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Consider a labelled data set having d attributes and n points in two linearly separable classes. In which of the following situations will the classes necessarily remain linearly separable? [Select ALL that apply.]Group of answer choicesA new labelled point is added.An attribute is removed.A new attribute is added.A labelled point is removed.

Question

Consider a labelled data set having d attributes and n points in two linearly separable classes. In which of the following situations will the classes necessarily remain linearly separable? [Select ALL that apply.]Group of answer choicesA new labelled point is added.An attribute is removed.A new attribute is added.A labelled point is removed.

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Solution

The classes will necessarily remain linearly separable in the following situations:

  1. A new labelled point is added: As long as the new point is on the correct side of the decision boundary, the classes will remain linearly separable.

  2. A labelled point is removed: Removing a point will not affect the linearity of the separation unless it was the only point making the classes linearly separable.

The classes may not necessarily remain linearly separable in the following situations:

  1. An attribute is removed: Removing an attribute can change the decision boundary, which may result in the classes no longer being linearly separable.

  2. A new attribute is added: Adding a new attribute can also change the decision boundary, which may result in the classes no longer being linearly separable.

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