Neural Models for Imputation of Missing Ozone Data in Air-Quality Datasets

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:4.46em"/><col style="width:6.13em"/><col style="width:6.05em"/><col style="width:3.62em"/><col style="width:3.44em"/></colgroup><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Method</td><td class="align_center" colspan="2">MSE</td><td class="align_center" colspan="2">Time (s)</td></tr><tr class="thead"><td class="align_center">Mean</td><td class="align_center">STD</td><td class="align_center">Mean</td><td class="align_center">STD</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">MLR</td><td class="align_center"><span style="width: 62.1637ptpx;"><svg height="8.98583pt" id="M34" style="vertical-align:-0.3499308pt" version="1.1" viewbox="-0.0498162 -8.6359 62.1637 8.98583" width="62.1637pt" 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="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path></g><g transform="matrix(.013,0,0,-0.013,15.444,0)"><path d="M244 635C114 635 38 519 38 422C38 317 111 240 217 240C236 240 255 244 277 256L345 292C311 140 203 39 59 15L64 -15C89 -15 150 -5 204 17C339 72 440 202 440 386C440 521 368 635 244 635ZM228 602C326 602 352 479 352 390C352 370 351 347 348 324C327 308 293 296 258 296C174 296 124 369 124 458C124 517 152 602 228 602Z" id="g113-58"></path></g><g transform="matrix(.013,0,0,-0.013,21.686,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.013,0,0,-0.013,27.926,0)"><path d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path></g><g transform="matrix(.013,0,0,-0.013,38.839,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,49.376,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.013,0,0,-0.013,55.616,0)"><path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z" id="g113-55"></path></g></svg></span></td><td class="align_center"><span style="width: 62.1637ptpx;"><svg height="8.98583pt" id="M35" style="vertical-align:-0.3499308pt" version="1.1" viewbox="-0.0498162 -8.6359 62.1637 8.98583" width="62.1637pt" 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="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path></g><g transform="matrix(.013,0,0,-0.013,15.444,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,21.684,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,27.924,0)"><path d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path></g><g transform="matrix(.013,0,0,-0.013,38.838,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,49.374,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.013,0,0,-0.013,55.614,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z" id="g113-57"></path></g></svg></span></td><td class="align_center"><b>0.089</b></td><td class="align_center">0.216</td></tr><tr><td class="align_left">MN-LR</td><td class="align_center"><span style="width: 63.2729ptpx;"><svg height="9.09023pt" id="M36" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.7403 63.2729 9.09023" width="63.2729pt" 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="M152 515H407L439 613L433 623H115L70 303C91 310 134 322 179 322C270 322 327 264 327 174C327 100 297 45 235 45C178 45 130 84 106 106C93 117 82 120 70 112C53 99 38 76 38 61S43 36 63 20C84 2 126 -12 166 -12C226 -11 297 15 354 56C424 105 455 164 455 226C455 312 382 394 254 394C228 394 175 380 125 362L152 515Z" id="g13-51"></path></g><g transform="matrix(.013,0,0,-0.013,6.5,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,9.464,0)"><path d="M486 174V231H396V629H324C229 512 123 368 15 215V174H269V116C269 55 264 41 179 34V0H477V34C403 41 396 51 396 112V174H486ZM269 231H90C155 335 219 427 267 493H269V231Z" id="g13-50"></path></g><g transform="matrix(.013,0,0,-0.013,15.964,0)"><path d="M409 0V34C329 39 322 56 322 125V635C234 611 160 593 94 583V554L145 551C186 547 190 541 190 488V125C190 54 181 39 102 34V0H409Z" id="g13-47"></path></g><g transform="matrix(.013,0,0,-0.013,22.464,0)"><path d="M152 515H407L439 613L433 623H115L70 303C91 310 134 322 179 322C270 322 327 264 327 174C327 100 297 45 235 45C178 45 130 84 106 106C93 117 82 120 70 112C53 99 38 76 38 61S43 36 63 20C84 2 126 -12 166 -12C226 -11 297 15 354 56C424 105 455 164 455 226C455 312 382 394 254 394C228 394 175 380 125 362L152 515Z" id="g13-51"></path></g><g transform="matrix(.013,0,0,-0.013,29.073,0)"><path d="M535 173C517 129 499 97 479 75C456 50 421 43 369 43C331 43 297 45 279 53C259 63 255 87 255 135V309H322C407 309 420 305 433 233H469V434H433C420 364 406 359 322 359H255V571C255 604 259 606 296 606H344C400 606 427 599 444 581C462 563 475 530 484 495L521 500C517 562 512 632 511 650H40V615C111 609 121 604 121 517V133C121 48 111 42 26 35V0H536C544 30 564 121 571 166L535 173Z" id="g13-67"></path></g><g transform="matrix(.013,0,0,-0.013,39.531,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,50.068,0)"><path d="M252 635C85 635 28 460 28 311C28 167 82 -12 250 -12C419 -12 472 166 472 312C472 457 419 635 252 635ZM248 594C314 594 335 455 335 314C335 174 318 29 252 29S165 180 165 315S181 594 248 594Z" id="g13-46"></path></g><g transform="matrix(.013,0,0,-0.013,56.568,0)"><path d="M179 359C209 485 294 542 343 567C378 584 421 597 450 603L443 641C405 636 339 624 294 609C178 570 28 456 28 243C28 84 127 -12 253 -12C385 -12 480 89 480 215C480 328 403 402 288 402C272 402 254 394 229 382L179 359ZM234 331C302 331 349 265 349 171C349 106 335 29 273 29C220 29 166 106 166 239C166 263 168 303 172 320C192 327 211 331 234 331Z" id="g13-52"></path></g></svg></span></td><td class="align_center"><span style="width: 62.1637ptpx;"><svg height="8.98583pt" id="M37" style="vertical-align:-0.3499308pt" version="1.1" viewbox="-0.0498162 -8.6359 62.1637 8.98583" width="62.1637pt" 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="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path></g><g transform="matrix(.013,0,0,-0.013,15.444,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path></g><g transform="matrix(.013,0,0,-0.013,21.684,0)"><path d="M447 623H65C61 580 56 530 47 475H76C100 541 106 550 172 550H388C308 376 196 170 91 -1L98 -12L172 -2C268 204 360 408 455 611L447 623Z" id="g113-56"></path></g><g transform="matrix(.013,0,0,-0.013,27.927,0)"><path d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path></g><g transform="matrix(.013,0,0,-0.013,38.84,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,49.377,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.013,0,0,-0.013,55.617,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z" id="g113-57"></path></g></svg></span></td><td class="align_center">2.143</td><td class="align_center">0.254</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Linear regression and nonlinear regression results for the WD.</div>

Complexity

tab3

Table 3

Table 3: Neural Models for Imputation of Missing Ozone Data in Air-Quality Datasets 