \frac{S_{train} - U}{D}

(8)

w h e r e, U = \frac{1}{m} \sum_{i = 1}^{m} ({S (i)}_{train})

和 (9)

D = \sqrt{\frac{{(\sum_{i = 1}^{m} ({S (i)}_{train} - U))}^{2}}{m}}

From Eqs. (7), (8) and (9),

S_{train}

are the individual matrices from the training set and

m

is the amount of all matrices in

S_{train}

. The final outputs of the distribution adaption are denoted as

Z_{train}

and

Z_{test}

for the training and test set respectively. Therefore, in this paper we refer

Z_{train}

and

Z_{test}

as the Non-Euclidean Riemannian-based Descriptors (NERD).
根据方程（7）、（8）和（9），

S_{train}

是训练集中的个体矩阵，

m

是

S_{train}

中所有矩阵的数量。分布适应的最终输出分别表示为训练集和测试集的

Z_{train}

和

Z_{test}

。因此，在本文中，我们将

Z_{train}

和

Z_{test}

称为非欧几里得黎曼基础描述符（NERD）。

2.3. Other state-of-the-art methods for comparison
2.3. 其他先进方法的比较

To highpoint the significance of the NERD in addressing the impact of muscle contraction force variations, a comparative study was conducted. This study involved evaluating the proposed feature adaptation scheme alongside the following state-of-the-art methods from previous studies.
为了强调 NERD 在应对肌肉收缩力变化影响方面的重要性，进行了比较研究。该研究涉及评估所提出的特征适应方案以及以下来自先前研究的最新方法。

1.
Invariant Time domain descriptors (invTDD): Is a combination of five robust time domain features developed by Asogbon et al, and was specificalized for mitigating the effects of variation of muscle contraction forces [10].
不变时间域描述符（invTDD）：是由 Asogbon 等人开发的五个稳健时间域特征的组合，专门用于减轻肌肉收缩力变化的影响[10]。
2.
Root mean square (RMS) feature: Is commonly utilized for characterizing the EMG signals [34].
均方根（RMS）特征：通常用于表征肌电信号 [34]。
3.
Time domain features (TD4): Commonly utilized in EMG-based PR. They include, slope sign change, wavelength, mean absolute value, and zero-crossings [35].
时间域特征 (TD4)：常用于基于肌电图的 PR。它们包括斜率符号变化、波长、均值绝对值和零交叉 [35]。

We considered these methods as a comparative techniques since they have been used by other previous works and demonstrated comparative good performance [1], [10], [36].
我们将这些方法视为比较技术，因为它们已被其他先前的工作使用，并且表现出相对良好的性能 [1], [10], [36]。

It is worth noting that the same window length and overlap (150 ms, and 50 ms respectively), were used during the generation of invTDD, RMS, and TD4 features.
值得注意的是，在生成 invTDD、RMS 和 TD4 特征时，使用了相同的窗口长度和重叠（分别为 150 毫秒和 50 毫秒）。

2.4. Experimental analysis
2.4. 实验分析

To analyze the effectiveness of the NERD features and compare them with other features, three commonly used machine learning classifiers, Linear discriminant analysis (LDA), Random forest (RF), and Support vector machine (SVM) were applied to decode the inherent motion tasks [6], [37]. The reason behind using these classifiers is because they have been used by many researchers in signal processing works and have shown outstanding performance [38], [39], [40], [41] Additionally, to analyze the results of the investigated techniques we used accuracy metric as it has been widely leveraged in the field of myoelectric pattern recognition, and F1-score which includes both recall and precision for its derivation. The definitions of the metrics are indicated in Eqs. (10), (11).(10)

Accuracy = \frac{TP + T N}{TP + F P + T N + F N}

(11)

F 1 - s c o r e = \frac{2 * R e c a l l * P r e c i s i o n}{Recall + P r e c i s i o n} = \frac{2 T P}{2 T P + F P + F N}

为了分析 NERD 特征的有效性并将其与其他特征进行比较，应用了三种常用的机器学习分类器：线性判别分析（LDA）、随机森林（RF）和支持向量机（SVM）来解码固有的运动任务[6]，[37]。使用这些分类器的原因是它们已被许多研究人员在信号处理工作中使用，并且表现出色[38]，[39]，[40]，[41]。此外，为了分析所研究技术的结果，我们使用了准确率指标，因为它在肌电模式识别领域得到了广泛应用，以及 F1-score，它的推导包括了召回率和精确率。这些指标的定义在公式（10）、（11）中给出。 (10)

Accuracy = \frac{TP + T N}{TP + F P + T N + F N}

(11)

F 1 - s c o r e = \frac{2 * R e c a l l * P r e c i s i o n}{Recall + P r e c i s i o n} = \frac{2 T P}{2 T P + F P + F N}

From Eqs. (10), (11), TN denotes the true negative samples, TP: denotes the true positive samples, while FN and FP represent false negative and false positive, respectively.
从方程(10)、(11)中，TN 表示真正负样本，TP 表示真正正样本，而 FN 和 FP 分别表示假负样本和假正样本。

Furthermore, to verify the statistical significance of the proposed method, a non-parametric Friedman’s test was carried out before Dunn’s post hoc test. It is necessary to note that for a particular feature (i.e. RMS or NERD etc), the statistical significance was calculated by appending together features from all force levels.
此外，为了验证所提方法的统计显著性，在 Dunn 事后检验之前进行了非参数 Friedman 检验。需要注意的是，对于特定特征（即 RMS 或 NERD 等），统计显著性是通过将所有力级的特征合并在一起计算的。

3. Results and discussion
3. 结果与讨论

In this part, we elucidate a range of experimental results to evaluate the robustness of the proposed features. Additionally, we investigated the most suitable force level for obtaining training data when focusing solely on a single level of contraction force. We distributed our analysis in two scenarios, Experimental scenario 1: The classifiers were trained with one type of force level and tested with the same kind of force level. This approach is often used in literature, in studies which do not consider the effects of variation of forces. (2) Experimental scenario 2: The classifier is trained using a single force level and then tested with two other force levels that were not part of the training data. It is worth noting that the results are presented as average across all 11 subjects across both databases.
在这一部分，我们阐明了一系列实验结果，以评估所提出特征的稳健性。此外，我们调查了在仅关注单一收缩力水平时，获取训练数据的最合适力水平。我们将分析分为两种情境，实验情境 1：分类器使用一种力水平进行训练，并在相同的力水平下进行测试。这种方法在文献中经常使用，尤其是在不考虑力的变化影响的研究中。（2）实验情境 2：分类器使用单一力水平进行训练，然后在两个未包含在训练数据中的其他力水平下进行测试。值得注意的是，结果是以两个数据库中所有 11 个受试者的平均值呈现的。

3.1. Experimental scenario 1
3.1. 实验场景 1

In this particular scenario, we utilized 5-fold cross-validation to train and test the classifiers. The average results across all subjects from both datasets (in-house and public) are presented in accuracy in Fig. 5.
在这种特定情况下，我们使用了 5 折交叉验证来训练和测试分类器。图 5 中展示了来自两个数据集（内部和公共）所有受试者的平均结果，结果以准确率表示。

By closely observing the results in Fig. 5, the proposed features (NERD) have performed better than all other state-of-the-art techniques in all force levels and classifiers. For example, when considering the average classification across all force levels in Random forest classifier (Fig. 5 (a)), the NERD performed better with accuracy of 87.5 ± 6.9 %, compared to invTDD with an accuracy of 81.6 ± 8.3 %, RMS with 76.5 ± 10.2 %, and TD4 with an accuracy of 82.1 ± 9.0 %. This trend is similar in other classifiers LDA (Fig. 5 (b)) and SVM (Fig. 5(c)) with large margins observed in SVM classifier (88.7 ± 7.6 %, 76.9 ± 11.3 %, 78.2 ± 10.6 %, 77.8 ± 12.0 % accuracy for NERD, invTDD, RMS, and TD4 features respectively) with statistical significance of P < 0.01 against invTDD, RMS, and TD4. When looking at the most suitable force level from which the training dataset can be considered, there is no substantial and consistent difference between levels at similar feature type and classifier. For example, the classification performance of NERD at three force levels when using Random forest are 87.3 ± 6.6 %, 88.7 ± 7.8 %, and 86.6 ± 6.3 % at moderate, low and high force respectively.
通过仔细观察图 5 中的结果，所提出的特征（NERD）在所有力级和分类器中表现优于所有其他最先进的技术。例如，在随机森林分类器中考虑所有力级的平均分类时（图 5（a）），NERD 的准确率为 87.5 ± 6.9%，相比之下，invTDD 的准确率为 81.6 ± 8.3%，RMS 为 76.5 ± 10.2%，TD4 的准确率为 82.1 ± 9.0%。在其他分类器 LDA（图 5（b））和 SVM（图 5（c））中，这一趋势相似，SVM 分类器中观察到较大的差距（NERD、invTDD、RMS 和 TD4 特征的准确率分别为 88.7 ± 7.6%、76.9 ± 11.3%、78.2 ± 10.6%和 77.8 ± 12.0%），与 invTDD、RMS 和 TD4 相比具有统计显著性 P < 0.01。当考虑训练数据集最合适的力级时，在相似特征类型和分类器之间没有实质性和一致性的差异。例如，使用随机森林时，NERD 在三个力级的分类性能分别为 87.3 ± 6.6%、88.7 ± 7.8%和 86.6 ± 6.3%（中等、低和高力）。

To investigate further the performance of the feature techniques, we conducted the analysis using F1-score and the obtained results are indicated in Table 2. By observing the results in Table 2, it can be observed that the NERD has performed better than other features (invTDD, RMS, and TD4). Besides, when looking for the best force level to be considered for training, there are no satisfactory differences between the performance of moderate, low, and high force at the same feature type and classifier. The results in F1-score correlate with the results in accuracy which further justify the superiority of the proposed features (NERD).
为了进一步研究特征技术的性能，我们使用 F1-score 进行了分析，获得的结果如表 2 所示。通过观察表 2 中的结果，可以看出 NERD 的表现优于其他特征（invTDD、RMS 和 TD4）。此外，在寻找最佳的训练力水平时，在相同特征类型和分类器下，中等、低和高力的性能之间没有令人满意的差异。F1-score 中的结果与准确率的结果相关，这进一步证明了所提特征（NERD）的优越性。

Table 2. The F1-score classification results (%) under experimental scenario 1 when training and testing data are taken from similar force level and classified using Random Forest (RF), Linear discriminant analysis (LDA), and Support vector machine (SVM). NERD is the propose feature scheme.
表 2. 在实验场景 1 下，当训练和测试数据来自相似的力水平并使用随机森林（RF）、线性判别分析（LDA）和支持向量机（SVM）进行分类时的 F1-score 分类结果（%）。NERD 是提出的特征方案。

Scenario1 场景 1	RF				LDA				SVM
Scenario1 场景 1	invTDD 反 TDD	RMS	NERD	TD4	invTDD 反 TDD	RMS	NERD	TD4	invTDD 反 TDD	RMS	NERD	TD4
Moderate 适度	80.7 ± 6.8 80.7 ± 6.8	75.6 ± 10.5	87.1 ± 6.9 87.1 ± 6.9	81.3 ± 8.5	89.3 ± 6.8 89.3 ± 6.8	75.2 ± 9.1 75.2 ± 9.1	90.6 ± 5.7	86.2 ± 7.3 86.2 ± 7.3	77.2 ± 9.9 77.2 ± 9.9	78.4 ± 9.6	89.2 ± 6.8	79.2 ± 10.5
Low 低	83.7 ± 7.9 83.7 ± 7.9	78.0 ± 9.2	88.5 ± 8.0 88.5 ± 8.0	84.1 ± 9.0	90.8 ± 7.9 90.8 ± 7.9	76.6 ± 12.6 76.6 ± 12.6	91.5 ± 6.9	87.0± 9.4	77.9 ± 12.6 77.9 ± 12.6	78.4 ± 11.7	89.1 ± 8.5	77.4 ± 13.6
High 高	79.9 ± 7.1 79.9 ± 7.1	74.9 ± 11.3 74.9 ± 11.3	86.6 ± 6.3 86.6 ± 6.3	80.2 ± 9.8	88.1 ± 7.1 88.1 ± 7.1	73.7 ± 10.5	89.2 ± 6.5 89.2 ± 6.5	84.4 ± 8.7 84.4 ± 8.7	74.7 ± 12.0 74.7 ± 12.0	76.9 ± 11.4	87.3 ± 7.7	75.8 ± 12.8
Average 平均	81.4 ± 7.3 81.4 ± 7.3	76.2 ± 10.3 76.2 ± 10.3	87.4 ± 7.1 87.4 ± 7.1	81.9 ± 9.1 81.9 ± 9.1	89.4 ± 7.3 89.4 ± 7.3	75.2 ± 10.7 75.2 ± 10.7	90.4 ± 6.3	85.9 ± 8.5 85.9 ± 8.5	76.6 ± 11.9 76.6 ± 11.9	77.9 ± 10.9	88.5 ± 7.7	77.5 ± 12.3

3.2. Experimental scenario 2
3.2. 实验场景 2

In this scenario we investigate the robustness of the features when there is a change in force level. The obtained results are presented in Fig. 6 (accuracy) and Table 3 (F1-score). It should be noted that, the results presented are referred to the force level used for training. ie…Train-M: is when moderate force is used for training while high and low force levels are used for testing. By analyzing the results displayed in Fig. 6, it can be revealed that the proposed NERD features had better classification performance than the other features (invTDD, RMS, and TD4) when it comes to handling dissimilar force levels during training and testing. For instance, when the moderate force is used for training (Train-M) while low and high forces are used for testing with Random Forest as a classifier (Fig. 6 (a)), the NERD has attains a motion intent decoding accuracy of 70.0 ± 12.0 %, while invTDD, RMS, and TD4 attain 56.5 ± 13.0 %, 54.3 ± 13.7 %, 56.1 ± 14.0 % accuracy respectively. The results are consistent in all force levels and classifiers (Random forest, LDA, and SVM). In that respect, the proposed features have the statistical significance of exactly P < 0.01 against invTDD, RMS, and TD4 methods. A similar trend is observed across all classifiers. Interestingly, more analysis involving the use of F1-score (in Table 3) coincides with the accuracy results, where the NERD demonstrated a substantial performance against the other state of the art feature extraction techniques for all the investigated classifiers (RF, LDA, and SVM).
在这种情况下，我们研究了在力水平变化时特征的鲁棒性。获得的结果如图 6（准确性）和表 3（F1-score）所示。需要注意的是，所呈现的结果是指用于训练的力水平。即……Train-M：是指在训练中使用中等力，而在测试中使用高和低力水平。通过分析图 6 中显示的结果，可以揭示所提出的 NERD 特征在处理训练和测试期间不同力水平时的分类性能优于其他特征（invTDD、RMS 和 TD4）。例如，当使用中等力进行训练（Train-M），而在测试中使用低和高力时，使用随机森林作为分类器（图 6（a）），NERD 的运动意图解码准确率为 70.0 ± 12.0%，而 invTDD、RMS 和 TD4 的准确率分别为 56.5 ± 13.0%、54.3 ± 13.7%、56.1 ± 14.0%。在所有力水平和分类器（随机森林、LDA 和 SVM）中，结果是一致的。在这方面，所提出的特征具有确切的统计显著性 P < 0。01 对抗 invTDD、RMS 和 TD4 方法。所有分类器中观察到类似的趋势。有趣的是，涉及使用 F1-score 的更多分析（见表 3）与准确性结果一致，其中 NERD 在所有调查的分类器（RF、LDA 和 SVM）中表现出相对于其他最先进特征提取技术的显著性能。

Table 3. The F1-score classification results (%) under experimental scenario 2. Train-M, means the classifiers were trained by features from moderate force and testing data was from low and high force levels. Train-L means training features were from Low force levels and other force levels were used for testing. NERD is the propose method.
表 3. 实验场景 2 下的 F1-score 分类结果（%）。Train-M 表示分类器是通过中等力度的特征进行训练的，测试数据来自低和高力度水平。Train-L 表示训练特征来自低力度水平，其他力度水平用于测试。NERD 是提出的方法。

Scenario2 场景 2	RF				LDA				SVM
	invTDD 反 TDD	RMS	NERD	TD4	invTDD 反 TDD	RMS	NERD	TD4	invTDD	RMS	NERD	TD4
Train-M 训练-M	55.2 ± 15.0 55.2 ± 15.0	53.6 ± 15.0 53.6 ± 15.0	69.6 ± 11.4 69.6 ± 11.4	55.0 ± 15.9 55.0 ± 15.9	66.5 ± 13.3 66.5 ± 13.3	54.6 ± 13.6 54.6 ± 13.6	73.2 ± 11.3	61.1 ± 14.2	56.4 ± 15.2	55.5 ± 14.5	71.2 ± 9.9	54.6 ± 13.1
Train-L 训练-L	45.6 ± 16.3 45.6 ± 16.3	44.4 ± 17.9 44.4 ± 17.9	61.3 ± 13.2	44.8 ± 17.2 44.8 ± 17.2	56.7 ± 13.7 56.7 ± 13.7	48.9 ± 13.4 48.9 ± 13.4	63.8 ± 15.2 63.8 ± 15.2	56.7 ± 12.3	44.7 ± 154	45.9 ± 13.7	61.6 ± 13.0	43.3 ± 10.3
Train-H 训练-H	46.8 ± 18.6	45.8 ± 19.3 45.8 ± 19.3	62.4 ± 17.6	48.0 ± 19.8 48.0 ± 19.8	61.1 ± 14.6	37.4 ± 10.0	64.8 ± 16.7 64.8 ± 16.7	46.9 ± 14.7 46.9 ± 14.7	42.9 ± 17.4	44.2 ± 13.9	64.5 ± 13.2	46.6 ± 12.8
Average 平均	49.2 ± 16.6 49.2 ± 16.6	47.9 ± 17.4 47.9 ± 17.4	64.4 ± 14.0	49.3 ± 17.6 49.3 ± 17.6	61.4 ± 13.9	47.0 ± 12.3 47.0 ± 12.3	67.3 ± 14.4	54.9 ± 13.8 54.9 ± 13.8	48.0 ± 16.0	48.5 ± 14.0	65.8 ± 12.0	48.1 ± 12.1

When examining for the best force to be used for training, the results in both accuracy (Fig. 6) and F1-score (Table 3) show that when moderate force is used for training all features perform better than when using low or high force levels. For example, the classification accuracy at moderate (Train-M), low (Train-L), and high (Train-H) force levels are 70.0 ± 12.0 %, 61.7 ± 13.6 %, and 63.6 ± 16.8 % when the NERD features and RF classifier are used. This observation correlates with the previous study [1], which also showed that training with moderate force gives better results than low/high force. While this scenario depicts the actual/real situation in the use of EMG based prosthesis, the results suggest moderate force as training force being the most suitable force level for having a robust motion decoding system.
在寻找最佳训练力量时，准确性（图 6）和 F1 分数（表 3）的结果显示，当使用中等力量进行训练时，所有特征的表现都优于使用低或高力量水平。例如，当使用 NERD 特征和 RF 分类器时，中等（Train-M）、低（Train-L）和高（Train-H）力量水平的分类准确率分别为 70.0 ± 12.0%、61.7 ± 13.6%和 63.6 ± 16.8%。这一观察与之前的研究[1]相关，该研究也表明，使用中等力量进行训练的结果优于低/高力量。虽然这一情景描绘了基于肌电图的假肢使用中的实际情况，但结果表明，中等力量作为训练力量是实现稳健运动解码系统的最合适力量水平。

3.3. The performance of the features across individual motion intents
3.3. 各个运动意图下特征的表现

The evaluation in the previous sections represent the average/overall results (performance) across motion intents, thus, it is crucial to look into the performance of the proposed feature adaptation scheme and other state-of-the-arts techniques in terms of individual motion intent decoding outcomes. In this section the results for the public and in-house dataset are indicated separately in Fig. 7 and Fig. 8 respectively. It should be noted that, the confusion matrices are presented across subjects and across all force levels. Moreover, the confusion matrices for different datasets (public and in-house) are presented separately due to having different types and number of motion intents.
前面章节中的评估代表了不同运动意图的平均/整体结果（性能），因此，深入研究所提出的特征适应方案和其他最先进技术在各个运动意图解码结果方面的表现至关重要。在本节中，公共数据集和内部数据集的结果分别在图 7 和图 8 中表示。需要注意的是，混淆矩阵是跨受试者和所有力量水平呈现的。此外，由于不同数据集（公共和内部）具有不同类型和数量的运动意图，因此混淆矩阵是单独呈现的。

By looking closely into the diagonal of the resultant confusion matrices in Fig. 7 and Fig. 8, it can be realized that the proposed feature adaptation scheme (NERD) has managed to decode all classes in both in-house and public dataset better than other techniques. This demonstrate the robustness of the proposed scheme against variation of force levels and can potentially ensure intuitive control of not only the EMG-based prostheses but also game control and rehabilitation robotic systems which are prone to motion intent decoding degradation due to variation of muscle contraction forces.
通过仔细观察图 7 和图 8 中结果混淆矩阵的对角线，可以发现所提出的特征适应方案（NERD）在内部和公共数据集上都比其他技术更好地解码了所有类别。这证明了所提出方案对力水平变化的鲁棒性，并有可能确保不仅是基于肌电图的假肢的直观控制，还包括由于肌肉收缩力变化而容易导致运动意图解码降级的游戏控制和康复机器人系统的直观控制。

To investigate more the capability of the proposed scheme on characterizing individual motion intents, we used the t-SNE visualization tool which is suitable for nonlinear data such as EMG. The feature visualization of the NERD, invTDD, RMS, and TD4 features for two subjects (taken as representative example) are presented in Fig. 9. By closely looking on the t-SNE scatter plots in Fig. 9, an obvious class-separation is demonstrated by the proposed NERD features compared to other methods (invTDD, RMS, and TD4). Such high-class separability exhibited by the suggested NERD features across different targeted limb movement classes further indicated the potential of the proposed method to develop a reliable and robust pattern recognition based control system even in the presence of muscle contraction force variation.
为了进一步研究所提方案在表征个体运动意图方面的能力，我们使用了适合非线性数据（如肌电图）的 t-SNE 可视化工具。图 9 展示了两个受试者（作为代表性例子）的 NERD、invTDD、RMS 和 TD4 特征的可视化。仔细观察图 9 中的 t-SNE 散点图，可以明显看出所提的 NERD 特征与其他方法（invTDD、RMS 和 TD4）相比，具有明显的类别分离。所建议的 NERD 特征在不同目标肢体运动类别中表现出的高类别可分性进一步表明了所提方法在肌肉收缩力变化的情况下开发可靠且稳健的基于模式识别的控制系统的潜力。

4. Ablation study 4. 切除研究

The feature adaptation scheme (NERD) proposed in this study consists of three main operations/stages. To evaluate the contribution of each stage, we performed ablation experiments on the public dataset. First the raw EMG of every segment was transformed to SPD matrix as demonstrated in section 2.2 (i). At this stage we performed the pilot test on the robustness of the SPDs only as input to the Random forest classifier and termed this operation as SPD only. Then, to reduce the discrepancy between the features in different force levels all the SPD features were projected to a common reference point as shown in section 2.2 (ii), we denote this operation as feature adaptation (FA). Later we performed a distribution adaptation (DA) on output of the previous stage as described in section 2.2 (iii), and denoted this as feature distribution adaptation (DA). Table 4 shows the classification performance of all stages. It should be noted that (during ablation study) in every stage the features from moderate force were used for training the classifier while the features from the low and high force levels were used for testing, and the results are presented as average across all subjects in the public dataset.
本研究提出的特征适应方案（NERD）由三个主要操作/阶段组成。为了评估每个阶段的贡献，我们在公共数据集上进行了消融实验。首先，将每个片段的原始肌电图（EMG）转换为 SPD 矩阵，如第 2.2 节（i）所示。在这一阶段，我们仅对 SPDs 作为随机森林分类器的输入进行鲁棒性初步测试，并将此操作称为仅 SPD。然后，为了减少不同力级特征之间的差异，所有 SPD 特征被投影到一个共同的参考点，如第 2.2 节（ii）所示，我们将此操作称为特征适应（FA）。随后，我们对前一阶段的输出进行了分布适应（DA），如第 2.2 节（iii）所述，并将其称为特征分布适应（DA）。表 4 显示了所有阶段的分类性能。需要注意的是（在消融研究中），在每个阶段，适中力度的特征用于训练分类器，而低和高力度水平的特征用于测试，结果以公共数据集中所有受试者的平均值呈现。

Table 4. Ablation study to observe the contribution of SPD stage, FA stage, and DA stage.
表 4. 切除研究以观察 SPD 阶段、FA 阶段和 DA 阶段的贡献。

Experimental scenario 实验场景	Accuracy 准确性			F1-score
Experimental scenario 实验场景	SPD	FA	DA	SPD	FA	DA
Train and test with moderate force level 以中等力量水平进行训练和测试	79.08	87.71	87.90	78.64	87.42	87.64
Train with moderate-Test with low force 以中等强度训练-以低强度测试	58.20	62.63	69.77	54.58	59.00	68.61
Train with moderate-Test with high force 以中等强度训练-以高强度测试	40.10	58.26	68.09	33.46	53.25	67.62

From the results in Table 4, we can observe an increase of performance in both accuracy and F1-score in all force levels as we shift from SPD to DA stage. For instance, when considering the performance in accuracy when the low force level is used for testing, the performance increases from 58.20 % to 62.63 %, and 69.77 % under the SPD, FA, and DA operations respectively. This trend shows that the FA and DA have a positive impact on reducing the feature discrepancy between different force levels.
从表 4 的结果中，我们可以观察到在所有力级别中，随着从 SPD 阶段转向 DA 阶段，准确率和 F1-score 的表现都有所提高。例如，当考虑在低力级别下进行测试时，准确率的表现分别从 58.20%提高到 62.63%和 69.77%，在 SPD、FA 和 DA 操作下。这一趋势表明，FA 和 DA 对减少不同力级别之间的特征差异具有积极影响。

5. Conclusion 5. 结论

This study proposes the feature and distribution adaptation scheme to enhance the robustness of the SPD features against MCFV. The study relies on the SPDs which are in non-Euclidean space thus allowing mining of distinct representative features for motor intents in EMG signals which are robust to MCFV. The feature adaptation phase relies on the geometric mean (Riemann mean) of the training set. Where all SPDs from training and tests data (of different force levels) are pooled to a common Riemann mean, by so doing the discrepancy of features of different force levels is reduced. Inspired by Nazarpour et al. who revealed that the decrease in classification performance caused by MCFV could be attributed to alterations in probability density function of EMG signals related to specific limb movements [9], therefore in the last stage of the proposed scheme we have projected all the features of different force levels into a common distribution similar to the training set. This has further improved the robustness of the proposed features against variation of forces when the subject is performing motion intents. The results show that the proposed features have significantly outperformed the other state of the art methods in the presence of MCFV. In that respect, the NERD features have outperformed other methods with the maximum difference of 15.02 % accuracy, and 16.50 % F1-score when using Random forest as a classifier, 19.10 % accuracy and 20.29 % F1-score when using LDA as a classifier, 16.11 % accuracy and 17.78 F1-score when SVM is utilized as a classifier. These results justify the robustness of the proposed scheme (NERD) against variation in muscle contraction forces which could potentially enhance the performance of the EMG based motor intent decoding system.
本研究提出了一种特征和分布适应方案，以增强 SPD 特征对 MCFV 的鲁棒性。该研究依赖于位于非欧几里得空间中的 SPD，从而允许挖掘对 MCFV 具有鲁棒性的运动意图在 EMG 信号中的独特代表特征。特征适应阶段依赖于训练集的几何平均（黎曼平均）。将来自训练和测试数据（不同力量水平）的所有 SPD 汇聚到一个共同的黎曼平均中，从而减少不同力量水平特征之间的差异。受到 Nazarpour 等人的启发，他们揭示了 MCFV 导致的分类性能下降可以归因于与特定肢体运动相关的 EMG 信号的概率密度函数的变化，因此在所提方案的最后阶段，我们将不同力量水平的所有特征投影到一个与训练集相似的共同分布中。这进一步提高了所提特征在受试者执行运动意图时对力量变化的鲁棒性。结果表明，所提出的特征在 MCFV 存在的情况下显著优于其他最先进的方法。在这方面，NERD 特征在使用随机森林作为分类器时，准确率最大差异为 15.02%，F1-score 为 16.50%；使用 LDA 作为分类器时，准确率为 19.10%，F1-score 为 20.29%；使用 SVM 作为分类器时，准确率为 16.11%，F1-score 为 17.78%。这些结果证明了所提出方案（NERD）在肌肉收缩力变化下的鲁棒性，这可能增强基于 EMG 的运动意图解码系统的性能。

Though the proposed scheme has shown promising results in offline experiments, there is a room for enhancement, particularly concerning evaluating its performance in an online context [42]. Therefore, in future work, we aim to validate the proposed method's effectiveness in real-time settings. Additionally, we anticipate the proposed method can be suitable for resolving other related issues which have been proven to degrade the decoding performance of EMG-based systems such as variation of signals due to the mobility of subjects [43] and change in arm position while executing predefined hand movements [44]. Thus, in future work we will test our hypothesis by implementing the NERD features in resolving these issues. Furthermore, to enhance the overall performance of our work, we anticipate that post-processing techniques, such as the longest consecutive repetition (LCR) method [45], would be suitable. Therefore, as part of our future plans, we intend to implement the LCR method to improve the effectiveness of our work.
尽管所提出的方案在离线实验中显示出良好的结果，但在评估其在线环境中的性能方面仍有提升空间[42]。因此，在未来的工作中，我们旨在验证所提方法在实时环境中的有效性。此外，我们预期所提方法可以适用于解决其他相关问题，这些问题已被证明会降低基于肌电图（EMG）系统的解码性能，例如由于受试者的移动而导致的信号变化[43]以及在执行预定义手部动作时手臂位置的变化[44]。因此，在未来的工作中，我们将通过实施 NERD 特征来验证我们的假设，以解决这些问题。此外，为了提高我们工作的整体性能，我们预期后处理技术，如最长连续重复（LCR）方法[45]，将是合适的。因此，作为我们未来计划的一部分，我们打算实施 LCR 方法以提高我们工作的有效性。

CRediT authorship contribution statement
CRediT 作者贡献声明

Frank Kulwa: Writing – original draft, Methodology, Formal analysis, Data curation, Conceptualization. Yongcheng Li: Writing – review & editing, Supervision, Investigation, Funding acquisition, Conceptualization. Oluwarotimi W. Samuel: Writing – review & editing, Validation, Supervision, Resources, Investigation, Funding acquisition. Haipeng Zhang: Validation, Methodology, Formal analysis. Tolulope T. Oyemakinde: . Mojisola G. Asogbon: Writing – review & editing, Validation, Methodology, Formal analysis. Alistair A. McEwan: Conceptualization, Resources. Guanglin Li: Writing – review & editing, Writing – original draft, Validation, Supervision, Resources, Investigation, Funding acquisition, Conceptualization.
弗兰克·库尔瓦：撰写 – 原始草稿，方法论，正式分析，数据管理，概念化。永城·李：撰写 – 审阅与编辑，监督，调查，资金获取，概念化。奥卢瓦罗提米·W·塞缪尔：撰写 – 审阅与编辑，验证，监督，资源，调查，资金获取。海鹏·张：验证，方法论，正式分析。托卢洛佩·T·奥耶马金德：莫吉索拉·G·阿索贡：撰写 – 审阅与编辑，验证，方法论，正式分析。阿利斯泰尔·A·麦克尤恩：概念化，资源。广林·李：撰写 – 审阅与编辑，撰写 – 原始草稿，验证，监督，资源，调查，资金获取，概念化。

Declaration of competing interest
竞争利益声明

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
作者声明，他们没有已知的竞争性财务利益或个人关系，这些关系可能会影响本文所报告的工作。

Acknowledgment 致谢

This work was supported in part by the Ministry of Science and Technology of China under grants (STI2030-Brain Science and Brain-Inspired Intelligence Technology-2022ZD0210400), the National Natural Science Foundation of China (#81927804), the Science and Technology Program of Guangdong Province (2022A0505090007), Guangdong Basic and Applied Basic Research Foundation (#2023A1515011478), the ANSO scholarship for young talented students, and the CAS President's International Fellowship Initiative (2024PVB0025).
本研究部分得到了中国科技部的资助（STI2030-脑科学与类脑智能技术-2022ZD0210400）、国家自然科学基金（#81927804）、广东省科技计划（2022A0505090007）、广东省基础与应用基础研究基金（#2023A1515011478）、ANSO 青年人才奖学金以及中国科学院院长国际 Fellowship Initiative（2024PVB0025）。

Data availability 数据可用性

Data will be made available on request.
数据将根据请求提供。

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Cited by (0)

View Abstract

[1] [1]
A.H. Al-Timemy, R.N. Khushaba, G. Bugmann, J. Escudero
Improving the performance against force variation of EMG controlled multifunctional upper-limb prostheses for transradial amputees
IEEE Trans. Neural Syst. Rehabil. Eng., 24 (6) (2015), pp. 650-661
Google Scholar

[2] [2]
E. Scheme, K. Englehart
Electromyogram pattern recognition for control of powered upper-limb prostheses: state of the art and challenges for clinical use
J. Rehabil. Res. Dev., 48 (6) (2011)
Google Scholar

[3] [3]
A. Nishad, A. Upadhyay, R.B. Pachori, U. Rajendra Acharya
Automated classification of hand movements using tunable-Q wavelet transform based filter-bank with surface electromyogram signals
Futur. Gener. Comput. Syst., 93 (2019), pp. 96-110
View PDF View article View in Scopus Google Scholar

[4] [4]
Samuel, Oluwarotimi Williams, Mojisola Grace Asogbon, Yanjuan Geng, Ali H. Al-Timemy, Sandeep Pirbhulal, Ning Ji, Shixiong Chen, Peng Fang, Guanglin Li. (2019) “Intelligent EMG pattern recognition control method for upper-limb multifunctional prostheses: advances, current challenges, and future prospects.” Ieee Access 7. 10150-10165.
Google Scholar

[5] [5]
Nishad, Anurag, and Abhay Upadhyay. “Empirical wavelet transform based classification of surface electromyogram signals for hand movements.” In Modelling and Analysis of Active Biopotential Signals in Healthcare, Volume 1, pp. 9-1. Bristol, UK: IOP Publishing, 2020.
Google Scholar

[6] [6]
O.W. Samuel, M.G. Asogbon, R. Khushaba, F. Kulwa, G. Li
Multiresolution dual-polynomial decomposition approach for optimized characterization of motor intent in myoelectric control systems
IEEE Trans. Biomed. Eng. (2022)
Google Scholar

[7] [7]
D. Tkach, H. Huang, T.A. Kuiken
Study of stability of time-domain features for electromyographic pattern recognition
J NeuroEng Rehabil, 7 (2010)
Google Scholar

[8] [8]
B.T. Carlsen, P. Prigge, J. Peterson
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J. Hand Ther., 27 (2) (2014), pp. 106-114
View PDF View article View in Scopus Google Scholar

[9] [9]
K. Nazarpour, A.H. Al-Timemy, G. Bugmann, A. Jackson
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Brain Res. Bull., 90 (2013), pp. 88-91
View PDF View article View in Scopus Google Scholar

[10] [10]
Asogbon, Mojisola Grace, Oluwarotimi Williams Samuel, Yanjuan Geng, Olugbenga Oluwagbemi, Ji Ning, Shixiong Chen, Naik Ganesh, Pang Feng, and Guanglin Li. “Towards resolving the co-existing impacts of multiple dynamic factors on the performance of EMG-pattern recognition based prostheses.” Computer methods and programs in biomedicine 184 (2020): 105278.
Google Scholar

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A.H. Al-Timemy, G. Bugmann, J. Escudero, N. Outram
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In 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) (2013), pp. 5758-5761
Crossref View in Scopus Google Scholar

[12] [12]
Li, Xiangxin, Rui Xu, Oluwarotimi Williams Samuel, Lan Tian, Haiqing Zou, Xiufeng Zhang, Shixiong Chen, Peng Fang, and Guanglin Li. “A new approach to mitigate the effect of force variation on pattern recognition for myoelectric control.” In 2016 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 1684-1687. IEEE, 2016.
Google Scholar

[13] [13]
S. Madhavan, R.K. Tripathy, R.B. Pachori
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IEEE Sens. J., 20 (6) (2019), pp. 3078-3086
Google Scholar

[14] [14]
A. Sharma, S. Patidar, A. Upadhyay, U. Rajendra Acharya
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Comput. Electr. Eng., 75 (2019), pp. 101-111
View PDF View article View in Scopus Google Scholar

[15] [15]
A. Nishad, A. Upadhyay, G. Ravi Shankar Reddy, V. Bajaj
Classification of epileptic EEG signals using sparse spectrum based empirical wavelet transform
Electron. Lett, 56 (25) (2020), pp. 1370-1372
Crossref View in Scopus Google Scholar

[16] [16]
S.K. Khare, A. Nishad, A. Upadhyay, V. Bajaj
Classification of emotions from EEG signals using time-order representation based on the S-transform and convolutional neural network
Electron. Lett, 56 (25) (2020), pp. 1359-1361
Crossref View in Scopus Google Scholar

[17] [17]
G. Maman, O.r. Yair, D. Eytan, R. Talmon
Domain adaptation using Riemannian geometry of SPD matrices
In ICASSP 2019–2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2019), pp. 4464-4468
Crossref View in Scopus Google Scholar

[18] [18]
R. Sharma, S.S. Sahu, A. Upadhyay, R.R. Sharma, A.K. Sahoo
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Computer-Aided Design and Diagnosis Methods for Biomedical Applications, CRC Press (2021), pp. 35-56
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[19] [19]
S. Patidar, R.B. Pachori, A. Upadhyay, U. Rajendra Acharya
An integrated alcoholic index using tunable-Q wavelet transform based features extracted from EEG signals for diagnosis of alcoholism
Appl. Soft Comput., 50 (2017), pp. 71-78
View PDF View article View in Scopus Google Scholar

[20] [20]
A. Mathur, N. Choudhary, A. Upadhyay, R.B. Pachori
Detection of glottal closure instants from voiced speech signals using the Fourier-bessel series expansion
In 2015 International Conference on Communications and Signal Processing (ICCSP) (2015), pp. 0474-0478
Crossref Google Scholar

[21] [21]
A. Upadhyay, R.B. Pachori
Speech enhancement based on mEMD-VMD method
Electron. Lett, 53 (7) (2017), pp. 502-504
Crossref View in Scopus Google Scholar

[22] [22]
F. Yger, F. Lotte, M. Sugiyama
Averaging covariance matrices for EEG signal classification based on the CSP: an empirical study
In 2015 23rd European Signal Processing Conference (EUSIPCO) (2015), pp. 2721-2725
View in Scopus Google Scholar

[23] [23]
H.-S. Cha, C.-H. Im
Improvement of robustness against electrode shift for facial electromyogram-based facial expression recognition using domain adaptation in VR-based metaverse applications
Virtual Reality (2023), pp. 1-12
Crossref Google Scholar

[24] [24]
M. Lorenzi, X. Pennec
Efficient parallel transport of deformations in time series of images: from Schild’s to pole ladder
J. Math. Imaging Vision, 50 (2014), pp. 5-17
Crossref View in Scopus Google Scholar

[25] [25]
A. Barachant, S. Bonnet, M. Congedo, C. Jutten
Multiclass brain–computer interface classification by Riemannian geometry
IEEE Trans. Biomed. Eng., 59 (4) (2012), pp. 920-928
View in Scopus Google Scholar

[26] [26]
J. He, D. Zhang, X. Sheng, S. Li, X. Zhu
Invariant surface EMG feature against varying contraction level for myoelectric control based on muscle coordination
IEEE J. Biomed. Health Inform., 19 (3) (2014), pp. 874-882
Google Scholar

[27] [27]
R.N. Khushaba, K. Nazarpour
Decoding hd-emg signals for myoelectric control-how small can the analysis window size be?
IEEE Rob. Autom. Lett., 6 (4) (2021), pp. 8569-8574
Crossref View in Scopus Google Scholar

[28] [28]
S. Kumar, F. Yger, F. Lotte
Towards adaptive classification using Riemannian geometry approaches in brain-computer interfaces
In 2019 7th International Winter Conference on Brain-Computer Interface (BCI) (2019), pp. 1-6
Google Scholar

[29] [29]
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Outline 大纲

Figures (9) 图 (9)

Tables (5)

Biomedical Signal Processing and Control
生物医学信号处理与控制

Highlights 亮点

Abstract 摘要

Keywords 关键词

1. Introduction 1. 引言

2. Materials and methods 2. 材料和方法

2.1. Data collection 2.1. 数据收集

2.2. Methods 2.2. 方法

2.3. Other state-of-the-art methods for comparison
2.3. 其他先进方法的比较

2.4. Experimental analysis
2.4. 实验分析

3. Results and discussion
3. 结果与讨论

3.1. Experimental scenario 1
3.1. 实验场景 1

3.2. Experimental scenario 2
3.2. 实验场景 2

3.3. The performance of the features across individual motion intents
3.3. 各个运动意图下特征的表现

4. Ablation study 4. 切除研究

5. Conclusion 5. 结论

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
竞争利益声明

Acknowledgment 致谢

Data availability 数据可用性

References

Cited by (0)

Biomedical Signal Processing and Control生物医学信号处理与控制

A robust feature adaptation approach against variation of muscle contraction forces for myoelectric pattern recognition-based gesture characterization一种针对肌肉收缩力变化的强健特征适应方法，用于基于肌电模式识别的手势特征化

Highlights 亮点

Abstract 摘要

Keywords 关键词

1. Introduction 1. 引言

2. Materials and methods 2. 材料和方法

2.1. Data collection 2.1. 数据收集

2.2. Methods 2.2. 方法

2.3. Other state-of-the-art methods for comparison2.3. 其他先进方法的比较

2.4. Experimental analysis2.4. 实验分析

3. Results and discussion3. 结果与讨论

3.1. Experimental scenario 13.1. 实验场景 1

3.2. Experimental scenario 23.2. 实验场景 2

3.3. The performance of the features across individual motion intents3.3. 各个运动意图下特征的表现

4. Ablation study 4. 切除研究

5. Conclusion 5. 结论

CRediT authorship contribution statementCRediT 作者贡献声明

Declaration of competing interest竞争利益声明

Acknowledgment 致谢

Data availability 数据可用性

References

Biomedical Signal Processing and Control
生物医学信号处理与控制

A robust feature adaptation approach against variation of muscle contraction forces for myoelectric pattern recognition-based gesture characterization
一种针对肌肉收缩力变化的强健特征适应方法，用于基于肌电模式识别的手势特征化

2.3. Other state-of-the-art methods for comparison
2.3. 其他先进方法的比较

2.4. Experimental analysis
2.4. 实验分析

3. Results and discussion
3. 结果与讨论

3.1. Experimental scenario 1
3.1. 实验场景 1

3.2. Experimental scenario 2
3.2. 实验场景 2

3.3. The performance of the features across individual motion intents
3.3. 各个运动意图下特征的表现

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
竞争利益声明