A convex combination is a linear combination of data points (which can be vectors or scalars) where all coefficients are positive and sum up to 1. It is called "convex combination", since all possible convex combinations (given the base vectors) will be within the convex hull of the given datapoints.
In fact, the set of all convex combinations constitutes the convex hull.
A special case is with only two data points, where the value of the new point (formed by the convex combination) will lie on a straight line between the two points.
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