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""" |
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Time Series Graphs |
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""" |
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import itertools |
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import networkx as nx |
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__all__ = ["visibility_graph"] |
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@nx._dispatchable(graphs=None, returns_graph=True) |
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def visibility_graph(series): |
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""" |
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Return a Visibility Graph of an input Time Series. |
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A visibility graph converts a time series into a graph. The constructed graph |
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uses integer nodes to indicate which event in the series the node represents. |
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Edges are formed as follows: consider a bar plot of the series and view that |
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as a side view of a landscape with a node at the top of each bar. An edge |
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means that the nodes can be connected by a straight "line-of-sight" without |
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being obscured by any bars between the nodes. |
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The resulting graph inherits several properties of the series in its structure. |
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Thereby, periodic series convert into regular graphs, random series convert |
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into random graphs, and fractal series convert into scale-free networks [1]_. |
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Parameters |
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---------- |
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series : Sequence[Number] |
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A Time Series sequence (iterable and sliceable) of numeric values |
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representing times. |
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Returns |
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------- |
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NetworkX Graph |
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The Visibility Graph of the input series |
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Examples |
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-------- |
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>>> series_list = [range(10), [2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3]] |
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>>> for s in series_list: |
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... g = nx.visibility_graph(s) |
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... print(g) |
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Graph with 10 nodes and 9 edges |
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Graph with 12 nodes and 18 edges |
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References |
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---------- |
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.. [1] Lacasa, Lucas, Bartolo Luque, Fernando Ballesteros, Jordi Luque, and Juan Carlos Nuno. |
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"From time series to complex networks: The visibility graph." Proceedings of the |
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National Academy of Sciences 105, no. 13 (2008): 4972-4975. |
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https://www.pnas.org/doi/10.1073/pnas.0709247105 |
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""" |
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G = nx.path_graph(len(series)) |
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nx.set_node_attributes(G, dict(enumerate(series)), "value") |
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for (n1, t1), (n2, t2) in itertools.combinations(enumerate(series), 2): |
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slope = (t2 - t1) / (n2 - n1) |
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offset = t2 - slope * n2 |
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obstructed = any( |
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t >= slope * n + offset |
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for n, t in enumerate(series[n1 + 1 : n2], start=n1 + 1) |
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) |
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if not obstructed: |
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G.add_edge(n1, n2) |
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return G |
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