For the last few decades, the application of signal-adaptive transform coding to video compression has been stymied by the large computational complexity of matrix-based solutions. In this paper, we propose a novel parametric approach to greatly reduce the complexity without degrading the compression performance. In our approach, instead of following the conventional technique of identifying full transform matrices that yield best compression efficiency, we look for the best transform parameters defining a new class of transforms, called HyGTs, which have low complexity implementations that are easy to parallelize. The proposed HyGTs are implemented as an extension of High Efficiency Video Coding (HEVC), and our comprehensive experimental results demonstrate that proposed HyGTs improve average coding gain by 6% bit rate reduction, while using 6.8 times less memory than KLT matrices.