Applying EM to each individual point. Like a separate mixture model for every journal.
nearest_cosine(idx, citations, communities, self = TRUE)
| idx | A journal name or index. Vectorised for |
|---|---|
| citations | a matrix of citations (from columns to rows) or an igraph object |
| communities | A membership vector or igraph::communities object |
| self | logical. Include self-citations? If |
An object exactly like that returned by nearest_point().
Use $cosine to extract the cosine similarity.
Find the nearest citation profile to x that is a convex combination of
the community profiles y.
In order for an \(n\)-vector to be a citation profile, the elements must be non-negative and sum to one. This is also true for any convex combination (finite mixture distribution) of citation profiles.
Geometrically, this represents a point on part of the surface of the unit \(n-1\)-sphere that is within the positive closed orthant in \(R^n\). In a 3-journal network, this corresponds to the eighth of the unit sphere in the first octant and in a 2-journal network, the quarter of the unit circle in the first quadrant.
The largest possible angle between two valid citation profiles is \(\theta = \frac{\pi}{2}\), with cosine similarity \(\cos\theta = 0\). For example, the most well-separated profiles in 2-d are \((1, 0)\) and \((0, 1)\) --- i.e. the \(x\)-axis and the \(y\)-axis.