Action recognition has been one of the most popular fields of computer vision. This paper presents a novel approach to action recognition problem using the dimension reduction method, local fisher discriminant analysis, to reduce the dimension of feature descriptors as the preprocessing step after feature extraction. We propose to use sparse matrix and randomized kd-tree to modify and accelerate the standard local fisher discriminant analysis and propose the modified local fisher discriminant analysis. We also propose an effective feature encoding called mix encoding to combine fisher vector encoding and locality-constrained linear coding to obtain video representations. The experiments show the methods clearly improve the recognition accuracy. Experimental results show our method outperforms our baseline method and can be the state of the art in the KTH dataset.