Although current proposed compression schemes achieve better performance than traditional data compression schemes,they have not fully exploited the spatial and temporal correlations among the data, and the design of the projection (measurement)matrix cannot satisfy the requirement of real scenarios adaptively. Hence, well-designed clustering algorithm is needed to furtherexplore strong spatial correlation, and an adaptive measurement matrix is also needed to ensure exact data recovery. In this paper, wepropose a fog-based optimized Kronecker-supported compression scheme to address above shortcomings and achieve bettercompression results in the industrial Internet of Things (IIoT). Our scheme first leverages a k-means-based clustering algorithm thatexplores the spatial correlation among sensory data, which can obtain better compression effects with less communication overhead. Itthen develops a novel Kronecker-supported two-dimensional data compression mechanism at the fog node, which can ensure therecovery of the original data from the compressed data with high precision; this mechanism can also reduce the communicationoverhead between fog and cloud nodes significantly. Next, a Kronecker concatenated measurement matrix optimization problem isformulated for meeting the requirement of real scenarios adaptively, and an efficient solution algorithm is developed to obtain theoptimal value and ensure that the stringent precision requirements of industrial applications are satisfied. Finally, simulation resultsshow that our proposed scheme is energy efficient and can achieve better clustering results and recovery performance for sensorydata, for example, the energy consumption is reduced by 6.8% after clustering operation, and the relative reconstruction error oftemperature data is improved by an average of 15.8% with the same energy saving effect.
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