Neuroscience and Neuroengineering Research Lab, Biomedical Engineering Department, School of Electrical Engineering, Iran University of Science & Technology (IUST), Narmak, Tehran, 16846-13114, Iran.
Control Engineering Department, School of Electrical Engineering, Iran University of Science & Technology (IUST), Tehran, Iran.
Neuroinformatics. 2020 Jun;18(3):465-477. doi: 10.1007/s12021-020-09455-x.
Continuous decoding is a crucial step in many types of brain-computer interfaces (BCIs). Linear regression techniques have been widely used to determine a linear relation between the input and desired output. A serious issue in this technique is the over-fitting phenomenon. Partial least square (PLS) is a well-known and popular method which tries to overcome this problem. PLS calculates a set of latent variables which are maximally correlated to the output and determines a linear relation between a low-rank estimation of the input and output data. However, this method has shown its potential to overfit the training data in many cases. In this paper, a regularized version of PLS (RPLS) is proposed which tries to determine a linear relation between the latent vector of the input and desired output using the regularized least square instead of the ordinary one. This approach is able to control the effect of non-efficient and non-generalized latent vectors in prediction. We have shown that the proposed method outperforms Ridge regression (RR), PLS, and PLS with regularized weights (PLSRW) in estimating the output in two different real BCI datasets, Neurotycho public electrocorticogram (ECoG) dataset for decoding trajectory of hand movements in monkeys and our own local field potential (LFP) dataset for decoding applied force performed by rats. Furthermore, the results indicate that RPLS is more robust against the increase in the number of latent vectors compared to PLS and PLSRW. Next, we evaluated the resistance of our proposed method against the presence of different noise levels in a BCI application and compared it to other techniques using a semi-simulated dataset. This approach revealed that RPLS offered a higher performance compared with other techniques in all levels of noise. Finally, to illustrate the usability of RPLS in other type of data, we presented the application of this method in predicting relative active substance content of pharmaceutical tablets using near-infrared (NIR) transmittance spectroscopy data. This application showed a superior performance of the proposed method compared to other decoding methods.
连续解码是许多类型的脑机接口 (BCI) 中的关键步骤。线性回归技术已被广泛用于确定输入和期望输出之间的线性关系。该技术的一个严重问题是过拟合现象。偏最小二乘法 (PLS) 是一种众所周知且流行的方法，旨在克服此问题。PLS 计算一组与输出最大相关的潜在变量，并确定输入和输出数据的低秩估计之间的线性关系。然而，在许多情况下，该方法已显示出其过度拟合训练数据的潜力。在本文中，提出了一种 PLS 的正则化版本 (RPLS)，它试图使用正则化最小二乘法而不是普通最小二乘法来确定输入的潜在向量与期望输出之间的线性关系。这种方法能够控制预测中效率低下和非广义潜在向量的影响。我们已经表明，该方法在估计两个不同的真实 BCI 数据集的输出时，优于 Ridge 回归 (RR)、PLS 和正则化权重的 PLS (PLSRW)，Neurotycho 公开的皮层脑电图 (ECoG) 数据集用于解码猴子手部运动轨迹，以及我们自己的局部场电位 (LFP) 数据集用于解码大鼠施加的力。此外，结果表明，与 PLS 和 PLSRW 相比，RPLS 对潜在向量数量增加的鲁棒性更强。接下来，我们在 BCI 应用中评估了我们提出的方法对不同噪声水平的存在的抵抗力，并使用半模拟数据集将其与其他技术进行了比较。该方法表明，与其他技术相比，RPLS 在所有噪声水平下都具有更高的性能。最后，为了说明 RPLS 在其他类型数据中的可用性，我们展示了该方法在使用近红外 (NIR) 透射光谱数据预测药物片剂的相对活性物质含量中的应用。该应用表明，与其他解码方法相比，所提出的方法具有更好的性能。
