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. 2010 Nov 10;5(11):e13541. doi: 10.1371/journal.pone.0013541

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Bettencourt et al.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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The cross-correlation between SAMI time-series gives a measure of similarity, which can be used to group cities into clusters with similar characteristics; A) sorted correlation matrix (heatmap) for personal income in US MSAs with population over 1 million. Red (blue) denotes greatest (dis)similarity; B)Dendrogram showing detailed urban taxonomy of USMAs according to personal income. This clearly manifests clustering among cities with similar time trajectories. Here we used a decorrelation measure as distance between any two cities, where is the cross-correlation of Figure 4A. When the decorrelation , , indicating no correlation(dashed line), revealing five families of kindred cities. See Figures S2, S3, S4, S5, S6, and S7 for other quantities.

Inline graphic — The cross-correlation between SAMI time-series gives a measure of similarity, which can be used to group cities into clusters with similar characteristics; A) sorted correlation matrix (heatmap) for personal income in US MSAs with population over 1 million. Red (blue) denotes greatest (dis)similarity; B)Dendrogram showing detailed urban taxonomy of USMAs according to personal income. This clearly manifests clustering among cities with similar time trajectories. Here we used a decorrelation measure as distance between any two cities, where is the cross-correlation of Figure 4A. When the decorrelation , , indicating no correlation(dashed line), revealing five families of kindred cities. See Figures S2, S3, S4, S5, S6, and S7 for other quantities.