The invention discloses a method and a device for establishing a projection space, which belong to the technical field of pattern recognition. The method comprises the steps of: establishing a weighted spectrogram according to N facial images of an original space; acquiring a Laplacian matrix according to the weighted spectrogram; based on a random walk model, utilizing the Laplacian matrix to acquire an interaction time matrix; utilizing the interaction time matrix to establish an optimization problem according to an optimization principle, and deoptimizing to obtain an generalized eigenvalue and an generalized eigenvector; and utilizing the generalized eigenvalue and the generalized eigenvector to establish the projection space. The device comprises a weighted spectrogram establishment module, a Laplacian matrix acquisition module, an eigenvalue and eigenvector acquisition module, and a projection space establishment module. The method and the device establish the projection space based on the random walk model by establishing the weighted spectrogram, and are applicable to image spaces with high non-linearity; and the method and the device consider local characteristics of the image space, also emphasize the optimization of global information of the image space, and improve the accuracy of the projection space.