Travel Matrix Decomposition for Understanding Spatial Long-Distance Travel Structure

<div>Observed matrix <span class="nowrap"><svg height="11.7293pt" id="M78" style="vertical-align:-3.29566pt" version="1.1" viewbox="-0.0498162 -8.43364 17.8429 11.7293" width="17.8429pt" 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="M401 353C473 367 557 406 557 502C557 551 535 592 498 616C460 640 410 650 333 650H41V615C112 608 121 602 121 516V134C121 49 112 42 35 35V0H289C372 0 449 14 500 43C556 74 593 126 593 193C593 288 517 335 401 349V353ZM253 363V553C253 574 255 589 262 596C268 602 284 609 307 609C361 609 415 575 415 484C415 401 372 363 276 363H253ZM253 323H273C386 323 445 276 445 182C445 84 382 43 326 42C273 41 253 62 253 136V323Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.312,3.132)"><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,-0.0091,12.434,3.132)"><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,-0.0091,14.846,3.132)"><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></svg>.</span></div>

Complexity

fig3

Figure 3

Figure 3: Travel Matrix Decomposition for Understanding Spatial Long-Distance Travel Structure 