  Machine learning techniques provide a chance to explore the coding
performance potential of transform. In this work, we propose an explainable
transform based intra video coding to improve the coding efficiency. Firstly,
we model machine learning based transform design as an optimization problem of
maximizing the energy compaction or decorrelation capability. The explainable
machine learning based transform, i.e., Subspace Approximation with Adjusted
Bias (Saab) transform, is analyzed and compared with the mainstream Discrete
Cosine Transform (DCT) on their energy compaction and decorrelation
capabilities. Secondly, we propose a Saab transform based intra video coding
framework with off-line Saab transform learning. Meanwhile, intra mode
dependent Saab transform is developed. Then, Rate Distortion (RD) gain of Saab
transform based intra video coding is theoretically and experimentally analyzed
in detail. Finally, three strategies on integrating the Saab transform and DCT
in intra video coding are developed to improve the coding efficiency.
Experimental results demonstrate that the proposed 8$\times$8 Saab transform
based intra video coding can achieve Bj{\o}nteggard Delta Bit Rate (BDBR) from
-1.19% to -10.00% and -3.07% on average as compared with the mainstream
8$\times$8 DCT based coding scheme.
