Abstract: The concepts of compression algebra of multilateral matrix subdivision were introduced, and many of the basic properties of compression algebra of multilateral matrix subdivision were presented, and both associative law and distributive law for the compression algebra of multilateral matrix subdivision were demonstrated. To promote the concepts of half-tensor product of two matrixes as commonly compression half-tensor product, the relationship among the compression algebra of multilateral matrix subdivision, matrix left half-tensor product, and the data mining was investigated.