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.

中文翻译：

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在脑机接口中进行连续解码的正则化偏最小二乘回归。

在许多类型的脑机接口（BCI）中，连续解码是至关重要的一步。线性回归技术已被广泛用于确定输入与所需输出之间的线性关系。该技术中的一个严重问题是过拟合现象。偏最小二乘（PLS）是一种众所周知的流行方法，试图克服此问题。PLS计算与输出最大相关的一组潜在变量，并确定输入数据和输出数据的低秩估计之间的线性关系。但是，这种方法在许多情况下都显示出过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），它试图使用正则化的最小二乘而不是普通的最小二乘来确定输入的潜矢量和所需输出之间的线性关系。这种方法能够控制预测中非有效和非广义潜在向量的影响。我们已经表明，在估计两个不同的实际BCI数据集（神经tychocho公共​​电皮质图（ECoG）数据集）中对猴子的手部运动轨迹进行解码时，所提出的方法胜过Ridge回归（RR），PLS和带正则化权重（PLSRW）的PLS以及我们自己的局部场电势（LFP）数据集，用于解码大鼠所施加的力。此外，结果表明，与PLS和PLSRW相比，RPLS对潜在载体数量增加的抵抗力更强。下一个，我们评估了我们提出的方法在BCI应用中针对不同噪声水平的抵抗力，并将其与使用半仿真数据集的其他技术进行了比较。这种方法表明，在所有噪声水平上，RPLS都比其他技术提供了更高的性能。最后，为了说明RPLS在其他类型数据中的可用性，我们介绍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。与其他解码方法相比，此应用程序显示了所提出方法的优越性能。这种方法表明，在所有噪声水平上，RPLS都比其他技术提供了更高的性能。最后，为了说明RPLS在其他类型数据中的可用性，我们介绍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。与其他解码方法相比，此应用程序显示了所提出方法的优越性能。这种方法表明，在所有噪声水平上，RPLS都比其他技术提供了更高的性能。最后，为了说明RPLS在其他类型数据中的可用性，我们介绍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。与其他解码方法相比，此应用程序显示了所提出方法的优越性能。