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Concatenating sequences of feature vectors helps to capture essential information about articulatory dynamics, at the cost of increasing the number of dimensions in the feature space, which may be characterized by the presence of manifolds. Existing supervised dimensionality reduction methods such as Linear Discriminant Analysis may destroy part of that manifold structure. In this paper, we propose a novel supervised dimensionality reduction algorithm, called Globality-Locality Consistent Discriminant Analysis (GLCDA), which aims to preserve global and local discriminant information simultaneously. Because it allows finding the optimal trade-off between global and local structure of data sets, GLCDA can provide a more faithful compact representation of high-dimensional observations than entirely global approaches or heuristic approaches aimed to preserve local information. Experimental results on the TIMIT phone classification task show the effectiveness of the proposed algorithm.