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Interaction and integration of multimodality media types such as visual, audio, and textual data in video are the essence of video semantic analysis. Contextual information propagation is useful for both intra- and inter-shot correlations. However, the traditional concatenated vector representation of videos weakens the power of the propagation and compensation among the multiple modalities. In this paper, we introduce a higher-order tensor framework for video analysis. We represent image frame, audio, and text in video shots as data points by the 3rd-order tensor. Then we propose a novel dimension reduction algorithm which explicitly considers the manifold structure of the tensor space from contextual temporal associated cooccurring multimodal media data. Our algorithm inherently preserves the intrinsic structure of the sub- manifold where tensorshots are sampled and is also able to map out-of-sample data points directly. We propose a new transductive support tensor machines algorithm to train effective classifier using large amount of unlabeled data together with the labeled data. Experiment results on TREVID 2005 data set show that our method improves the performance of video semantic concept detection.