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From Artificial Intelligence: A Modern Approach, a book by Stuart Russell and Peter Norvig, this is the definition of AI:

We define AI as the study of agents that receive percepts from the environment and perform actions. Each such agent implements a function that maps percept sequences to actions, and we cover different ways to represent these functions, such as reactive agents, real-time planners, and decision-theoretic systems. We explain the role of learning as extending the reach of the designer into unknown environments, and we show how that role constrains agent design, favoring explicit knowledge representation and reasoning.

Given the definition of AI above, is unsupervised learning (e.g. clustering) a branch of AI? I think the definition above is more suitable for supervised or reinforcement learning.

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There is a problem with confining Artificial Intelligence to a single definition, because it has become an umbrella term encompassing many fields of science. It has come a long way from the "thinking machines" of the 50s. Actually, the term was coined in a summer workshop in 1956, whose proposal was:

The study is to proceed on the basis of the conjecture that every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it.

So even from its very first introduction the field of AI included learning. Personally, I've never seen a definition of AI, that doesn't include learning, of which unsupervised learning is clearly a part. So by any means clustering algorithms, which are unsupervised learning algorithms, can be considered AI. This can be confirmed in multiple sources, e.g. wikipedia.

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