## 3 Haptic Recognition Method  
### MoAS-CNN Framework  
Aiming to improve the feature description and utilization efficiency of the network, a shallow MoAS-CNN is constructed. Figure 3a illustrates the proposed structure, where spatial interactive-based second-order features enhance the nonlinear response of the network and a hybrid strategy of summing up the multiorder features makes the extracted  
Figure 2: Nonideal effects of haptic images. (**a**)The letter-shape samples obtained by a 32 \(\times\) 32 sensor array, (**b**) the grayscale distribution histograms of the samples, (**c**) the Bhattacharyya coefficient of the 26 letter shapes. features fully utilized. It consists of three parts: first-order feature extractor, second-order feature generation, and multiorder feature hybridization. In particular, for low-resolution pressure inputs, the samples contain limited information and additional dimensionality reduction of the features is not expected. In our case, the pooling layers are removed and only the convolutional layers are retained to reduce the feature dimensionality loss [15; 16]. An all-convolutional dual-stream neural network with the channel attention module inserted is constructed as a first-order feature extractor. The channel attention module based on squeeze and excitation operations is added for improving the first-order feature response. For second-order response, a cross-stream spatial interactive feature is generated to improve the feature nonlinear description. High-order features have been proved to be more sensitive to texture and edges [17; 18]. Six (3 \(\times\) 3) convolutional kernels (steam1) and three [\(5\times 5\)] convolutional kernels (steam2) are applied. Multiorder features are fused to enhance the utilization of different orders of features by summation. Features of different orders have different emphases, and complementary utilization promotes the overall nonlinearity of the network without wasting information [19]. This is beneficial for applications where the original information mapping is not sufficient or the network depth is limited. All-Convolutional Neural Network-Based First-Order Feature Extractor with Channel Attentional Module Inserted  
An asymmetric all-convolutional dual-stream CNN is configured as a feature extractor to automatically extract first-order features. CNN streams of different structures focus on respective priorities, which can fully mine image features. Mathematically, the feature maps at \(i\)th layer are calculated as:  
\[f^{i}=\varphi(w^{i}\otimes f^{i-1}+b^{i}) \tag{2}\]  
where \(\varphi\) denotes the activation function \(ReLU\), and \(w\) and \(b\) represent the convolutional kernels and bias [20]. To highlight the emphasized parts of the features, the channel attention module including squeeze and excitation operations is inserted after the convolution layer [21]. As shown in Figure 3b, the feature maps are assigned scaling according to the channel importance to improve the feature representation. For a set of features \(f\)\(\in\)R\({}^{h\times w\times c}\), the  
Figure 3: The MoAS-CNN framework. (**a**) The overall framework, (**b**) the squeeze–excitation channel attention module, (**c**) the spatial interactive feature generation and multiorder summation. squeeze operation is performed to obtain the global distribution Z{1 \(\times\) 1 \(\times\) _c_}, reflecting the features response over the channels. The specific mathematical expression is as follows:  
\[ \begin{split} Z&=\frac{\mathcal{G}P(f^{c})}{\hbar \times\omega},\\ GP(f^{c})&=\sum\limits_{i=1}^{h}\sum\limits_{j=1}^{w}f^{ c}(i,j)\end{split}  \tag{3}\]  
Here, the global average pooling is chosen to compress the feature into real numbers by spatial dimension. For excitation operation, \(Z\) is fed into two fully connected layers to further learn factor _S_:  
\[S=\varphi(fc(Z)) \tag{4}\]  
where \(\varphi\) denotes the activation function _ReLU_ and _fc_ represents the fully connected layer.