Locality preserving projections (LPP) can find an embedding that preserves local information and discriminates data well. However, only one projection matrix over the whole data is not enough to discriminate complex data. In this paper, we proposed locality preserving projections mixture models (LPP mixtures), where the set of all data were partitioned into several clusters and a projection matrix for each cluster was obtained. In each cluster, We performed LPP via QR-decomposition, which is efficient computationally in under-sampled situations. Its theoretical foundation was presented. Experiments on a synthetic data set and the Yale face database showed the superiority of LPP mixtures.