CNN models have superior capabilities in extracting local features [28]. They can be employed in computer vision and time series prediction and analysis [29]. CNN models consist of convolutional layers, pooling layers, activation functions, and dense layers (Fig. (Fig.4).4). For our time series data, 1D kernels were used to slide across the data (x) and compute dot products between the kernel and local data at each step, eventually generating feature maps. We then used max pooling on feature maps to reduce dimensions while retaining important features. After adding non-linearity to pooled data using a tanh function, data were input into the dense layer and produced a CNN model using the following formula:
where denotes the convolution operation, is a bias term is a set of consecutive elements in the input feature sequence, is a maximum extraction operation, is a weight matrix, and is a matrix multiplication operation.
Architecture of the convolutional neural network
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