Abstract

The paper proposes a new manifold learning algorithm called Supervised Locally Multi-linear Embedding (SLME). The algorithm adopts tensor representation in a supervised manner. According to the reconstruction criteria of Locally Linear Embedding (LLE), SLME preserves the local manifold structure within the same class. Moreover, the algorithm enforces the separability between different classes by maximizing margins between point pairs in different classes with weighted distance. SLME also solves the out-of-sample problem perfectly and can be generalized to any high order tensor data easily. The experiments on face recognition indicate that SLME achieves better performance than other dimensionality reduction algorithms for the small sample size problems.

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