The description you provided aligns primarily with online recommendation engines. These systems often use a combination of content-based filtering (which recommends items similar to those the user has liked in the past) and collaborative filtering (which recommends items based on the preferences of similar users).
Here are brief explanations of the options mentioned:
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Offline Recommendation Systems: These systems process data and generate recommendations in a batch mode without needing real-time data. They typically do not take live user interactions into account.
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Online Recommendation Engines: These systems provide real-time recommendations based on current user behavior and preferences, often using a mix of content-based and collaborative filtering techniques.
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Online Filtering Systems: This term can refer to systems that filter data in real-time but may not necessarily be focused solely on recommendations. They could be more general data filtering systems.
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Digital Algorithms: This is a broad term referring to any algorithm that processes digital data, which could include recommendation systems but is not specific to them.
Based on the context you've given, online recommendation engines would be the most fitting term.