In tensor data mining, discovering itemset-like patterns can be highly computationally intensive. This paper introduces a method for reducing the search space by pre-processing tensors to eliminate cells that cannot contribute to valid patterns. The proposed approach involves analyzing intersections between different tensor slices and applying noise limits to refine the search process. By removing subspaces that do not meet the specified criteria, we optimize the efficiency of the mining process without losing information about potential patterns. This technique enhances the computational feasibility of pattern discovery in large-scale tensor data and provides a practical solution for the problem.