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This paper presents a method for recognizing sign language using hand movement trajectory. By applying Kernel Principal Component Analysis (KPCA), the motion trajectory data are firstly mapped into a higher-dimensional feature space for analysis. The advantage of using high dimensionality is that it allows a more flexible decision boundary and thus helps us to achieve better classification accuracy. Then we perform the Nonparametric Discriminant Analysis (NDA) in the higher-dimensional feature space, so that the most helpful information can be extracted. We have tested the proposed method using the Australian Sign Language (ASL) data set. The results demonstrate that our approach outperforms the current state-of-the-art for trajectory-based sign language recognition.