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In a wide range of business areas dealing with text data streams, including CRM, knowledge management, and Web monitoring services, it is an important issue to discover topic trends and analyze their dynamics in real-time. Specifically we consider the following three tasks in topic trend analysis: 1)Topic Structure Identification; identifying what kinds of main topics exist and how important they are, 2)Topic Emergence Detection; detecting the emergence of a new topic and recognizing how it grows, 3)Topic Characterization; identifying the characteristics for each of main topics. For real topic analysis systems, we may require that these three tasks be performed in an on-line fashion rather than in a retrospective way, and be dealt with in a single framework. This paper proposes a new topic analysis framework which satisfies this requirement from a unifying viewpoint that a topic structure is modeled using a finite mixture model and that any change of a topic trend is tracked by learning the finite mixture model dynamically. In this framework we propose the usage of a time-stamp based discounting learning algorithm in order to realize real-time topic structure identification. This enables tracking the topic structure adaptively by forgetting out-of-date statistics. Further we apply the theory of dynamic model selection to detecting changes of main components in the finite mixture model in order to realize topic emergence detection. We demonstrate the effectiveness of our framework using real data collected at a help desk to show that we are able to track dynamics of topic trends in a timely fashion.