Image and video classification research has made great progress through the development of handcrafted local features and learning based features. These two architectures were proposed roughly at the same time and have flourished at overlapping stages of history. However, they are typically viewed as distinct approaches. In this paper, we emphasize their structural similarities and show how such a unified view helps us in designing features that balance efficiency and effectiveness. As an example, we study the problem of designing efficient video feature learning algorithms for action recognition. We approach this problem by first showing that local handcrafted features and Convolutional Neural Networks (CNNs) share the same convolution-pooling network structure. We then propose a two-stream Convolutional ISA (ConvISA) that adopts the convolution-pooling structure of the state-of-the-art handcrafted video feature with greater modeling capacities and a cost-effective training algorithm. Through custom designed network structures for pixels and optical flow, our method also reflects distinctive characteristics of these two data sources. Our experimental results on standard action recognition benchmarks show that by focusing on the structure of CNNs, rather than end-to-end training methods, we are able to design an efficient and powerful video feature learning algorithm.