Predict Sugar Content in Grape Berries Using PLS Regression on Hyperspectral Data
This example shows how to perform non-destructive testing (NDT) using hyperspectral data to predict sugar content in grape berries.
Hyperspectral images provide significant information about the quality and composition of the imaged materials. This makes hyperspectral imaging a useful tool for non-destructive testing (NDT) applications, such as maturity monitoring of fruits, without causing any damage to the items being imaged.
This example requires the Image Processing Toolbox™ Hyperspectral Imaging Library. You can install the Image Processing Toolbox Hyperspectral Imaging Library from Add-On Explorer. For more information about installing add-ons, see Get and Manage Add-Ons. The Image Processing Toolbox Hyperspectral Imaging Library requires desktop MATLAB®, as MATLAB® Online™ and MATLAB® Mobile™ do not support the library.
About the Data Set
In this example, you use a spectral data set of grape berries of three varieties— Syrah, Fer Servadou, and Mauzac— obtained using hyperspectral imaging [1]. The sampling of grape berries started one or two weeks after veraison and preharvest, in the summer of 2020, in three plots in Gaillac, France. As grape berries mature, their density increases because of the increasing sugar content. The plucked grape berries were sorted based on their maturity using densimetric sorting. The grape berries were divided into 274 samples. Each sample of grape berries consists of 100 berries of the same variety and similar maturity level. The grape berries in a sample were arranged in a tray and a hyperspectral camera was set up to acquire top view images of the tray such that no grape berry is occluded. The hyperspectral image was segmented to identify the grape berries in the image.
The data set comprises the average spectrum of all 100 berries in each sample for different wavelengths computed from the hyperspectral image of each sample. The hyperspectral data provides information about the chemical composition of the grape berries.
Load Data Set
Read the contents of the GrapeBerriesSpectralDataset.csv file, attached to this example as a supporting file, into the workspace as a table. The table contains 274 observations consisting of the data for the 274 samples across 207 variables. The first variable Var1 is the index of the sample, the second variable Variety is the variety of the grape berries in the sample, and the third variable SugarContent_g_l_ is the sugar content in the sample in grams per liter (g/L). The rest of the variables comprise the average spectrum of the sample for 204 different wavelengths.
warning off T = readtable("GrapeBerriesSpectralDataset.csv")
T=274×207 table
Var1 Variety SugarContent_g_l_ x_397_32 x_400_2 x_403_09 x_405_97 x_408_85 x_411_74 x_414_63 x_417_52 x_420_4 x_423_29 x_426_19 x_429_08 x_431_97 x_434_87 x_437_76 x_440_66 x_443_56 x_446_45 x_449_35 x_452_25 x_455_16 x_458_06 x_460_96 x_463_87 x_466_77 x_469_68 x_472_59 x_475_5 x_478_41 x_481_32 x_484_23 x_487_14 x_490_06 x_492_97 x_495_89 x_498_8 x_501_72 x_504_64 x_507_56 x_510_48 x_513_4 x_516_33 x_519_25 x_522_18 x_525_1 x_528_03 x_530_96 x_533_89 x_536_82 x_539_75 x_542_68 x_545_62 x_548_55 x_551_49 x_554_43 x_557_36 x_560_3 x_563_24 x_566_18 x_569_12 x_572_07 x_575_01 x_577_96 x_580_9 x_583_85 x_586_8 x_589_75 x_592_7 x_595_65 x_598_6 x_601_55 x_604_51 x_607_46 x_610_42 x_613_38 x_616_34 x_619_3 x_622_26 x_625_22 x_628_18 x_631_15 x_634_11 x_637_08 x_640_04 x_643_01 x_645_98 x_648_95 x_651_92 x_654_89 x_657_87 x_660_84 x_663_81 x_666_79 x_669_77 x_672_75 x_675_73 x_678_71 x_681_69 x_684_67 x_687_65 x_690_64 x_693_62 x_696_61 x_699_6 x_702_58 x_705_57 x_708_57 x_711_56 x_714_55 x_717_54 x_720_54 x_723_53 x_726_53 x_729_53 x_732_53 x_735_53 x_738_53 x_741_53 x_744_53 x_747_54 x_750_54 x_753_55 x_756_56 x_759_56 x_762_57 x_765_58 x_768_6 x_771_61 x_774_62 x_777_64 x_780_65 x_783_67 x_786_68 x_789_7 x_792_72 x_795_74 x_798_77 x_801_79 x_804_81 x_807_84 x_810_86 x_813_89 x_816_92 x_819_95 x_822_98 x_826_01 x_829_04 x_832_07 x_835_11 x_838_14 x_841_18 x_844_22 x_847_25 x_850_29 x_853_33 x_856_37 x_859_42 x_862_46 x_865_5 x_868_55 x_871_6 x_874_64 x_877_69 x_880_74 x_883_79 x_886_84 x_889_9 x_892_95 x_896_01 x_899_06 x_902_12 x_905_18 x_908_24 x_911_3 x_914_36 x_917_42 x_920_48 x_923_55 x_926_61 x_929_68 x_932_74 x_935_81 x_938_88 x_941_95 x_945_02 x_948_1 x_951_17 x_954_24 x_957_32 x_960_4 x_963_47 x_966_55 x_969_63 x_972_71 x_975_79 x_978_88 x_981_96 x_985_05 x_988_13 x_991_22 x_994_31 x_997_4 x_1000_4 x_1003_5
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1 {'SYRAH'} 144.74 0.14352 0.12199 0.10853 0.098045 0.090435 0.084515 0.078604 0.074226 0.070202 0.066113 0.062973 0.06103 0.058249 0.05695 0.055669 0.054468 0.053297 0.052331 0.051966 0.050817 0.050311 0.049195 0.048511 0.047603 0.046411 0.045673 0.044925 0.044238 0.043639 0.043185 0.042498 0.041802 0.041429 0.041135 0.040697 0.040195 0.040121 0.0398 0.039679 0.039507 0.03944 0.039293 0.039167 0.038939 0.038828 0.038569 0.038418 0.03825 0.03809 0.037976 0.037988 0.037776 0.037621 0.037418 0.037387 0.037258 0.037303 0.037248 0.037338 0.037343 0.037304 0.037437 0.03782 0.038009 0.03838 0.038679 0.039105 0.039613 0.040235 0.040832 0.041586 0.04237 0.043149 0.043909 0.044551 0.045223 0.046112 0.046956 0.047817 0.048573 0.049695 0.050492 0.051144 0.051761 0.052264 0.052524 0.053222 0.053937 0.054916 0.055152 0.054853 0.053983 0.053637 0.053591 0.054212 0.055731 0.057987 0.062159 0.069776 0.081673 0.097671 0.11577 0.13359 0.14994 0.16512 0.17908 0.19198 0.20339 0.21521 0.22529 0.23591 0.24542 0.25461 0.26295 0.27155 0.27897 0.28664 0.2939 0.30107 0.3079 0.31431 0.3213 0.32774 0.33251 0.3354 0.34154 0.34655 0.35065 0.35628 0.35999 0.36426 0.36872 0.37219 0.37606 0.38049 0.38415 0.38852 0.39138 0.39561 0.3984 0.40089 0.4029 0.40519 0.40706 0.40916 0.40969 0.40964 0.40936 0.40954 0.41082 0.41236 0.41475 0.41704 0.42148 0.4244 0.4254 0.42666 0.42625 0.42555 0.42578 0.42514 0.42649 0.42615 0.42554 0.42663 0.426 0.42516 0.42572 0.42531 0.4245 0.42491 0.42457 0.42486 0.42406 0.4234 0.42356 0.42067 0.41718 0.41373 0.40839 0.40271 0.39406 0.3859 0.37794 0.36805 0.35556 0.34312 0.32769 0.31661 0.3094 0.30607 0.30322 0.30686 0.30505 0.30583 0.31296 0.31595 0.32199 0.32836 0.33327 0.34317 0.35192 0.35996 0.34038
2 {'SYRAH'} 163.25 0.14203 0.12158 0.1076 0.096139 0.089941 0.083718 0.077647 0.072666 0.068645 0.064228 0.061463 0.059249 0.056922 0.05533 0.053839 0.052356 0.05144 0.050577 0.049504 0.048914 0.047966 0.047096 0.046179 0.045225 0.044439 0.043522 0.042784 0.042033 0.041502 0.040862 0.040222 0.039661 0.039288 0.038861 0.038468 0.038025 0.037809 0.037495 0.037441 0.037161 0.037109 0.036901 0.036692 0.036643 0.036443 0.036299 0.03609 0.035946 0.035645 0.035521 0.035637 0.035493 0.03522 0.034972 0.034867 0.034636 0.034749 0.034626 0.034503 0.034449 0.034558 0.034581 0.034695 0.034788 0.035088 0.035186 0.03532 0.035584 0.035982 0.036286 0.036685 0.037075 0.037571 0.038049 0.038474 0.038648 0.039148 0.039507 0.039914 0.040428 0.040915 0.041397 0.042062 0.042541 0.043017 0.043492 0.04422 0.045028 0.045964 0.046288 0.046483 0.046452 0.046805 0.047334 0.048376 0.050055 0.052404 0.056056 0.062173 0.071268 0.083469 0.097018 0.11076 0.12351 0.13625 0.14832 0.15991 0.1706 0.18137 0.1917 0.20228 0.21219 0.22166 0.23061 0.24008 0.24887 0.25744 0.26578 0.27408 0.28202 0.28991 0.29743 0.30548 0.31174 0.31591 0.3229 0.32918 0.33467 0.34164 0.34655 0.35208 0.35702 0.36231 0.36758 0.37308 0.37697 0.38305 0.38705 0.3921 0.39614 0.39997 0.40195 0.40624 0.40848 0.41065 0.41262 0.41438 0.41503 0.41564 0.41732 0.41924 0.42271 0.42587 0.43133 0.43462 0.43568 0.43701 0.43641 0.43645 0.43713 0.43833 0.43863 0.44012 0.43854 0.4392 0.43943 0.43939 0.43973 0.43881 0.43849 0.43899 0.43816 0.43818 0.43845 0.43767 0.43711 0.43528 0.43181 0.42742 0.423 0.41584 0.40912 0.40042 0.39148 0.38089 0.36905 0.35472 0.33882 0.32677 0.31838 0.31277 0.31256 0.31236 0.31304 0.31402 0.31576 0.32116 0.32547 0.33323 0.34021 0.35028 0.35794 0.36547 0.34206
3 {'SYRAH'} 178.4 0.15241 0.12848 0.11514 0.10437 0.097142 0.090982 0.0846 0.080265 0.076254 0.072553 0.069389 0.066697 0.064854 0.062721 0.061434 0.05986 0.058787 0.057749 0.056716 0.055729 0.055043 0.053938 0.053172 0.052053 0.050919 0.050077 0.049289 0.048376 0.047713 0.047176 0.046678 0.045928 0.045453 0.044994 0.044504 0.044093 0.043828 0.043506 0.043297 0.043184 0.043047 0.042781 0.042677 0.042518 0.042312 0.042084 0.041871 0.041531 0.041414 0.041363 0.041472 0.041271 0.040913 0.040518 0.040363 0.040225 0.040207 0.040109 0.040066 0.039969 0.039977 0.039982 0.040154 0.040216 0.040457 0.040478 0.040756 0.040984 0.041443 0.041863 0.042268 0.042741 0.043324 0.043771 0.044117 0.044347 0.04475 0.044964 0.045452 0.045748 0.046371 0.046634 0.047201 0.047554 0.048058 0.048658 0.049324 0.050129 0.05091 0.051587 0.052008 0.05203 0.052189 0.052493 0.05336 0.0547 0.056747 0.059845 0.065259 0.073386 0.083597 0.095119 0.10705 0.11805 0.12957 0.14059 0.15159 0.16165 0.17214 0.18194 0.19272 0.20261 0.21274 0.2221 0.23205 0.24131 0.25099 0.25996 0.26914 0.27856 0.28675 0.29548 0.30523 0.31324 0.32033 0.32747 0.33571 0.34227 0.34959 0.35734 0.36465 0.37081 0.37772 0.38395 0.39017 0.39617 0.40295 0.40962 0.4153 0.42099 0.42584 0.43023 0.43459 0.43865 0.44156 0.44514 0.44744 0.44863 0.45065 0.45287 0.45573 0.45942 0.46375 0.46956 0.47496 0.47898 0.48064 0.48117 0.48175 0.48235 0.48266 0.48421 0.48524 0.4859 0.48684 0.48627 0.48561 0.48709 0.48647 0.48695 0.48621 0.48674 0.48685 0.48575 0.48473 0.48305 0.48125 0.47683 0.47269 0.46499 0.45668 0.44716 0.43887 0.42931 0.41677 0.40067 0.38661 0.36793 0.35196 0.34411 0.33999 0.33436 0.33625 0.33527 0.33391 0.33924 0.34082 0.34757 0.35299 0.36137 0.37059 0.37614 0.3874 0.35448
4 {'SYRAH'} 193.54 0.15067 0.12968 0.11573 0.10583 0.097539 0.091167 0.085804 0.081407 0.077536 0.073961 0.071315 0.068573 0.066456 0.064907 0.063023 0.061727 0.060656 0.059686 0.058813 0.058057 0.057028 0.056062 0.055267 0.054235 0.053128 0.05226 0.051507 0.050742 0.050071 0.049359 0.04883 0.048067 0.047577 0.047008 0.046692 0.046218 0.04588 0.045661 0.045535 0.045415 0.04532 0.045042 0.04482 0.044751 0.04466 0.044356 0.044138 0.04386 0.043574 0.043537 0.04356 0.043283 0.043017 0.042697 0.042675 0.042467 0.042411 0.042305 0.042267 0.042107 0.042115 0.042103 0.042303 0.042315 0.042542 0.042575 0.042833 0.043031 0.043427 0.043698 0.044174 0.044492 0.044983 0.045391 0.045647 0.045754 0.0461 0.046371 0.046821 0.047071 0.04739 0.047741 0.048115 0.048462 0.048916 0.049469 0.050199 0.050862 0.051792 0.05245 0.052704 0.05283 0.05315 0.053667 0.054802 0.056372 0.058434 0.061504 0.066572 0.073598 0.082544 0.092403 0.10279 0.1125 0.1226 0.13268 0.14259 0.15197 0.16196 0.17129 0.18109 0.19057 0.20018 0.20908 0.21844 0.22776 0.23669 0.24561 0.25439 0.26302 0.2713 0.27946 0.28929 0.29722 0.3036 0.31089 0.31802 0.32449 0.33199 0.33925 0.3461 0.3521 0.3583 0.36442 0.37032 0.37628 0.38319 0.38903 0.39491 0.40059 0.4049 0.40904 0.41346 0.41722 0.42087 0.42378 0.42573 0.42766 0.42908 0.43207 0.43544 0.43746 0.44222 0.44704 0.45308 0.45678 0.4578 0.4576 0.45894 0.45971 0.46004 0.46152 0.46232 0.4631 0.46271 0.46313 0.46228 0.46393 0.46313 0.46351 0.46409 0.46371 0.46377 0.46265 0.46198 0.46198 0.45898 0.45511 0.45296 0.44634 0.43976 0.43135 0.42183 0.41335 0.4012 0.38944 0.37472 0.35766 0.34487 0.33529 0.33053 0.32944 0.32742 0.32624 0.32619 0.32961 0.33472 0.33743 0.34273 0.34818 0.35808 0.36281 0.37441 0.34218
5 {'SYRAH'} 156.52 0.14941 0.12574 0.11301 0.1014 0.093891 0.087433 0.081891 0.076906 0.072377 0.068974 0.06596 0.063036 0.060964 0.059301 0.0575 0.056183 0.055264 0.054196 0.053303 0.052386 0.05174 0.050648 0.04963 0.048762 0.047948 0.047022 0.046491 0.045702 0.045177 0.044522 0.043878 0.043236 0.042772 0.042416 0.041964 0.041629 0.041309 0.041169 0.041148 0.041121 0.04112 0.040922 0.040903 0.040837 0.040677 0.040451 0.040253 0.040064 0.039968 0.039971 0.040102 0.039887 0.039677 0.039344 0.039376 0.03932 0.039279 0.039285 0.039284 0.039265 0.039386 0.039487 0.039751 0.040001 0.040397 0.040628 0.041006 0.041503 0.042114 0.042581 0.04343 0.0442 0.045037 0.045796 0.046529 0.047007 0.04774 0.048312 0.049205 0.049927 0.050864 0.051513 0.052031 0.052719 0.053283 0.053841 0.05467 0.055527 0.056608 0.057265 0.057284 0.056738 0.056406 0.056423 0.057319 0.058661 0.060919 0.064857 0.071917 0.082818 0.097144 0.11311 0.1293 0.14401 0.15835 0.17153 0.18411 0.19555 0.20695 0.21761 0.2284 0.23846 0.24838 0.25744 0.26647 0.27536 0.28401 0.29223 0.3004 0.30826 0.31562 0.32304 0.33182 0.33878 0.34423 0.34959 0.35624 0.36125 0.36682 0.37262 0.37835 0.38348 0.38832 0.39298 0.39736 0.40175 0.40748 0.41164 0.41671 0.42025 0.42362 0.4256 0.42976 0.43152 0.43356 0.43472 0.43425 0.43528 0.4359 0.4369 0.43823 0.44081 0.44384 0.44771 0.45305 0.4551 0.45636 0.45518 0.4547 0.45511 0.45497 0.45558 0.45595 0.45486 0.45501 0.45507 0.4549 0.45469 0.45359 0.45343 0.45235 0.45287 0.45281 0.45248 0.45043 0.44803 0.44817 0.44362 0.43922 0.43189 0.42456 0.41554 0.40834 0.3988 0.3874 0.37368 0.35787 0.34307 0.33105 0.32248 0.31529 0.31469 0.3161 0.31664 0.31708 0.32285 0.32456 0.33147 0.33705 0.34468 0.35458 0.36018 0.37375 0.34212
6 {'SYRAH'} 161.57 0.16084 0.13783 0.12082 0.10868 0.10081 0.093185 0.087158 0.081672 0.076695 0.073037 0.069684 0.066359 0.063897 0.062556 0.060657 0.058564 0.057902 0.05677 0.055824 0.054813 0.053835 0.052594 0.051861 0.050677 0.049396 0.048561 0.047916 0.047067 0.046488 0.045774 0.045094 0.044407 0.044037 0.043507 0.043123 0.042658 0.042371 0.042214 0.042053 0.041883 0.041931 0.041649 0.041587 0.041393 0.041357 0.041031 0.040936 0.040609 0.040487 0.040364 0.040412 0.040334 0.040119 0.03984 0.039826 0.039665 0.039637 0.039734 0.03974 0.039705 0.03983 0.039904 0.040248 0.040421 0.040839 0.041077 0.041479 0.042027 0.042636 0.043246 0.044051 0.044795 0.045625 0.046447 0.047123 0.047592 0.048431 0.049146 0.050032 0.050751 0.051759 0.052477 0.053288 0.053818 0.054535 0.055002 0.055923 0.056958 0.058108 0.058805 0.05885 0.058509 0.05842 0.058557 0.059625 0.061438 0.064195 0.068612 0.076346 0.087937 0.10282 0.11937 0.13601 0.15128 0.16585 0.1799 0.1928 0.20507 0.21737 0.22856 0.24044 0.25143 0.26206 0.27198 0.28266 0.29226 0.30193 0.31107 0.32003 0.32877 0.33688 0.34497 0.35485 0.362 0.36869 0.37532 0.38221 0.38815 0.39513 0.4018 0.40802 0.41397 0.41989 0.42529 0.43156 0.43646 0.44273 0.44806 0.45379 0.45909 0.46292 0.46747 0.47066 0.47418 0.47668 0.47889 0.48006 0.48161 0.48316 0.48492 0.48719 0.49069 0.49473 0.499 0.50548 0.50884 0.51014 0.50941 0.50956 0.51097 0.5122 0.51234 0.51366 0.51185 0.51279 0.51324 0.51375 0.51285 0.51215 0.51256 0.51341 0.51312 0.51355 0.51255 0.51209 0.51031 0.50908 0.50507 0.50308 0.4935 0.48551 0.47577 0.46774 0.45623 0.44297 0.43006 0.41332 0.39348 0.37828 0.37086 0.36355 0.36138 0.36096 0.36102 0.36446 0.36474 0.37159 0.37497 0.3831 0.38993 0.39988 0.40616 0.41912 0.38283
7 {'SYRAH'} 166.62 0.14462 0.12211 0.10695 0.095976 0.088384 0.081747 0.076841 0.071082 0.067949 0.064671 0.061443 0.058034 0.056287 0.054407 0.053002 0.051462 0.050352 0.04959 0.04873 0.047557 0.04684 0.046031 0.044983 0.043931 0.043248 0.042232 0.041592 0.040952 0.040122 0.039478 0.039079 0.038502 0.037915 0.037599 0.037235 0.036895 0.036684 0.036408 0.036321 0.036207 0.036201 0.03591 0.035787 0.03549 0.035405 0.03535 0.035207 0.034947 0.034736 0.034535 0.034831 0.034653 0.034501 0.034232 0.034044 0.034007 0.034028 0.033932 0.033967 0.033935 0.033969 0.034063 0.034222 0.03445 0.034643 0.034888 0.035231 0.03559 0.036114 0.036583 0.037198 0.037886 0.038473 0.039146 0.039771 0.040029 0.040658 0.04119 0.041958 0.042618 0.043267 0.043863 0.044486 0.044816 0.045421 0.045999 0.046717 0.047409 0.048405 0.049019 0.049009 0.048739 0.048587 0.048784 0.049709 0.050996 0.053217 0.057081 0.063575 0.073504 0.086485 0.10081 0.11525 0.12856 0.14147 0.15358 0.16496 0.17565 0.18617 0.19607 0.20655 0.21589 0.22546 0.23398 0.2427 0.25113 0.25933 0.26721 0.27526 0.2829 0.29009 0.29723 0.30572 0.31185 0.31759 0.32304 0.32959 0.33453 0.3402 0.34589 0.35167 0.35698 0.36145 0.36644 0.3713 0.37532 0.3809 0.3853 0.3898 0.3942 0.3971 0.40014 0.40361 0.40575 0.40763 0.41027 0.4103 0.41075 0.41197 0.41366 0.41541 0.41746 0.4216 0.42511 0.43078 0.43323 0.43318 0.4325 0.43367 0.43351 0.43349 0.43483 0.43425 0.43397 0.43482 0.4338 0.43425 0.43435 0.43214 0.43264 0.43361 0.43269 0.43317 0.43216 0.42977 0.43018 0.42726 0.42356 0.41982 0.41364 0.40697 0.39925 0.39057 0.38255 0.37151 0.35812 0.34354 0.32752 0.31708 0.30787 0.30478 0.30373 0.30261 0.30282 0.3033 0.30826 0.30968 0.31357 0.31992 0.32686 0.33501 0.3414 0.35435 0.32589
8 {'SYRAH'} 169.98 0.16365 0.13879 0.12246 0.10988 0.1015 0.094093 0.087427 0.082324 0.077943 0.073791 0.069677 0.066982 0.06492 0.062796 0.060874 0.059313 0.058041 0.05705 0.055847 0.05478 0.054116 0.052764 0.051346 0.050447 0.049595 0.048325 0.047587 0.046755 0.046063 0.045308 0.044688 0.04409 0.043626 0.043014 0.04262 0.042158 0.041787 0.041474 0.041257 0.041117 0.041116 0.040767 0.040776 0.040495 0.04033 0.040068 0.039838 0.039474 0.039471 0.039409 0.039538 0.039378 0.038984 0.038663 0.038595 0.038412 0.038452 0.03835 0.038312 0.038338 0.038378 0.038403 0.038624 0.038834 0.03907 0.039221 0.039585 0.03999 0.040349 0.04088 0.041478 0.042143 0.042728 0.043368 0.043963 0.044232 0.044902 0.045356 0.046037 0.046701 0.047338 0.047959 0.048674 0.049227 0.049889 0.050496 0.051373 0.052281 0.053305 0.054237 0.054571 0.054361 0.054686 0.055158 0.056374 0.058064 0.060801 0.064997 0.071825 0.081651 0.094118 0.10809 0.12224 0.13516 0.14823 0.16069 0.17282 0.18415 0.19567 0.20666 0.21788 0.22862 0.2398 0.24974 0.26024 0.27012 0.28021 0.28988 0.29964 0.30871 0.31735 0.32673 0.33693 0.34485 0.35168 0.35957 0.36813 0.37427 0.38219 0.38981 0.39733 0.40403 0.411 0.4175 0.42391 0.4299 0.43755 0.44377 0.45026 0.45663 0.46143 0.4656 0.4708 0.47385 0.47759 0.48097 0.48305 0.48492 0.48675 0.48972 0.49278 0.49646 0.50074 0.50665 0.51318 0.51649 0.51855 0.5189 0.51999 0.52 0.52196 0.52295 0.5233 0.52383 0.52556 0.52522 0.52499 0.52558 0.52421 0.52532 0.52514 0.52508 0.52615 0.52575 0.52357 0.52241 0.52148 0.51545 0.51135 0.50403 0.49589 0.4865 0.47618 0.46376 0.45033 0.43375 0.41717 0.39685 0.38331 0.37303 0.36521 0.36426 0.36377 0.36401 0.36525 0.36594 0.37223 0.37629 0.38482 0.39078 0.39805 0.40542 0.41912 0.37999
9 {'SYRAH'} 176.72 0.14929 0.12357 0.1102 0.10046 0.092379 0.085111 0.079623 0.074674 0.070239 0.067097 0.063361 0.060997 0.058657 0.057144 0.055334 0.054356 0.052931 0.052217 0.051317 0.050251 0.049262 0.048289 0.047267 0.046357 0.045544 0.044601 0.043875 0.043031 0.042614 0.041904 0.041484 0.040626 0.040272 0.039652 0.039345 0.03902 0.038669 0.038521 0.038317 0.03827 0.038342 0.038006 0.037891 0.037856 0.037673 0.037494 0.037261 0.036919 0.036849 0.036802 0.036843 0.036637 0.036319 0.036122 0.036129 0.035973 0.035841 0.035793 0.03579 0.035812 0.035907 0.035978 0.036143 0.036162 0.036537 0.036699 0.036963 0.037326 0.037832 0.038187 0.038736 0.039217 0.039849 0.040363 0.040843 0.04108 0.041682 0.042026 0.042657 0.043071 0.043674 0.044087 0.044554 0.045002 0.045485 0.045998 0.04676 0.047527 0.048383 0.048974 0.049155 0.049161 0.049317 0.049733 0.050707 0.052309 0.054788 0.058343 0.064212 0.072573 0.083031 0.094649 0.10646 0.11742 0.12854 0.13926 0.14977 0.1596 0.1696 0.17923 0.18907 0.19876 0.20828 0.21715 0.22634 0.23494 0.24401 0.25233 0.26106 0.26945 0.27716 0.28509 0.29413 0.301 0.30735 0.31378 0.32088 0.32665 0.33318 0.34036 0.34638 0.35208 0.35813 0.36303 0.36853 0.37394 0.3803 0.38536 0.39138 0.39589 0.40027 0.40364 0.40778 0.41078 0.41359 0.416 0.41728 0.41896 0.4199 0.42184 0.42406 0.42718 0.43135 0.43621 0.44154 0.44366 0.44485 0.44542 0.44543 0.44531 0.44646 0.44776 0.44775 0.44817 0.44853 0.44754 0.44787 0.44758 0.44638 0.44657 0.44724 0.44608 0.44563 0.44599 0.4449 0.44489 0.44292 0.43799 0.4352 0.42784 0.4204 0.41303 0.40526 0.39561 0.38522 0.36908 0.35614 0.34016 0.32695 0.31561 0.3128 0.30968 0.30959 0.31088 0.30804 0.31349 0.31577 0.32202 0.32425 0.33111 0.34091 0.34837 0.35784 0.3328
10 {'SYRAH'} 183.45 0.16152 0.13784 0.1209 0.10973 0.10038 0.093568 0.087626 0.08191 0.07705 0.073116 0.069792 0.066448 0.06443 0.062808 0.060363 0.058848 0.058194 0.0572 0.056101 0.054764 0.053268 0.052491 0.05171 0.050627 0.049367 0.048449 0.047633 0.046832 0.046205 0.045395 0.044868 0.044092 0.043529 0.043054 0.042558 0.042125 0.041885 0.04162 0.041482 0.041298 0.041146 0.04087 0.040746 0.040636 0.040488 0.040154 0.039975 0.039607 0.039529 0.039376 0.039349 0.039272 0.039007 0.038679 0.038494 0.038332 0.038335 0.03824 0.038176 0.038145 0.03821 0.038335 0.038404 0.038625 0.038825 0.038939 0.039169 0.039416 0.039899 0.040208 0.040726 0.041212 0.041689 0.042327 0.042661 0.042936 0.043346 0.043709 0.044288 0.044647 0.045273 0.045646 0.046148 0.046593 0.047251 0.047831 0.0485 0.049291 0.050326 0.051007 0.05136 0.051355 0.051708 0.052101 0.053074 0.054784 0.057117 0.060766 0.066851 0.07529 0.086037 0.097882 0.11013 0.12145 0.13303 0.14455 0.15568 0.16618 0.17716 0.18755 0.19845 0.20875 0.21932 0.22887 0.23978 0.2493 0.25925 0.26887 0.27843 0.28807 0.29699 0.30589 0.31694 0.32521 0.33306 0.34063 0.34882 0.35614 0.36419 0.37202 0.38 0.3869 0.39395 0.40059 0.40801 0.41445 0.42201 0.42823 0.43578 0.44159 0.44633 0.4512 0.4569 0.46074 0.46486 0.46805 0.47074 0.47224 0.47529 0.4777 0.48137 0.4856 0.49033 0.49579 0.50309 0.50672 0.50823 0.509 0.50956 0.51097 0.51223 0.51365 0.51572 0.51495 0.5157 0.51727 0.5177 0.51726 0.51746 0.51748 0.51784 0.5181 0.51777 0.51757 0.5159 0.51494 0.5123 0.50877 0.50505 0.49593 0.48792 0.4791 0.46899 0.45717 0.44413 0.42811 0.40989 0.39103 0.37551 0.36558 0.36048 0.35494 0.35497 0.35415 0.35592 0.36079 0.36321 0.36638 0.3735 0.38237 0.38778 0.40013 0.40677 0.37688
11 {'SYRAH'} 161.57 0.15107 0.12769 0.11283 0.1021 0.094121 0.085879 0.080362 0.075438 0.071305 0.067135 0.063958 0.06086 0.058893 0.056974 0.054965 0.053768 0.052606 0.05192 0.050603 0.049837 0.048783 0.048014 0.047106 0.045965 0.045107 0.044081 0.043421 0.042728 0.041968 0.041452 0.04073 0.040233 0.03979 0.039234 0.038863 0.038436 0.038119 0.038001 0.038041 0.037917 0.037802 0.037397 0.037462 0.037278 0.037188 0.036942 0.036856 0.036624 0.036482 0.036451 0.036485 0.036339 0.036138 0.035956 0.035842 0.03577 0.035687 0.035624 0.035836 0.035727 0.03584 0.035828 0.036117 0.036358 0.036792 0.037003 0.037369 0.037758 0.038326 0.039002 0.039592 0.040298 0.041116 0.041688 0.042284 0.042705 0.043565 0.044049 0.044812 0.045351 0.046195 0.046809 0.047428 0.047961 0.048524 0.049104 0.049787 0.050639 0.051732 0.05227 0.052287 0.051979 0.051833 0.052187 0.053219 0.054717 0.057107 0.061181 0.068052 0.078065 0.091092 0.10547 0.11999 0.13336 0.14642 0.15883 0.17038 0.18125 0.19213 0.2024 0.21297 0.2229 0.23255 0.24162 0.25082 0.25951 0.26844 0.27658 0.28473 0.29239 0.2997 0.30716 0.31589 0.32219 0.32778 0.33367 0.3398 0.34508 0.35051 0.35685 0.36267 0.36768 0.37231 0.37707 0.382 0.38618 0.39194 0.39699 0.40163 0.40538 0.4087 0.41196 0.41458 0.41701 0.41888 0.4214 0.42172 0.42271 0.42291 0.42546 0.4266 0.42852 0.43186 0.43612 0.44103 0.44358 0.44528 0.44438 0.4442 0.44324 0.44391 0.44498 0.44548 0.44488 0.44512 0.44403 0.44417 0.44389 0.44386 0.4439 0.44293 0.44348 0.44337 0.44146 0.44025 0.44029 0.43785 0.43313 0.43054 0.42551 0.4178 0.40887 0.40106 0.39164 0.38062 0.36666 0.35323 0.33694 0.32413 0.31665 0.31065 0.31144 0.30992 0.30974 0.31262 0.31429 0.317 0.32033 0.32903 0.33578 0.34221 0.34938 0.36339 0.33925
12 {'SYRAH'} 164.93 0.16505 0.13903 0.12255 0.11103 0.10126 0.094408 0.087234 0.081801 0.077233 0.073324 0.070119 0.066285 0.064126 0.062554 0.060528 0.05904 0.05777 0.057012 0.055628 0.054755 0.053716 0.052519 0.05154 0.050405 0.049507 0.048564 0.0475 0.046609 0.045994 0.045443 0.044666 0.044123 0.043696 0.043037 0.042573 0.04216 0.041936 0.041552 0.041411 0.041411 0.041392 0.041205 0.041041 0.040756 0.040735 0.040516 0.040313 0.040073 0.040015 0.039885 0.039957 0.039767 0.039592 0.039251 0.039157 0.039188 0.039221 0.039158 0.039301 0.039195 0.039329 0.03947 0.039793 0.040005 0.040422 0.040665 0.041092 0.041671 0.042266 0.042994 0.043697 0.044475 0.045342 0.046132 0.04682 0.047406 0.048177 0.048765 0.049849 0.050703 0.051609 0.052413 0.053303 0.053885 0.054575 0.055227 0.05611 0.057071 0.058229 0.059064 0.05903 0.058644 0.058659 0.058894 0.060052 0.062195 0.065287 0.070089 0.078227 0.090051 0.10519 0.12153 0.13805 0.15292 0.16735 0.18113 0.19416 0.20602 0.21832 0.22944 0.24135 0.25246 0.26315 0.27307 0.28345 0.29363 0.30333 0.31272 0.32159 0.33068 0.33876 0.34779 0.35784 0.36477 0.37131 0.37841 0.38599 0.392 0.39867 0.40582 0.41279 0.41904 0.42453 0.43033 0.43618 0.44177 0.44901 0.45479 0.46009 0.46617 0.46973 0.47353 0.47763 0.48103 0.48413 0.48643 0.4873 0.48884 0.49097 0.49267 0.4956 0.49877 0.50301 0.50874 0.51399 0.51709 0.51881 0.51888 0.51954 0.51947 0.52008 0.52105 0.52137 0.52182 0.52352 0.52136 0.52147 0.5223 0.52215 0.52186 0.52346 0.52339 0.5229 0.52252 0.52059 0.51985 0.51892 0.51327 0.50892 0.50232 0.49216 0.48309 0.47278 0.46331 0.45105 0.43569 0.41875 0.39992 0.38419 0.37413 0.3665 0.36543 0.36852 0.36455 0.36614 0.37132 0.37355 0.37852 0.38476 0.39119 0.40246 0.4098 0.41636 0.38522
13 {'SYRAH'} 168.3 0.14617 0.12542 0.11053 0.099629 0.092235 0.085458 0.079833 0.074771 0.071013 0.067414 0.063814 0.061694 0.05956 0.057847 0.055968 0.054678 0.0537 0.05268 0.051814 0.050738 0.049961 0.049089 0.048006 0.047188 0.046368 0.045439 0.044731 0.043846 0.04336 0.042766 0.042179 0.04136 0.041065 0.040619 0.040228 0.039924 0.039668 0.039422 0.039379 0.039245 0.039131 0.038963 0.038793 0.038571 0.038636 0.038349 0.038201 0.037983 0.037897 0.037718 0.037766 0.037621 0.037451 0.037191 0.037235 0.036959 0.037096 0.037041 0.037077 0.037037 0.037163 0.037248 0.037384 0.037596 0.037994 0.038219 0.038519 0.039002 0.039521 0.04009 0.040846 0.041514 0.04221 0.042896 0.043397 0.04388 0.044558 0.045079 0.045874 0.046459 0.047276 0.047747 0.048383 0.048776 0.049384 0.049956 0.050669 0.051508 0.052545 0.053084 0.053183 0.052826 0.052932 0.053255 0.05437 0.056111 0.058832 0.062953 0.069771 0.079662 0.092388 0.10627 0.12029 0.13311 0.14556 0.15767 0.16905 0.17957 0.1902 0.20033 0.21074 0.22057 0.23039 0.23923 0.24889 0.25749 0.26621 0.27433 0.28299 0.29079 0.29833 0.30598 0.31487 0.32134 0.32712 0.33323 0.34009 0.34519 0.35149 0.35758 0.36376 0.36898 0.37379 0.37898 0.38475 0.38943 0.39492 0.39988 0.40503 0.40972 0.41307 0.41631 0.41992 0.42262 0.42533 0.42662 0.42822 0.42825 0.43018 0.43194 0.43467 0.43681 0.44033 0.44449 0.45028 0.45293 0.45387 0.45416 0.45418 0.45319 0.45418 0.45526 0.45611 0.45537 0.45573 0.45455 0.45493 0.45532 0.45425 0.45464 0.45528 0.45449 0.45461 0.45303 0.4525 0.45101 0.44968 0.44563 0.44153 0.43431 0.42739 0.41898 0.41161 0.40082 0.38958 0.37748 0.36147 0.34482 0.33233 0.32479 0.31977 0.31788 0.31758 0.31702 0.31937 0.3212 0.32695 0.32966 0.33598 0.3417 0.35141 0.35544 0.36661 0.33483
14 {'SYRAH'} 175.03 0.15369 0.13393 0.11643 0.10465 0.097385 0.088729 0.08357 0.077779 0.073886 0.069832 0.066285 0.063427 0.061276 0.059821 0.057666 0.055914 0.054783 0.054028 0.053167 0.052083 0.050917 0.049824 0.048963 0.047939 0.046925 0.04587 0.045215 0.044514 0.043848 0.043174 0.042461 0.041754 0.041338 0.040805 0.040482 0.040094 0.039748 0.039341 0.039415 0.03921 0.039065 0.038934 0.038836 0.038559 0.038411 0.038264 0.038065 0.03786 0.037689 0.037576 0.037546 0.037341 0.037236 0.036947 0.036807 0.03679 0.036791 0.036658 0.03668 0.036671 0.036818 0.036866 0.036999 0.037175 0.037443 0.037637 0.037835 0.038299 0.038679 0.039127 0.03963 0.040135 0.040823 0.041378 0.041763 0.042109 0.042662 0.043038 0.043559 0.044025 0.04475 0.045264 0.045833 0.046424 0.047053 0.047664 0.048568 0.049432 0.050504 0.051375 0.051733 0.051795 0.052167 0.052747 0.053727 0.055504 0.058105 0.062044 0.068768 0.078488 0.090681 0.10397 0.1176 0.13024 0.14298 0.15546 0.16743 0.17871 0.19002 0.20116 0.21229 0.22313 0.23384 0.24392 0.25455 0.26462 0.27468 0.28422 0.29397 0.30317 0.31216 0.3212 0.33145 0.33989 0.34714 0.35427 0.36301 0.36962 0.37667 0.38473 0.39186 0.3988 0.40562 0.41226 0.41846 0.42476 0.43182 0.43857 0.44476 0.45091 0.45587 0.46052 0.4652 0.46888 0.47184 0.4757 0.47743 0.47889 0.48122 0.4836 0.48712 0.49028 0.49481 0.50007 0.50716 0.5109 0.51346 0.51326 0.51399 0.51544 0.51566 0.51721 0.51836 0.51781 0.51892 0.51807 0.51872 0.5188 0.51774 0.51983 0.51911 0.51973 0.5184 0.51926 0.51808 0.51661 0.51496 0.50981 0.5071 0.49952 0.49087 0.4807 0.46964 0.45925 0.44508 0.43111 0.41279 0.39301 0.37863 0.36834 0.36293 0.35994 0.35902 0.35667 0.36115 0.36461 0.36599 0.37414 0.37954 0.38745 0.39541 0.40156 0.41569 0.37264
15 {'SYRAH'} 168.3 0.14286 0.11993 0.10663 0.097183 0.088758 0.081789 0.076941 0.072091 0.067824 0.064185 0.060482 0.058388 0.055893 0.054449 0.052796 0.0516 0.050245 0.049505 0.048455 0.048058 0.047052 0.046095 0.045341 0.044335 0.043062 0.042384 0.041535 0.040889 0.040567 0.039896 0.039212 0.038625 0.038166 0.037785 0.037503 0.037109 0.036871 0.036668 0.036396 0.036426 0.036454 0.036157 0.036152 0.035953 0.035783 0.035506 0.035338 0.035262 0.03522 0.035133 0.035135 0.035016 0.034841 0.034602 0.034584 0.034359 0.034426 0.03438 0.034459 0.034449 0.034628 0.034575 0.034916 0.035005 0.035346 0.035655 0.035837 0.036235 0.03679 0.037317 0.03787 0.038417 0.039113 0.039815 0.040363 0.040687 0.041297 0.041801 0.042498 0.043088 0.043815 0.044318 0.044892 0.045478 0.045904 0.046532 0.047374 0.048106 0.049117 0.049834 0.049987 0.049877 0.049972 0.050379 0.051454 0.053178 0.05585 0.059918 0.066571 0.076513 0.088937 0.10235 0.11583 0.12827 0.14053 0.15202 0.16332 0.17363 0.18397 0.1938 0.20407 0.21372 0.22314 0.23184 0.2411 0.24957 0.25822 0.26622 0.27443 0.28235 0.28939 0.29711 0.30608 0.31234 0.31836 0.32429 0.33085 0.33588 0.34172 0.34805 0.35419 0.35922 0.36457 0.36903 0.37466 0.37947 0.38516 0.38983 0.39517 0.39994 0.40245 0.40631 0.40998 0.41228 0.41455 0.41706 0.41717 0.41822 0.41957 0.42104 0.423 0.42585 0.42863 0.43329 0.43819 0.44193 0.44261 0.44197 0.44177 0.44251 0.44323 0.44316 0.44384 0.44297 0.44344 0.44232 0.44275 0.44243 0.4418 0.44182 0.44225 0.44124 0.44175 0.44044 0.43925 0.4389 0.43588 0.43355 0.42942 0.42227 0.41512 0.4068 0.39819 0.38898 0.37921 0.36562 0.35016 0.33367 0.32147 0.31293 0.3078 0.30651 0.30602 0.30483 0.30894 0.30924 0.31456 0.31858 0.32623 0.3307 0.33833 0.34814 0.35358 0.32664
16 {'SYRAH'} 158.2 0.15493 0.12988 0.11542 0.10329 0.095183 0.088027 0.081363 0.076411 0.072261 0.068154 0.065145 0.062033 0.059432 0.057475 0.055949 0.054613 0.052989 0.052049 0.051316 0.050435 0.04926 0.048007 0.046952 0.045939 0.045292 0.044378 0.043339 0.042831 0.042016 0.041191 0.040811 0.040339 0.039769 0.03943 0.039017 0.03865 0.038381 0.038128 0.037785 0.037748 0.037801 0.03748 0.037434 0.037355 0.037063 0.036845 0.036774 0.03664 0.036505 0.03634 0.0364 0.036307 0.036153 0.035891 0.035845 0.035778 0.035881 0.03582 0.035967 0.035969 0.036132 0.036201 0.036502 0.036753 0.037142 0.037406 0.037837 0.038337 0.038887 0.039558 0.040283 0.041009 0.0419 0.042564 0.043218 0.043843 0.044563 0.04528 0.046193 0.047013 0.047902 0.048646 0.04942 0.050045 0.050709 0.051253 0.052199 0.053088 0.054316 0.05499 0.055056 0.054753 0.054628 0.055099 0.056496 0.058405 0.061487 0.066205 0.074182 0.085759 0.1005 0.117 0.13337 0.14846 0.16285 0.17669 0.18982 0.20217 0.2143 0.22565 0.23744 0.24849 0.25932 0.26948 0.27964 0.28953 0.29896 0.30817 0.31705 0.32571 0.33384 0.3426 0.35229 0.35933 0.36581 0.37251 0.37949 0.38554 0.39244 0.3997 0.40613 0.41176 0.41772 0.42368 0.42963 0.43472 0.44178 0.44701 0.45302 0.45844 0.46214 0.46603 0.47015 0.47278 0.47594 0.47837 0.47921 0.48 0.48138 0.48331 0.48636 0.48879 0.49363 0.49858 0.5049 0.50814 0.51032 0.50977 0.51097 0.50986 0.51072 0.51186 0.51282 0.51219 0.51304 0.51304 0.51235 0.51205 0.51257 0.51294 0.51236 0.51309 0.5111 0.5134 0.51059 0.51055 0.5069 0.50422 0.49864 0.49092 0.48221 0.47184 0.46333 0.45019 0.43905 0.42277 0.40495 0.38795 0.37151 0.36351 0.35863 0.35355 0.35563 0.35438 0.35517 0.36008 0.36585 0.36867 0.37547 0.38139 0.39158 0.3988 0.41004 0.37699
⋮
Verify the number of samples in the table.
n = size(T,1)
n = 274
Extract the average spectra of the samples from the table as a matrix of predictor variables, X.
X = table2array(T(:,4:end));
Extract the sugar content of the samples from the table as a vector of response variables, y.
y = table2array(T(:,3));
Create Training and Test Data Sets
Split the data into 70 percent training data and 30 percent test data using holdout validation.
rng("default") p = 0.3; datapartition = cvpartition(n,"Holdout",p); idxTrain = training(datapartition); nTrain = nnz(idxTrain); idxTest = test(datapartition); nTest = nnz(idxTest);
Extract the average spectra for the training and test data sets from the predictor variables into separate matrices.
XTrain = X(idxTrain,:); XTest = X(idxTest,:);
Extract the sugar content for the training and test data sets from the response variables into separate vectors.
yTrain = y(idxTrain); yTest = y(idxTest);
Perform PLS Regression on Training Data
Partial least squares (PLS) regression finds combinations of the predictors that have a large covariance with the response values. Perform PLS regression on the training data set, with 10 components, using the plsregress (Statistics and Machine Learning Toolbox) function and compute the coefficient matrix.
numComponents = 10; [~,~,~,~,coeff,~,~,~] = plsregress(XTrain,yTrain,numComponents);
Predict the sugar content of the training data using the coefficient matrix.
yTrainPredicted = [ones(nTrain,1) XTrain]*coeff;
Evaluate the fit to the training data by computing the total sum of squares (TSS), and residual sum of squares (RSS), and then use them to find the R-square value, which indicates the variance in the sugar content explained by a small change in the average spectrum of the sample.
TSS_train = sum((yTrain - mean(yTrain)).^2); RSS_train = sum((yTrain - yTrainPredicted).^2); Rsquared_train = 1 - RSS_train/TSS_train
Rsquared_train = 0.7897
Plot the predicted sugar content against the actual sugar content of the training data. Observe that the PLS regression model is a good fit to the training data.
figure scatter(yTrain,yTrainPredicted) axis equal xlabel("Actual Sugar Content (g/L)") ylabel("Predicted Sugar Content (g/L)") title("PLS Regression for Training Data")
Perform PLS Regression on Test Data
Predict the sugar content of the test data using the coefficient matrix.
yTestPredicted = [ones(nTest,1) XTest] * coeff;
Evaluate the fit to the test data by computing the total sum of squares (TSS) and residual sum of squares (RSS), and then use them to find the R-square value, which indicates the variance in the sugar content explained by a small change in the average spectrum of the sample.
TSS_test = sum((yTest - mean(yTest)).^2); RSS_test = sum((yTest - yTestPredicted).^2); Rsquared_test = 1 - RSS_test/TSS_test
Rsquared_test = 0.6670
Plot the predicted sugar content against the actual sugar content of the test data. Observe that the PLS regression model is a good fit to the test data.
figure scatter(yTest,yTestPredicted) axis equal xlabel("Actual Sugar Content (g/L)") ylabel("Predicted Sugar Content (g/L)") title("PLS Regression for Test Data")
References
[1] Maxime Ryckewaert. “Spectral Dataset of Grape Berries from Hyperspectral Imaging for Maturity Monitoring,” January 26, 2022. https://doi.org/10.17632/GJWX64SGKP.1, licensed under CC-BY-4.0.
See Also
plsregress (Statistics and Machine Learning Toolbox)
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