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Twitter is a microblogging platform that generates large volumes of data with high velocity. This daily generation of unbounded and continuous data leads to Big Data streams that often require real-time distributed and fully automated processing. Hashtags, hyperlinked words in tweets, are widely used for tweet topic classification, retrieval, and clustering. Hashtags are used widely for analyzing tweet sentiments where emotions can be classified without contexts. However, regardless of the wide usage of hashtags, general tweet topic classification using hashtags is challenging due to its evolving nature, lack of context, slang, abbreviations, and non-standardized expression by users. Most existing approaches, which utilize hashtags for tweet topic classification, focus on extracting hashtag concepts from external lexicon resources to derive semantics. However, due to the rapid evolution and non-standardized expression of hashtags, the majority of these lexicon resources either suffer from the lack of hashtag words in their knowledge bases or use multiple resources at once to derive semantics, which make them unscalable. Along with scalable and automated techniques for tweet topic classification using hashtags, there is also a requirement for real-time analytics approaches to handle huge and dynamic flows of textual streams generated by Twitter. To address these problems, this paper first presents a novel semi-automated technique that derives semantically relevant hashtags using a domain-specific knowledge base of topic concepts and combines them with the existing tweet-based-hashtags to produce Hybrid Hashtags. Further, to deal with the speed and volume of Big Data streams of tweets, we present an online approach that updates the preprocessing and learning model incrementally in a real-time streaming environment using the distributed framework, Apache Storm. Finally, to fully exploit the batch and stream environment performance advantages, we propose a comprehensive framework (Hybrid Hashtag-based Tweet topic classification (HHTC) framework) that combines batch and online mechanisms in the most effective way. Extensive experimental evaluations on a large volume of Twitter data show that the batch and online mechanisms, along with their combination in the proposed framework, are scalable, efficient, and provide effective tweet topic classification using hashtags.