Time Correlation of Time-invariant Linear Models in Neural Decoding for the Macaque's Moving Finger
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摘要: 利用猕猴运动皮层神经元峰电位数信号估计其手指移动位置是一神经解码问题, 通常采用时不变线性模型(Time-invariant linear model, TILM)来解决.本文分析了传统TILM模型的时间相关性问题, 依据猕猴手指移动位置的连续性特点, 采用一种新的模型去解码其手指移动位置, 称之为卷积空间模型(Convolution space model, CSM).与传统的模型相比, 卷积空间模型不但将当前时刻的状态与前一个时刻建立了相关, 而且与前多个时刻的状态也有相关.在实验中, 利用公开数据来评判本文方法的解码性能, 实验结果表明, 传统方法的解码误差要大于CSM模型的方法, 因此CSM模型具有更好的解码准确性.Abstract: It is a neural decoding problem to estimate the position of a macaque$'$s moving finger through neuron spike signals in motor cortex, which is usually solved by a time-invariant linear model (TILM). This paper analyzes the temporal correlation of the traditional TILM model. According to the continuity characteristics of the position of a macaque's moving finger, a new model is adopted to decode the finger movement, which is called CSM (Convolution space model). Compared with traditional decoding models, the CSM model can express that a state at the current time will be related to states at multiple previous times, rather than only one previous time. In experiments, we use the public data to evaluate the decoding performance of our method. The experimental results show that the CSM model has lower decoding errors than traditional methods and thus has better decoding accuracy.
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Key words:
- Neural decoding /
- macaque's moving finger /
- CSM model /
- TILM model
1) 本文责任编委 秦涛 -
图 4 实验1中位置估计与手指移动真实位置曲线
Fig. 4 Position estimation and finger movement real position curve in experiment 1
图 5 手指移动横坐标估计误差随延迟数据长度$P$的变化
Fig. 5 Finger movement abscissa estimation error with delay data length $P$ changes
图 6 手指移动横坐标估计误差随迭代次数$T$的变化
Fig. 6 Finger movement abscissa estimation error with the number of iterations cycle $T$ changes
表 1 参数$P$对算法的训练复杂度
Table 1 Training complexity of parameter $P$ for algorithm
CSM模型算法 LS RLS GDA 复杂度 ${\rm O}(P^3)$ ${\rm O}(TP^3)$ ${\rm O}(TP^2)$ 
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表 2 $X$轴和$Y$轴(括号内)的估计误差(cm) (保留三位)
Table 2 $X$-axis and $Y$-axis (in parentheses) estimated error (cm) (three places reserved)
算法$X(Y)$ 实验2 实验3 实验4 实验5 平均 Linear 3.813 (2.003) 3.941 (2.513) 4.135 (2.991) 3.919 (2.120) 3.952 (2.407) KF 3.060 (1.498) 3.908 (2.042) 4.540 (2.939) 3.637 (1.656) 3.786 (2.034) RBE 3.637 (1.727) 4.699 (2.295) 3.907 (2.400) 3.913 (1.936) 4.015 (2.089) UCKD 6.596 (4.235) 6.949 (5.504) 7.500 (5.775) 6.220 (4.868) 6.816 (5.096) CSM-LS 2.959 (1.411) 3.450 (2.154) 3.937 (2.921) 3.109 (1.724) 3.364 (2.052) CSM-RLS 2.964 (1.411) 3.443 (2.153) 3.957 (2.891) 3.106 (1.726) 3.368 (2.045) CSM-GDA 2.896 (1.500) 3.270 (2.095) 4.581 (2.406) 3.233 (1.709) 3.495 (1.927)
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表 3 二维平面的估计误差(cm) (保留三位)
Table 3 The estimated error of the two-dimensional plane (cm) (three places reserved)
算法$XY$ 实验2 实验3 实验4 实验5 平均 Linear 4.307 4.674 5.103 4.455 4.635 KF 3.407 4.409 5.408 3.996 4.305 RBE 4.026 5.230 4.585 4.366 4.552 UCKD 7.839 8.865 9.466 7.896 8.787 CSM-LS 3.278 4.068 4.902 3.555 3.951 CSM-RLS 3.283 4.061 4.901 3.553 3.950 CSM-GDA 3.261 3.883 5.174 3.656 3.994
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表 4 CSM模型算法的训练时间(保留三位)
Table 4 The training time of CSM model algorithm (three places reserved)
CSM模型算法 LS RLS GDA 训练时间(s) 1.061 23.853 1.285
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