Travel Matrix Decomposition for Understanding Spatial Long-Distance Travel Structure

<div>Estimated matrix <span class="nowrap"><svg height="12.584pt" id="M83" style="vertical-align:-3.29567pt" version="1.1" viewbox="-0.0498162 -9.28833 59.4958 12.584" width="59.4958pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M687 0V35C623 43 611 56 577 144C512 316 450 490 386 665L335 652L130 138C97 54 84 43 18 35V0H242V35C169 44 166 58 181 106C193 146 206 182 217 213H409C424 173 439 130 449 100C465 56 460 44 401 35V0H687ZM390 266H234C260 337 285 410 313 483H316L390 266Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.71,3.132)"><path d="M442 39L431 68C420 63 406 57 394 57C377 57 359 71 359 118V301C359 353 349 393 314 424C291 443 261 451 230 451C171 438 107 401 79 381C59 366 46 355 46 340C46 316 72 295 91 295C106 295 117 303 122 319C131 350 139 371 152 384C163 397 178 404 197 404C246 404 281 365 281 293V278C260 262 186 232 124 213C69 194 41 161 41 112C41 47 92 -12 163 -12C195 -12 243 25 283 51C288 35 293 22 308 7C319 -4 339 -12 354 -12L442 39ZM281 87C262 68 226 51 199 51C169 51 129 74 129 126C129 162 151 181 190 198C211 208 259 229 281 240V87Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.833,3.132)"><path d="M244 0V30C178 35 170 41 170 107V710C136 697 72 680 18 675V647C83 642 89 639 89 572V107C89 43 80 35 16 30V0H244Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.244,3.132)"><path d="M244 0V30C178 35 170 41 170 107V710C136 697 72 680 18 675V647C83 642 89 639 89 572V107C89 43 80 35 16 30V0H244Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.047,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.584,0)"><path d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,45.405,3.132)"><path d="M442 39L431 68C420 63 406 57 394 57C377 57 359 71 359 118V301C359 353 349 393 314 424C291 443 261 451 230 451C171 438 107 401 79 381C59 366 46 355 46 340C46 316 72 295 91 295C106 295 117 303 122 319C131 350 139 371 152 384C163 397 178 404 197 404C246 404 281 365 281 293V278C260 262 186 232 124 213C69 194 41 161 41 112C41 47 92 -12 163 -12C195 -12 243 25 283 51C288 35 293 22 308 7C319 -4 339 -12 354 -12L442 39ZM281 87C262 68 226 51 199 51C169 51 129 74 129 126C129 162 151 181 190 198C211 208 259 229 281 240V87Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,49.527,3.132)"><path d="M244 0V30C178 35 170 41 170 107V710C136 697 72 680 18 675V647C83 642 89 639 89 572V107C89 43 80 35 16 30V0H244Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,51.939,3.132)"><path d="M244 0V30C178 35 170 41 170 107V710C136 697 72 680 18 675V647C83 642 89 639 89 572V107C89 43 80 35 16 30V0H244Z"></path></g><g transform="matrix(.013,0,0,-0.013,54.836,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg>.</span></div>

Complexity

fig4

Figure 4

Figure 4: Travel Matrix Decomposition for Understanding Spatial Long-Distance Travel Structure 