Representing similarities, distinctiveness, and features of map projections: An approach to dual sampling schemes, approximate integral computation, and dimensionality reductions
Creators: name: Yan, Jin
name: Zhang, Jun
name: Xu, TianSheng
name: Gao, Jing
name: Li, Ni
name: Gong, Guanghong
Publisher: name: figshare
Year: 2024
Subjects: classificationCode: 401301
subject: Cartography and digital mapping
classificationCode: 460306
subject: Image processing
classificationCode: 460807
subject: Information visualisation

description: <i>Source code:</i>stage_sample_formula.jl # Formula-based scheme in the first stagestage_sample_image.jl # Image-based scheme in the first stagestage_approx_int_distmat.jl # Calculating distance matrix in the second stagestage_dim_reduction.py # Dimensionality reduction in the second stage<i>Folders:</i><b>latlon-image</b> # Samples of latitude and Longitude images for the image-based scheme<b>stage1_formula</b> # Samples of output JLD2 files for formula-based scheme in the first stage<b>stage1_image</b> # Samples of output JLD2 files for image-based scheme in the first stage<b>stage_dr_iter</b> # Examples of iteration results of dimensionality reduction in the second stage<i>Files:</i>distmat_Q_total_num_is_14.csv # Example of distance matrix $\mathbf{Q}$ as defined in Tobler (1986) for 14 map projectionsdistmat_D_total_num_is_14.csv # Example of distance matrix $\mathbf{D}$, an improved version of integration used in this study, for 14 map projectionsdistmat_D_total_num_is_345_with_distortion.csv # Distance matrix $\mathbf{D}$ for 345 map projections, with first two columns containing distortionsresult_345.txt # Samples of multiple iteration output of dimensionality reduction<br><i>Sample Stage: Formula-based scheme</i><b>PS C:\distance&gt; &amp; julia .\stage_sample_formula.jl</b>[512, 3145728]<br>arden~~~~~~<br>bertin1953~~~~~~<br>(-0.26020655450843494, -0.6852260581423438)<br>boggs~~~~~~<br>cabot=0.8~~~~~~<br>cabot=1.0~~~~~~<br>cabot=1.27~~~~~~<br>cabot=1.33~~~~~~<br>cabot=1.6~~~~~~<br>cabot=1.8~~~~~~<br>cabot=2.0~~~~~~<br>larr~~~~~~<br>mayr~~~~~~<br>merc~~~~~~<br>81.314381 seconds (505.70 M allocations: 20.491 GiB, 2.02% gc time, 4.70% compilation time: 4% of which was recompilation)<br><i>Sample Stage: Image-based scheme</i><b>PS C:\distance&gt; &amp; julia.exe .\stage_sample_image.jl</b>[512, 3145728]<br>bertin~~~~~~<br>36.681385 seconds (15.93 M allocations: 10.360 GiB, 5.93% gc time, 43.31% compilation time: 4% of which was recompilation)<br>50.328785 seconds (161.25 k allocations: 6.517 GiB, 0.06% gc time, 0.22% compilation time)<br>boggs~~~~~~<br>16.404210 seconds (15.03 k allocations: 9.328 GiB, 11.74% gc time, 0.06% compilation time: 100% of which was recompilation)<br>56.283401 seconds (32 allocations: 6.743 GiB, 2.31% gc time)<br>193.230057 seconds (33.48 M allocations: 47.537 GiB, 4.21% gc time, 10.00% compilation time: 4% of which was recompilation)<br><i>Approximate Integrals Calculation Stage: Calculate distance matrix</i><b>PS C:\distance&gt; &amp; julia.exe .\stage_approx_int_distmat.jl</b>[512, 3145728]<br>[12, 2, 14]<br>./stage1_formula/arden v.s. ./stage1_formula/bertin1953~~~~~~<br>2.567788 seconds (2.79 M allocations: 268.264 MiB, 2.25% gc time, 91.38% compilation time: 5% of which was recompilation)<br>0.456522 seconds (184 allocations: 138.743 MiB, 1.90% gc time)<br>30.864253812236182<br>14.15301065958934<br>./stage1_formula/arden v.s. ./stage1_formula/cabot=0.8~~~~~~<br>0.247594 seconds (190 allocations: 106.273 MiB, 7.17% gc time)<br>0.259103 seconds (190 allocations: 119.400 MiB, 2.45% gc time)<br>9.410581736653155<br>9.758357467327096<br>./stage1_formula/arden v.s. ./stage1_formula/cabot=1.0~~~~~~<br>0.234897 seconds (190 allocations: 106.273 MiB)<br>0.232637 seconds (187 allocations: 100.120 MiB, 3.38% gc time)<br>5.173519093159532<br>7.240094823506276<br><b>[due to space limitation, some output not included here]</b>91.243785 seconds (3.26 M allocations: 59.761 GiB, 5.50% gc time, 3.10% compilation time: 4% of which was recompilation)<br><br><i>Dimensionality Reduction </i><i>Stage with Multiple Iteration</i><b>PS C:\distance&gt; python .\stage_dim_reduction.py</b>(345, 347)<br>(345, 2)<br>(345, 345)<br>345<br>0.02104933076744079write csv: 00.020680825567365817write csv: 10.02057085531406485write csv: 20.021176700490530085write csv: 30.0210250715492998write csv: 40.02092652260654796write csv: 50.021223903879462973write csv: 60.021038297528828402write csv: 70.02086673552231143write csv: 80.020723344630538126write csv: 9<br><b>[due to space limitation, some output not included here]</b>