In this letter, we present a radix-R regular interconnection pattern family of factorizations for the WHT-FFT with identical stage-to-stage interconnection pattern in a unified form, where R is any power of 2. This family of algorithms has identical sparse matrix factorization in each stage and can be implemented in a merged butterfly structure, which conduce to regular and efficient memory managing scalable to high radices. And in each stage, the butterflies with same twiddle factor set are aggregated together, which can reduce the twiddle factor evaluations or accesses to the lookup table. The kinds of factorization can also be extended to FFT, WHT and SCHT with identical stage-to-stage interconnection pattern.