In this paper, we determine whether incomplete videos that are often discarded carry useful information for action recognition, and if so, how one can represent such mixed collection of video data (complete versus incomplete, and labeled versus unlabeled) in a unified manner. We propose a novel framework to handle incomplete videos in action classification, and make three main contributions: (1) We cast the action classification problem for a mixture of complete and incomplete data as a semi-supervised learning problem of labeled and unlabeled data. (2) We introduce a two-step approach to convert the input mixed data into a uniform compact representation. (3) Exhaustively scrutinizing 280 configurations, we experimentally show on our two created benchmarks that, even the videos are extremely sparse and incomplete, it is still possible to recover useful information from them, and classify unknown actions by a graph based semi-supervised learning framework.