The conventional Laplacian Eigenmap preserves neighborhood relationships based on Euclidean distance, that is, the neighboring high-dimensional data points are mapped into neighboring points in the low-dimensional space. However, the selections of neighborhood may influence the global low-dimensional coordinates. In this paper, both the geodesic distance and generalized Gaussian function are incorporated into Laplacian eigenmap algorithm. At first, a generalized Gaussian Laplacian eigenmap algorithm based on geodesic distance (GGLE) is proposed. The global low-dimensional coordinates obtained by GGLE have different clustering properties when different generalized Gaussian functions are used to measure the similarity between the high-dimensional data points. Then, this paper utilizes these properties to further propose the ensemble-based discriminant algorithm of the above-motioned GGLE. The main advantages of the ensemble-based algorithm are: The neighborhood parameter K is fixed and to construct the neighborhood graph and geodesic distance matrix needs one time only. Finally, the recognition experimental results on wood texture dataset show that it is an efficient ensemble discriminant algorithm based on manifold.