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51 lines
2.0 KiB
Markdown
51 lines
2.0 KiB
Markdown
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What is it
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----------
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The SAG module is used to create the embeddings of graphs, and to render them.
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In general, this works by mapping the nodes of a graph to the
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cells of a RogueViz-supported tessellation or honeycomb. The number of
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usable cells is limited (that is, a fixed region is set in advance for the embedding).
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Simulated Annealing is used to find the 'optimal' mapping. The function optimized
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depends on the method. Currently, there are three main 'methods' implemented:
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NEAREST: we minimize the sum of w * d over all edges, where w is the edge weight,
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and d is the distance between the endpoints of that edge. In other words,
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we want to place all nodes all close as possible, especially if the node weights are
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big. See the following visualizations as an example of visualizations obtained using
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this method:
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https://www.youtube.com/watch?v=mDG3_f8R2Ns (SAG boardgames)
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https://www.youtube.com/watch?v=WSyygk_3j9o (SAG roguelikes)
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https://www.youtube.com/watch?v=HWQkDkeEUeM (SAG programming languages)
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MATCH: we minimize the sum of squares of (d - a/w - b), where w and d are as above.
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In other words, we want the distance between nodes to represent 1/w as well as possible;
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a and b are scaling parameters.
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(no examples for now)
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LIKELIHOOD: this method is based on the Hyperbolic Random Graph model. According to
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that model, each pair of nodes in distance d are connected with probability
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1/(1+\exp((d-R)/T)). We maximize the likelihood, i.e., the product of these probabilities
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for actual edges, and their complements for non-edges. In other words, nodes connected
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with edges want to be close, while nodes not connected with edges want to be distant.
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The following embeddings have been obtained using this method:
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https://youtu.be/GQKaKF_yOL4 (brain connectomes)
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The rest of this README details how to use SAG.
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Cells
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-----
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Not yet documented
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Graph
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-----
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Just use `-sag-weighted` to read a weighted graph (in format `node1;node2;weight`),
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or `-sag-unweighted` to read an unweighted graph (in format `node1 node2`).
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