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Mathematics
General Math
Label propagation equation: what are the terms?
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[QUOTE="Master1022, post: 6628405, member: 650268"] [B]TL;DR Summary:[/B] What terms in the equation (from the linked paper) are vectors or scalars? Hi, This is a simple question that I just wanted to clarify. I was reading the following paper on [B]label propagation[/B]: [U][URL='https://pure.mpg.de/rest/items/item_1792131/component/file_3180996/content']HERE[/URL][/U] and I can't understand whether the terms are vectors or scalars in one of the equations - specifically, equation (2.15) shown in the image below. [ATTACH type="full"]300953[/ATTACH] [B]My understanding:[/B] - ##f## is a vector - ## S ## is a matrix - ## \alpha ## is a scalar - I am not too sure about ##y##: could be a vector or a scalar. - ##\nu##: I am not too sure, but I think it could be referring to a specific node? That is, ## f(\nu) ## could be the value of the vector ## f## at node ## \nu ##. - ## y ##: I am not sure, but I think it is a vector (see reasoning below). [I]Case is ## y ## is a scalar:[/I] - That would make sense mathematically, but does that mean that we are using the same scalar ## y ## the equation for all nodes. That is, it doesn't matter what node ## \nu ## we are considering, we will always have the same ## y ## scalar in the equation? However, there is another equation above (shown below) which uses y as follows. This suggests that ##y## is a vector because then we have matrix-vector multiplication: [ATTACH type="full"]300954[/ATTACH] [I]Case if ## y ## is a vector:[/I] - It could be a vector (as suggested by image above), but then we are adding a vector ## (1 - \alpha) y ## to a scalar ## \alpha S f ## is a vector, and we are extracted the value at a certain node ## \nu ##, so it is a scalar. Therefore, it seems unlikely that ## y ## is a vector unless my interpretation of ## \nu ## is incorrect.Apologies if this is sparse with information. I didn't want to rewrite the paper in this post and I am unsure of some of the definitions of variables in there. Any help would be greatly appreciated. [/QUOTE]
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Label propagation equation: what are the terms?
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