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The convolutional neural network (CNN) has been widely applied to process theindustrial data based tensor input, which integrates data records ofdistributed industrial systems from the spatial, temporal, and system dynamicsaspects. However, unlike images, information in the industrial data basedtensor is not necessarily spatially ordered. Thus, directly applying CNN isineffective. To tackle such issue, we propose a plug and play module, theRubik's Cube Operator (RCO), to adaptively permutate the data organization ofthe industrial data based tensor to an optimal or suboptimal order ofattributes before being processed by CNNs, which can be updated with subsequentCNNs together via the gradient-based optimizer. The proposed RCO maintains Kbinary and right stochastic permutation matrices to permutate attributes of Kaxes of the input industrial data based tensor. A novel learning process isproposed to enable learning permutation matrices from data, where theGumbel-Softmax is employed to reparameterize elements of permutation matrices,and the soft regularization loss is proposed and added to the task-specificloss to ensure the feature diversity of the permuted data. We verify theeffectiveness of the proposed RCO via considering two representative learningtasks processing industrial data via CNNs, the wind power prediction (WPP) andthe wind speed prediction (WSP) from the renewable energy domain. Computationalexperiments are conducted based on four datasets collected from different windfarms and the results demonstrate that the proposed RCO can improve theperformance of CNN based networks significantly.

Rubik's Cube Operator: A Plug And Play Permutation Module for Better Arranging High Dimensional Industrial Data in Deep Convolutional Processes