We present a novel feature extraction method for face recognition called neighborhood discriminant embedding (NDE), which incorporates graph embedding and Fisher's criterion and includes an individual discriminative factor (IDF). Graph embedding is able to reveal the representative and discriminative features from the underlying nonlinear face data structure. Fisher's criterion is recognized as an effective technique for discriminative feature extraction. IDF is proposed as an individual property of each sample to describe the contribution to classification. NDE can remain the local structure of the nearest neighbors of each data point during the dimensionality reduction as well as gather the within-class points and separate the between-class points in the low-dimensional projected space. Utilizing Fisher's criterion and taking into account IDF, the discriminative capability of NDE is further enhanced. Comprehensive experiments are conducted using the Olivetti Research Laboratory (ORL) and Facial Recognition Technology (FERET) face databases to demonstrate the effectiveness of our methods.