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Exploring the tremendous amount of data efficiently to make a decision, similar to answering a complicated question, is challenging with many real-world application scenarios. In this context, automatic summarization has substantial importance as it will provide the foundation for big data analytic. Traditional summarization approaches optimize the system to produce a short static summary that fits all users that do not consider the subjectivity aspect of summarization, i.e., what is deemed valuable for different users, making these approaches impractical in real-world use cases. This paper proposes an interactive concept-based summarization model, called Adaptive Summaries, that helps users make their desired summary instead of producing a single inflexible summary. The system learns from users' provided information gradually while interacting with the system by giving feedback in an iterative loop. Users can choose either reject or accept action for selecting a concept being included in the summary with the importance of that concept from users' perspectives and confidence level of their feedback. The proposed approach can guarantee interactive speed to keep the user engaged in the process. Furthermore, it eliminates the need for reference summaries, which is a challenging issue for summarization tasks. Evaluations show that Adaptive Summaries helps users make high-quality summaries based on their preferences by maximizing the user-desired content in the generated summaries.