Mining and representing similarities, distinctiveness, and distortions of map projections: An approach of approximate integral computation, hybrid sampling scheme, dimensionality reduction, and visualization
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>stage1_formula.jl # Formula-based scheme in the first stagestage1_image.jl # Image-based scheme in the first stagestage2_distmat.jl # Calculating distance matrix in the second stagestage2_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>stage2_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 distortions<br>sum_curvature_345.txt Samples of multiple iteration output of dimensionality reduction<br><i>Stage 1: Formula-based scheme</i><b>PS C:\distance&gt; &amp; julia .\stage1_formula.jl</b>[512, 3145728]arden~~~~~~bertin1953~~~~~~(-0.26020655450843494, -0.6852260581423438)boggs~~~~~~cabot=0.8~~~~~~cabot=1.0~~~~~~cabot=1.27~~~~~~cabot=1.33~~~~~~cabot=1.6~~~~~~cabot=1.8~~~~~~cabot=2.0~~~~~~larr~~~~~~mayr~~~~~~merc~~~~~~81.314381 seconds (505.70 M allocations: 20.491 GiB, 2.02% gc time, 4.70% compilation time: 4% of which was recompilation)<i>Stage 1: Image-based scheme</i><b>PS C:\distance&gt; &amp; julia.exe .\stage1_image.jl</b>[512, 3145728]bertin~~~~~~36.681385 seconds (15.93 M allocations: 10.360 GiB, 5.93% gc time, 43.31% compilation time: 4% of which was recompilation)50.328785 seconds (161.25 k allocations: 6.517 GiB, 0.06% gc time, 0.22% compilation time)boggs~~~~~~16.404210 seconds (15.03 k allocations: 9.328 GiB, 11.74% gc time, 0.06% compilation time: 100% of which was recompilation)56.283401 seconds (32 allocations: 6.743 GiB, 2.31% gc time)193.230057 seconds (33.48 M allocations: 47.537 GiB, 4.21% gc time, 10.00% compilation time: 4% of which was recompilation)<i>Stage 2: Calculate distance matrix</i><b>PS C:\distance&gt; &amp; julia.exe .\stage2_distmat.jl</b>[512, 3145728][12, 2, 14]./stage1_formula/arden v.s. ./stage1_formula/bertin1953~~~~~~2.567788 seconds (2.79 M allocations: 268.264 MiB, 2.25% gc time, 91.38% compilation time: 5% of which was recompilation)0.456522 seconds (184 allocations: 138.743 MiB, 1.90% gc time)30.86425381223618214.15301065958934./stage1_formula/arden v.s. ./stage1_formula/cabot=0.8~~~~~~0.247594 seconds (190 allocations: 106.273 MiB, 7.17% gc time)0.259103 seconds (190 allocations: 119.400 MiB, 2.45% gc time)9.4105817366531559.758357467327096./stage1_formula/arden v.s. ./stage1_formula/cabot=1.0~~~~~~0.234897 seconds (190 allocations: 106.273 MiB)0.232637 seconds (187 allocations: 100.120 MiB, 3.38% gc time)5.1735190931595327.240094823506276<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)<i>Stage 2: Dimensionality Reduction with Multiple Iteration</i><b>PS C:\distance&gt; python .\stage2_dim_reduction.py</b>(345, 347)(345, 2)(345, 345)3450.019013476013999116write csv: 0sum_curvature:(5.093807354253561e-06, 0.00021853536837068197)0.019057246673338073write csv: 1sum_curvature:(3.313713300502116e-06, 1.4942707388277949e-05)0.019223798611896027write csv: 2sum_curvature:(8.635948155976976e-06, 1.730881212449167e-05)0.01913428972808122write csv: 3sum_curvature:(0.00014343241699400875, 0.000215764401248496)0.01904508645863762write csv: 4sum_curvature:(2.9107685406817017e-05, 1.4825223806319212e-05)0.01910674306855642write csv: 5sum_curvature:(4.932848696391897e-06, 5.955810538779444e-06)0.019072604225831406write csv: 6sum_curvature:(8.625720421959653e-06, 1.885124974922429e-05)0.019116629476532615write csv: 7sum_curvature:(4.584032838619913e-05, 5.8666351031042596e-05)0.018954589398249694write csv: 8sum_curvature:(4.250225319784442e-06, 1.5497849092709274e-05)0.018987487967490377write csv: 9sum_curvature:(9.221306795274901e-06, 8.311430379552489e-05)0.01920159083695674write csv: 10sum_curvature:(1.407767101505483e-05, 1.4294453058128618e-05)<b>[due to space limitation, some output not included here]</b>