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Multiple pooling operators and transformations for fast and effective time series classification

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MultiRocket

Multiple pooling operators and transformations for fast and effective time series classification

Preprint: arxiv:2102.00457

We propose MultiRocket, a fast time series classification (TSC) algorithm that achieves state-of-the-art performance with a tiny fraction of the time and without the complex ensembling structure of many state-of-the-art methods. MultiRocket improves on MiniRocket, one of the fastest TSC algorithms to date, by adding multiple pooling operators and transformations to improve the diversity of the features generated. In addition to processing the raw input series, MultiRocket also applies first order differences to transform the original series. Convolutions are applied to both representations, and four pooling operators are applied to the convolution outputs. When benchmarked using the University of California Riverside TSC benchmark datasets, MultiRocket is significantly more accurate than MiniRocket, and competitive with the best ranked current method in terms of accuracy, HIVE-COTE 2.0, while being orders of magnitude faster.

Reference

If you use any part of this work, please cite:

@article{Tan2021MultiRocket,
  title={{MultiRocket}: Multiple pooling operators and transformations for fast and effective time series classification},
  author={Tan, Chang Wei and Dempster, Angus and Bergmeir, Christoph and Webb, Geoffrey I},
  year={2021},
  journal={arxiv:2102.00457}
}

Requirements

All python packages needed are listed in requirements.txt file and can be installed simply using the pip command.

Code

The main.py file contains a simple code to run the program on a single UCR dataset.

The main_ucr_109.py file runs the program on all 109 UCR datasets.

The main_mtsc.py file contains a simple code to run the program on a single MTSC dataset.

Arguments:
-d --data_path          : path to dataset
-p --problem            : dataset name
-i --iter               : determines the resample of the UCR datasets
-n --num_features       : number of features 
-t --num_threads        : number of threads (> 0)
-s --save               : 0=don't save results, 1=save results
-v --verbose            : verbosity

Results

These are the results on 30 resamples of the 109 UCR Time Series archive from the UCR Time Series Classification Archive. MultiRocket is on average the current most accurate scalable TSC algorithm, that is not significantly less accurate than HIVE-COTE 2.0.

The following shows the total compute time for 109 UCR datasets. Compute times are averaged over 30 resamples of 109 UCR datasets and run on a cluster using 32 threads on AMD EPYC 7702 CPUs.

The following compares the total training time for 112 UCR datasets against some state of the arts. The first four algorithms are computed using a single thread on AMD EPYC 7702 CPU. The single thread timing results can be found in training time, test time and total time. The rest of the results are obtained from the paper HIVE-COTE 2.0: a new meta ensemble for time series classification

TSC algorithm Total train time
MiniRocket (default 10k features) 2.44 minutes
MultiRocket (10k features) 4.38 minutes
MiniRocket (50k features) 5.25 minutes
MultiRocket (default 50k features) 15.77 minutes
Rocket 2.85 hours
Arsenal 27.91 hours
DrCIF 45.40 hours
TDE 75.41 hours
InceptionTime (GPU) 86.58 hours
STC 115.88 hours
HIVE-COTE 2.0 340.21 hours
HIVE-COTE 1.0 427.18 hours
TS-CHIEF 1016.87 hours

The following table contains the averaged accuracy over 30 resamples of 109 UCR datasets, found in results. The results for other classifiers can also be obtained from timeseriesclassification.com.

dataset_name MultiRocket MultiRocket_100k MultiRocket_10k Arsenal BOSS CIF DrCIF HIVE-COTE 2.0 HIVE-COTEv1_0 InceptionTime MiniRocket ProximityForest RISE ROCKET ResNet S-BOSS STC TDE TS-CHIEF TSF WEASEL cBOSS
ACSF1 0.833666667 0.834666667 0.826666667 0.805333333 0.768333333 0.767 0.784333333 0.833333333 0.85 0.826666667 0.822333333 0.638333333 0.76 0.807 0.824 0.815 0.838333333 0.797666667 0.807 0.635 0.818 0.757333333
Adiac 0.823103154 0.822421142 0.811167945 0.772122762 0.749019608 0.767263427 0.809633419 0.795140665 0.796248934 0.822250639 0.801705067 0.722165388 0.757971014 0.771952259 0.81543052 0.742710997 0.793179881 0.751577153 0.779710145 0.711935209 0.798806479 0.74629156
ArrowHead 0.895238095 0.896 0.893714286 0.862666667 0.868761905 0.82 0.825333333 0.886285714 0.876 0.880380952 0.880952367 0.883619048 0.828190476 0.859047619 0.858666667 0.887809524 0.806666667 0.900571429 0.881142857 0.796761905 0.848380952 0.877904762
BME 1 1 1 0.997555556 0.865777778 0.996888889 0.999555556 0.999555556 0.982222222 0.996444444 0.992222133 0.999111111 0.786 0.997333333 0.999111111 0.865111111 0.929777778 0.911555556 0.996444444 0.962444444 0.947777778 0.784666667
Beef 0.77 0.773333333 0.77 0.755555556 0.612222222 0.725555556 0.791111111 0.796666667 0.735555556 0.682222222 0.7611111 0.594444444 0.742222222 0.76 0.676666667 0.655555556 0.735555556 0.683333333 0.632222222 0.688888889 0.74 0.571111111
BeetleFly 0.896666667 0.895 0.895 0.886666667 0.943333333 0.868333333 0.878333333 0.903333333 0.963333333 0.893333333 0.906666667 0.86 0.871666667 0.885 0.853333333 0.936666667 0.933333333 0.941666667 0.958333333 0.833333333 0.886666667 0.975
BirdChicken 0.888333333 0.886666667 0.893333333 0.886666667 0.983333333 0.866666667 0.948333333 0.951666667 0.94 0.951666667 0.908333333 0.903333333 0.868333333 0.881666667 0.945 0.968333333 0.87 0.971666667 0.963333333 0.815 0.865 0.976666667
CBF 0.99262963 0.993 0.992555556 0.995962963 0.998925926 0.986481482 0.984777778 0.997925926 0.998259259 0.996111111 0.996222333 0.99362963 0.949037037 0.995925926 0.988222222 0.999074074 0.985296296 0.997407407 0.998444444 0.971851852 0.979777778 0.99837037
Car 0.92 0.922777778 0.918333333 0.915555556 0.848333333 0.812222222 0.843888889 0.907777778 0.868888889 0.901111111 0.9211111 0.805555556 0.753333333 0.911666667 0.908333333 0.859444444 0.858333333 0.87 0.878888889 0.766111111 0.834444444 0.843333333
Chinatown 0.966666667 0.966958212 0.966958212 0.967826087 0.877065112 0.963188406 0.979903382 0.973566569 0.962779397 0.964917396 0.968999 0.948019324 0.888532556 0.96686103 0.970144928 0.879105928 0.962973761 0.955458937 0.961835749 0.952964043 0.957337221 0.94763285
ChlorineConcentration 0.780711806 0.782586806 0.762274306 0.780286458 0.658246528 0.731579861 0.739427083 0.769019097 0.733949653 0.86359375 0.753350767 0.631137153 0.764756944 0.796137153 0.841006944 0.659114583 0.735225694 0.693402778 0.660842014 0.723064236 0.754861111 0.664956597
CinCECGTorso 0.949613527 0.947077295 0.949589372 0.865652174 0.914758454 0.987294686 0.993961353 0.998236715 0.993743961 0.832753623 0.875797133 0.937657005 0.947439614 0.864130435 0.767874396 0.94263285 0.977777778 0.98326087 0.953429952 0.958188406 0.984975845 0.829154589
Coffee 1 1 0.997619048 1 0.985714286 0.995238095 0.998809524 0.998809524 0.992857143 0.998809524 0.998809533 0.991666667 0.98452381 1 0.996428571 0.980952381 0.989285714 0.992857143 0.99047619 0.986904762 0.989285714 0.99047619
Computers 0.8508 0.8504 0.8412 0.842266667 0.800533333 0.7732 0.816666667 0.858533333 0.811066667 0.8656 0.793866667 0.714266667 0.778933333 0.842933333 0.8604 0.82 0.799066667 0.818133333 0.753866667 0.6488 0.778533333 0.7788
CricketX 0.82 0.822136752 0.815213675 0.833589744 0.762393162 0.762649573 0.772735043 0.83991453 0.816153846 0.853247863 0.825128233 0.80042735 0.706239316 0.838974359 0.808119658 0.784102564 0.792051282 0.814273504 0.83042735 0.692735043 0.775726496 0.764273504
CricketY 0.841709402 0.841367521 0.831709402 0.841452991 0.75042735 0.778376068 0.799059829 0.85042735 0.80982906 0.86 0.8413674 0.79982906 0.709145299 0.845042735 0.81017094 0.771367521 0.777948718 0.803333333 0.817008547 0.685897436 0.77957265 0.751282051
CricketZ 0.837692308 0.838974359 0.825128205 0.852307692 0.769316239 0.781880342 0.792393162 0.859487179 0.833931624 0.861111111 0.8424787 0.802820513 0.721623932 0.853247863 0.813247863 0.786752137 0.807179487 0.828461538 0.838205128 0.705897436 0.78991453 0.772478632
Crop 0.773912698 0.779380952 0.764305556 0.744916667 0.685688492 0.767365079 0.77727381 0.763886905 0.768162698 0.793194444 0.752248 0.753109127 0.73 0.751684524 0.763801587 0.707785714 0.736700397 0.724994048 0.76210119 0.745593254 0.723825397 0.700888889
DiatomSizeReduction 0.952178649 0.952287582 0.953485839 0.959259259 0.945206972 0.921568627 0.91459695 0.922331155 0.914270153 0.950653595 0.942810333 0.956753813 0.932135076 0.95795207 0.30620915 0.945424837 0.859259259 0.883986928 0.945860566 0.941721133 0.908061002 0.883551198
DistalPhalanxOutlineAgeGroup 0.8117506 0.812709832 0.816546763 0.816786571 0.820623501 0.818705036 0.821582734 0.820863309 0.823980815 0.765707434 0.8038368 0.802158273 0.821582734 0.811510791 0.776019185 0.821342926 0.79616307 0.795683453 0.828057554 0.809352518 0.792805755 0.805515588
DistalPhalanxOutlineCorrect 0.843115942 0.842149758 0.838405797 0.823188406 0.811714976 0.821618358 0.833816425 0.828381643 0.823550725 0.81557971 0.8213769 0.823429952 0.811231884 0.824396135 0.809178744 0.810990338 0.827294686 0.766425121 0.819323671 0.805797101 0.819202899 0.780193237
DistalPhalanxTW 0.70263789 0.702398082 0.699760192 0.700239808 0.67146283 0.697601919 0.697841727 0.701678657 0.69616307 0.665947242 0.6959232 0.692086331 0.694484412 0.701199041 0.667146283 0.669544365 0.689928058 0.665947242 0.691846523 0.691127098 0.678657074 0.673141487
ECG200 0.890666667 0.891666667 0.888666667 0.898666667 0.878333333 0.860666667 0.861 0.888666667 0.858666667 0.895666667 0.899333333 0.873 0.851 0.899 0.883666667 0.871666667 0.839 0.847333333 0.855 0.86 0.859 0.829666667
ECG5000 0.947059259 0.94682963 0.946488889 0.947133333 0.940059259 0.944066667 0.945637037 0.948014815 0.945622222 0.942051852 0.946133233 0.939511111 0.936688889 0.947385185 0.937022222 0.940696296 0.941777778 0.943422222 0.948459259 0.943377778 0.945881481 0.943214815
ECGFiveDays 0.995121951 0.994889663 0.994579946 0.996205962 0.99229578 0.954936121 0.988888889 0.99701897 0.993766938 0.99585753 0.9904763 0.882810685 0.972861014 0.995973674 0.951025939 0.992218351 0.977893922 0.984552846 0.994425087 0.951955091 0.99353465 0.983933411
EOGHorizontalSignal 0.866482505 0.867679558 0.855524862 0.807458564 0.706721915 0.771270718 0.795948435 0.815469613 0.795672192 0.883609576 0.836279933 0.824401473 0.624861878 0.813812155 0.864732965 0.708287293 0.75985267 0.722099448 0.853683241 0.705985267 0.74732965 0.720441989
EOGVerticalSignal 0.810773481 0.814732965 0.788213628 0.779558011 0.660313076 0.747237569 0.778268877 0.789871087 0.762983425 0.814548803 0.7980663 0.777624309 0.603499079 0.781123389 0.75174954 0.68305709 0.713167587 0.67320442 0.809484346 0.672559853 0.697513812 0.668692449
Earthquakes 0.748920863 0.748681055 0.747961631 0.748201439 0.746043165 0.74676259 0.748201439 0.748201439 0.747482014 0.732134293 0.748680667 0.749640288 0.748201439 0.748441247 0.717026379 0.747482014 0.741966427 0.74676259 0.748201439 0.747482014 0.747482014 0.747482014
ElectricDevices 0.900345826 0.896252107 0.894955259 0.890239052 0.797384689 0.872818052 0.882397441 0.898474041 0.879708641 0.890213115 0.8743656 0.842441534 0.824030606 0.893156962 0.888380236 0.805969827 0.881774954 0.831236761 0.865041283 0.79306186 0.871698439 0.813145723
EthanolLevel 0.712666667 0.723933333 0.691333333 0.620333333 0.508733333 0.803666667 0.775 0.835533333 0.849 0.875466667 0.664 0.324066667 0.661066667 0.625266667 0.852533333 0.5056 0.855733333 0.5336 0.6056 0.669266667 0.705066667 0.490733333
FaceAll 0.983609467 0.983530572 0.983984221 0.987771203 0.970098619 0.953333333 0.959428008 0.986725838 0.979723866 0.983313609 0.983451667 0.977061144 0.964852071 0.98800789 0.981854043 0.975069034 0.953688363 0.979013807 0.982721893 0.949960552 0.973116371 0.969033531
FaceFour 0.897348485 0.898484848 0.899242424 0.93219697 0.995454545 0.952272727 0.94280303 0.967045455 0.973106061 0.938636364 0.940151567 0.945454545 0.876893939 0.931439394 0.925 0.981818182 0.656439394 0.989015152 0.999621212 0.906818182 0.981060606 0.996969697
FacesUCR 0.970373984 0.970243902 0.96904065 0.971934959 0.951300813 0.909073171 0.915186992 0.974601626 0.961349593 0.976861789 0.9686505 0.956097561 0.89195122 0.971284553 0.964260163 0.95695935 0.910097561 0.961756097 0.972926829 0.90398374 0.956195122 0.952471545
FiftyWords 0.84014652 0.841978022 0.833772894 0.821758242 0.705860806 0.763296703 0.771501832 0.825787546 0.771648352 0.826813187 0.829010967 0.825934066 0.666593407 0.825054945 0.723956044 0.765054945 0.736556777 0.796556777 0.842710623 0.721684982 0.776996337 0.717875458
Fish 0.983428571 0.983619048 0.981714286 0.977142857 0.969714286 0.927428571 0.942095238 0.982285714 0.979428571 0.972571429 0.975047667 0.933904762 0.859047619 0.974095238 0.969904762 0.971238095 0.949904762 0.979428571 0.98152381 0.83047619 0.950857143 0.97447619
FordA 0.956035354 0.958030303 0.952828283 0.943813131 0.921363636 0.908308081 0.967020202 0.953989899 0.944116162 0.959141414 0.948181933 0.850025253 0.940025253 0.942449495 0.931515152 0.907575758 0.934242424 0.933131313 0.94739899 0.815757576 0.968686869 0.915732323
FordB 0.931851852 0.933580247 0.928271605 0.919588477 0.90744856 0.883621399 0.921316872 0.930329218 0.928024691 0.94090535 0.926790133 0.839382716 0.917325103 0.923004115 0.912798354 0.919835391 0.914650206 0.919465021 0.790658436 0.937119342 0.895473251
FreezerRegularTrain 0.998339181 0.997929825 0.997824561 0.995391813 0.98805848 0.998994152 0.999403509 0.999883041 0.999087719 0.995754386 0.9991227 0.942350877 0.95225731 0.994374269 0.996736842 0.976105263 0.999251462 0.995321637 0.998491228 0.997076023 0.990608187 0.993929825
FreezerSmallTrain 0.991976608 0.991391813 0.991918129 0.99019883 0.961637427 0.998690058 0.99922807 0.998187135 0.983660819 0.948912281 0.9873216 0.823380117 0.878725146 0.987204678 0.949473684 0.947602339 0.988561404 0.962619883 0.995461988 0.961438596 0.900573099 0.966818713
GunPoint 0.997777778 0.997555556 0.997333333 0.993111111 0.996444444 0.981333333 0.989333333 0.998888889 0.998222222 0.995111111 0.9924443 0.991333333 0.980888889 0.992 0.990888889 0.996666667 0.986444444 1 1 0.955333333 0.993111111 0.999777778
GunPointAgeSpan 0.995991561 0.996097046 0.995886076 0.993670886 0.994936709 0.983966245 0.984493671 0.995675105 0.996624473 0.983860759 0.992299467 0.996940928 0.98628692 0.993459916 0.994409283 0.99535865 0.966033755 0.998839662 0.999578059 0.977742616 0.981329114 0.998628692
GunPointMaleVersusFemale 1 1 1 0.99978903 0.999578059 0.997468354 0.998734177 1 0.999894515 0.998312236 0.9998945 0.999367089 0.991139241 0.999894515 0.990084388 0.999578059 0.98649789 0.998839662 0.999367089 0.995991561 0.993881857 0.999156118
GunPointOldVersusYoung 1 1 1 0.989100529 0.999153439 1 1 1 1 1 1 1 0.99978836 0.98962963 1 0.999153439 0.978306878 0.998941799 1 1 0.986031746 0.999153439
Ham 0.843809524 0.843809524 0.829206349 0.86 0.837460317 0.823809524 0.821587302 0.858730159 0.84 0.85015873 0.8447618 0.783492063 0.81968254 0.855238095 0.807301587 0.834920635 0.810793651 0.82 0.805079365 0.799365079 0.821269841 0.811428571
Haptics 0.550757576 0.55021645 0.550649351 0.532683983 0.467424242 0.503354978 0.519047619 0.546753247 0.539393939 0.536580087 0.546212133 0.458333333 0.478787879 0.534199134 0.496536797 0.492207792 0.541666667 0.525541126 0.523268398 0.465584416 0.449242424 0.480194805
Herring 0.613020833 0.615625 0.615625 0.623958333 0.595833333 0.606770833 0.595833333 0.626041667 0.611979167 0.625 0.609375 0.574479167 0.5984375 0.625 0.596875 0.608333333 0.6328125 0.6015625 0.597395833 0.604166667 0.602083333 0.574479167
HouseTwenty 0.975910364 0.975630252 0.977871148 0.964145658 0.956022409 0.937535014 0.940056022 0.98627451 0.978711485 0.953501401 0.965826433 0.93697479 0.929691877 0.962745098 0.955462185 0.929691877 0.975070028 0.988515406 0.970308123 0.837815126 0.810644258 0.93977591
InlineSkate 0.48169697 0.482727273 0.480848485 0.465575758 0.505636364 0.454363636 0.561212121 0.545575758 0.515151515 0.534363636 0.4646667 0.561030303 0.390424242 0.437939394 0.410121212 0.514242424 0.439272727 0.533818182 0.571878788 0.372787879 0.674606061 0.503454545
InsectEPGRegularTrain 1 1 1 0.987014726 0.996787149 1 1 1 1 1 1 1 0.992904953 0.987014726 1 0.977376171 0.993440428 0.999330656 1 1 0.971753681 1
InsectEPGSmallTrain 0.995983936 0.996251673 0.996117805 0.934270415 0.984872825 0.995983936 0.99437751 0.998527443 1 1 0.9934405 1 0.972155288 0.934270415 0.396251673 0.975502008 0.88768407 0.999062918 1 0.995850067 0.90669344 0.990896921
InsectWingbeatSound 0.671700337 0.671666667 0.671430976 0.657828283 0.511835017 0.648181818 0.661986532 0.661868687 0.64026936 0.627340067 0.6596801 0.606902357 0.636363636 0.656683502 0.491380471 0.518686869 0.628552189 0.582474747 0.632222222 0.603451178 0.619494949 0.538989899
ItalyPowerDemand 0.964496275 0.964820214 0.964528669 0.961483641 0.870877875 0.962876579 0.965079365 0.961839974 0.958179462 0.960349854 0.959572433 0.95600907 0.944541626 0.961613217 0.957110463 0.86835115 0.953806284 0.948817622 0.962423064 0.959475219 0.9468092 0.926465824
LargeKitchenAppliances 0.941422222 0.940533333 0.934488889 0.928533333 0.835822222 0.867288889 0.867377778 0.935288889 0.920088889 0.952355556 0.903200033 0.810133333 0.735822222 0.930044444 0.953866667 0.836977778 0.929866667 0.840088889 0.860177778 0.636266667 0.792711111 0.836977778
Lightning2 0.750819672 0.751912568 0.744262295 0.77431694 0.819125683 0.764480874 0.756830601 0.783606557 0.773224044 0.816393443 0.751912467 0.84863388 0.681967213 0.776502732 0.800546448 0.808196721 0.658469945 0.774863388 0.768852459 0.764480874 0.627322404 0.79726776
Lightning7 0.79543379 0.792694064 0.77716895 0.797716895 0.671232877 0.742922374 0.752511416 0.797716895 0.757534247 0.821461187 0.7789955 0.792237443 0.697716895 0.797716895 0.810045662 0.681278539 0.743378995 0.705479452 0.793607306 0.720547945 0.712785388 0.720091324
Mallat 0.951656006 0.952793177 0.955024876 0.957725657 0.949793888 0.970675195 0.978464819 0.979061834 0.967192608 0.962487562 0.955892033 0.972011372 0.954072495 0.957171286 0.968969439 0.948457711 0.908031272 0.880341151 0.976702203 0.935721393 0.966439232 0.940909737
Meat 0.982777778 0.985555556 0.982777778 0.990555556 0.980555556 0.986666667 0.983333333 0.990555556 0.986111111 0.983888889 0.9933333 0.987222222 0.986666667 0.988888889 0.993888889 0.983888889 0.967777778 0.980555556 0.984444444 0.983888889 0.976666667 0.977222222
MedicalImages 0.809078947 0.811798246 0.803377193 0.804605263 0.715833333 0.768157895 0.795964912 0.809605263 0.740350877 0.796315789 0.804385933 0.771447368 0.666710526 0.805131579 0.792236842 0.716798246 0.709824561 0.756842105 0.799122807 0.74622807 0.70877193 0.689605263
MiddlePhalanxOutlineAgeGroup 0.721428571 0.721212121 0.723809524 0.715151515 0.656277056 0.691558442 0.71017316 0.717532468 0.697835498 0.594588745 0.708008667 0.658874459 0.69978355 0.710822511 0.596536797 0.659090909 0.667532468 0.693506493 0.694372294 0.65952381 0.66038961 0.677489177
MiddlePhalanxOutlineCorrect 0.848109966 0.850973654 0.84467354 0.832760596 0.809507446 0.802634593 0.826345934 0.836311569 0.812943872 0.834020619 0.842726267 0.824054983 0.805498282 0.834478809 0.823596793 0.806643757 0.831500573 0.765635739 0.805841924 0.79954181 0.828293242 0.772164948
MiddlePhalanxTW 0.58982684 0.590692641 0.593939394 0.591558442 0.532251082 0.580735931 0.59025974 0.592424242 0.583766234 0.526623377 0.590909267 0.549134199 0.585064935 0.58982684 0.531168831 0.541558442 0.578571429 0.577922078 0.573160173 0.568614719 0.554329004 0.567316017
MixedShapesRegularTrain 0.978694158 0.978597938 0.977896907 0.965333333 0.917910653 0.952398625 0.958611684 0.972893471 0.965924399 0.966295533 0.969360833 0.96380756 0.937704467 0.96566323 0.970075601 0.932068729 0.960233677 0.972646048 0.971381443 0.922996564 0.963285223 0.933924399
MixedShapesSmallTrain 0.9524811 0.952439863 0.95228866 0.931477663 0.871697595 0.909457045 0.914749141 0.951642612 0.944687285 0.913360825 0.941388233 0.928054983 0.898281787 0.930680412 0.916247423 0.929773196 0.936810997 0.953099656 0.947257732 0.840151203 0.924467354 0.893127148
MoteStrain 0.902981896 0.902529286 0.905378062 0.905644302 0.844195953 0.905138445 0.908280085 0.932747604 0.936501597 0.880644302 0.912912633 0.914962726 0.878035144 0.905484558 0.903115016 0.850985091 0.908892439 0.899201278 0.930111821 0.855457934 0.904765708 0.896698616
OSULeaf 0.961707989 0.961019284 0.957300275 0.939669421 0.969146006 0.744903581 0.860606061 0.965564738 0.974793388 0.95261708 0.957575733 0.858539945 0.654269972 0.938705234 0.974655647 0.976859504 0.956336088 0.954958678 0.973553719 0.643250689 0.851790634 0.960055096
OliveOil 0.913333333 0.913333333 0.901111111 0.897777778 0.875555556 0.91 0.905555556 0.903333333 0.883333333 0.874444444 0.914444467 0.878888889 0.893333333 0.902222222 0.862222222 0.874444444 0.878888889 0.893333333 0.916666667 0.893333333 0.913333333 0.874444444
PhalangesOutlinesCorrect 0.857575758 0.857187257 0.845687646 0.843356643 0.817365967 0.828321678 0.844483294 0.845415695 0.826495726 0.861499611 0.842229933 0.829098679 0.812509713 0.844716395 0.847668998 0.818881119 0.833682984 0.778049728 0.825330225 0.805710956 0.821717172 0.779176379
Phoneme 0.35302391 0.349525316 0.351547117 0.273857243 0.254606188 0.366279888 0.413800985 0.39092827 0.37116737 0.334616737 0.2718706 0.320411392 0.346624473 0.275140647 0.345675105 0.279588608 0.356522504 0.348329817 0.369848805 0.193653305 0.25947609 0.272609001
PigAirwayPressure 0.647275641 0.656410256 0.571955128 0.162339744 0.941826923 0.314583333 0.289903846 0.955448718 0.957692308 0.922115385 0.8727564 0.275480769 0.182532051 0.195512821 0.437019231 0.957371795 0.977403846 0.945512821 0.960096154 0.280128205 0.537820513 0.950961538
PigArtPressure 0.927884615 0.924038462 0.917467949 0.908814103 0.967628205 0.785576923 0.858333333 0.973237179 0.966826923 0.933173077 0.962499967 0.715705128 0.794551282 0.90849359 0.953685897 0.975 0.945673077 0.979166667 0.968910256 0.307211538 0.937820513 0.962179487
PigCVP 0.828044872 0.830128205 0.809615385 0.881089744 0.959455128 0.485416667 0.635096154 0.92900641 0.953044872 0.905288462 0.9185898 0.500480769 0.682532051 0.881730769 0.45400641 0.958012821 0.899679487 0.938942308 0.961378205 0.178205128 0.897916667 0.952884615
Plane 1 1 1 1 0.998095238 0.998412698 1 1 1 0.996825397 1 1 0.996507937 1 1 0.997777778 0.999047619 1 1 0.995873016 0.994920635 1
PowerCons 0.977037037 0.976851852 0.976481481 0.954814815 0.89 0.991851852 0.988888889 0.968888889 0.992407407 0.986111111 0.983703633 0.987407407 0.957962963 0.956111111 0.886111111 0.897037037 0.940555556 0.938333333 0.979444444 0.993148148 0.919444444 0.897592593
ProximalPhalanxOutlineAgeGroup 0.853170732 0.853495935 0.854308943 0.851382114 0.828455285 0.853170732 0.850081301 0.85398374 0.855934959 0.822113821 0.856585567 0.840162602 0.857235772 0.852357724 0.817398374 0.832520325 0.845528455 0.857886179 0.846341463 0.84504065 0.844878049 0.849756098
ProximalPhalanxOutlineCorrect 0.905269187 0.907216495 0.899770905 0.896105384 0.865521191 0.877892325 0.894730813 0.896334479 0.885223368 0.906300115 0.8941581 0.865864834 0.873654066 0.899312715 0.905612829 0.866208477 0.895303551 0.867697594 0.875486827 0.848911798 0.87628866 0.864604811
ProximalPhalanxTW 0.80796748 0.804065041 0.804715447 0.803577236 0.768617886 0.810731707 0.81300813 0.811219512 0.816097561 0.780650407 0.8021138 0.790731707 0.813170732 0.803577236 0.789430894 0.774634146 0.807642276 0.801788618 0.811056911 0.801626016 0.801463415 0.794634146
RefrigerationDevices 0.731288889 0.733511111 0.722844444 0.716533333 0.782844444 0.698488889 0.740177778 0.767022222 0.790933333 0.759377778 0.6969779 0.672355556 0.651822222 0.729955556 0.786844444 0.7784 0.777155556 0.770755556 0.726844444 0.611644444 0.739733333 0.762933333
Rock 0.86 0.861333333 0.857333333 0.804 0.802666667 0.866 0.864666667 0.888666667 0.855333333 0.627333333 0.815333333 0.774666667 0.782 0.804666667 0.416 0.826 0.867333333 0.875333333 0.832 0.76 0.854666667 0.801333333
ScreenType 0.657688889 0.655911111 0.638222222 0.5968 0.5848 0.615911111 0.669866667 0.707022222 0.724177778 0.7056 0.542222233 0.572 0.605866667 0.608977778 0.755288889 0.588977778 0.717866667 0.643555556 0.594222222 0.471822222 0.595911111 0.577066667
SemgHandGenderCh2 0.949444444 0.950222222 0.938055556 0.924833333 0.887666667 0.9515 0.952111111 0.961277778 0.969166667 0.884555556 0.9098889 0.963111111 0.87 0.923111111 0.808888889 0.885166667 0.932277778 0.880277778 0.938888889 0.947388889 0.781444444 0.879111111
SemgHandMovementCh2 0.794296296 0.796518519 0.750222222 0.640592593 0.664888889 0.87637037 0.875259259 0.861925926 0.888962963 0.551037037 0.675036967 0.890888889 0.724 0.652592593 0.420962963 0.681777778 0.788296296 0.707481482 0.884962963 0.864148148 0.460296296 0.692148148
SemgHandSubjectCh2 0.926888889 0.927259259 0.906222222 0.914222222 0.835111111 0.931925926 0.933185185 0.938888889 0.950592593 0.763925926 0.878666667 0.938074074 0.824148148 0.911851852 0.554740741 0.842740741 0.913333333 0.866074074 0.933111111 0.916 0.793481481 0.845407407
ShapeletSim 1 1 1 0.997777778 1 0.96 0.973333333 1 1 0.923518519 0.9996296 0.789259259 0.767592593 0.998148148 0.727222222 1 0.99962963 0.995 1 0.513703704 0.997407407 0.985185185
ShapesAll 0.946 0.944833333 0.940333333 0.923555556 0.9085 0.860166667 0.874666667 0.934277778 0.931277778 0.938166667 0.934777767 0.890055556 0.850055556 0.923222222 0.933055556 0.920444444 0.865333333 0.931833333 0.941055556 0.804277778 0.916 0.904055556
SmallKitchenAppliances 0.825422222 0.8288 0.820266667 0.817955556 0.747111111 0.832888889 0.844622222 0.841244444 0.828266667 0.770577778 0.8133333 0.738133333 0.805955556 0.818311111 0.796622222 0.790933333 0.8128 0.811644444 0.837955556 0.788177778 0.805244444 0.773777778
SmoothSubspace 0.979555556 0.978222222 0.979777778 0.974888889 0.407333333 0.990888889 0.988444444 0.982666667 0.986222222 0.984888889 0.957999967 0.998 0.848444444 0.974888889 0.992888889 0.411777778 0.935777778 0.874222222 0.997333333 0.987333333 0.855333333 0.444
SonyAIBORobotSurface1 0.947975596 0.94786467 0.949195785 0.957903494 0.897670549 0.869495286 0.917803661 0.952190793 0.826344981 0.954187465 0.948031133 0.920133111 0.866999445 0.958069884 0.960399334 0.895341098 0.800942873 0.710094287 0.889739323 0.863727121 0.909262341 0.622850804
SonyAIBORobotSurface2 0.949003148 0.948863239 0.947604057 0.935362015 0.879363414 0.908674362 0.928681357 0.947219307 0.936656173 0.95127667 0.941727933 0.899020637 0.912486884 0.935047219 0.968870234 0.884260231 0.936970969 0.904756908 0.901084295 0.874326688 0.93529206 0.875795733
StarLightCurves 0.981196374 0.981398737 0.980957585 0.981257083 0.976578436 0.979164643 0.979779828 0.981686094 0.979557228 0.978124494 0.981220667 0.97956937 0.974380767 0.98099401 0.972029302 0.952096487 0.978606119 0.977679294 0.98112757 0.970426582 0.980431439 0.977752145
Strawberry 0.978918919 0.979189189 0.978288288 0.979459459 0.97045045 0.975585586 0.973783784 0.978918919 0.975135135 0.975495495 0.979819767 0.96045045 0.972972973 0.978738739 0.974864865 0.966036036 0.971711712 0.973513514 0.973963964 0.967477477 0.978558559 0.972162162
SwedishLeaf 0.972373333 0.97264 0.969173333 0.959786667 0.92016 0.937706667 0.960426667 0.96352 0.94944 0.969813333 0.962933333 0.953066667 0.922933333 0.9632 0.95856 0.92544 0.933973333 0.93744 0.96192 0.897866667 0.9576 0.91056
Symbols 0.97319933 0.972328308 0.972495812 0.96760469 0.96318258 0.949145729 0.952227806 0.971457286 0.968509213 0.969480737 0.966834 0.967035176 0.912730318 0.968576214 0.946700168 0.964154104 0.901407035 0.967035176 0.970820771 0.877889447 0.953232831 0.962512563
SyntheticControl 0.995 0.994777778 0.993111111 0.997333333 0.966555556 0.991222222 0.994 0.998444444 0.994222222 0.995777778 0.990111167 0.998333333 0.677888889 0.997777778 0.994444444 0.964888889 0.991888889 0.987111111 0.999 0.991555556 0.987 0.951111111
ToeSegmentation1 0.927923977 0.92748538 0.925146199 0.930555556 0.924853801 0.859502924 0.901461988 0.955409357 0.959649123 0.953216374 0.941081733 0.835526316 0.880409357 0.932894737 0.954239766 0.920321637 0.953362573 0.959064328 0.959795322 0.667105263 0.942982456 0.951754386
ToeSegmentation2 0.935897436 0.936666667 0.932564103 0.931538462 0.961538462 0.897948718 0.897435897 0.96025641 0.968205128 0.963589744 0.939999967 0.885897436 0.911794872 0.932564103 0.953076923 0.963076923 0.945128205 0.973846154 0.962564103 0.802564103 0.928461538 0.964871795
Trace 1 1 1 1 1 1 1 1 1 1 1 1 0.983 1 1 1 1 1 1 0.992 1 1
TwoLeadECG 0.997570969 0.9976295 0.997922154 0.998478197 0.984723442 0.921480831 0.984957565 0.999034241 0.996283289 0.994820018 0.997248933 0.981796898 0.910740416 0.998536728 0.999443957 0.985601405 0.999122037 0.997980685 0.990079017 0.870646766 0.997541703 0.993766462
TwoPatterns 1 1 0.999991667 1 0.991691667 0.99895 0.999691667 1 0.999483333 1 0.995283333 0.999991667 0.438966667 1 0.999775 0.99575 0.990258333 0.997391667 0.999991667 0.993825 0.9814 0.99205
UMD 0.982407407 0.980092593 0.984027778 0.981481481 0.966435185 0.906944444 0.915740741 0.98587963 0.967361111 0.979861111 0.990277967 0.954398148 0.541203704 0.98287037 0.952546296 0.93912037 0.936805556 0.918287037 0.983333333 0.833333333 0.932175926 0.921759259
UWaveGestureLibraryAll 0.984347664 0.984189466 0.983240275 0.975227992 0.944853899 0.972389726 0.971877908 0.974865066 0.966620138 0.951172529 0.9749116 0.973059743 0.917373907 0.977265959 0.868993114 0.947710776 0.957965755 0.954075935 0.970742602 0.962367393 0.957761027 0.944853899
UWaveGestureLibraryX 0.875060488 0.875507165 0.866378187 0.856523358 0.752587009 0.830764936 0.845049321 0.860348036 0.833454309 0.833603201 0.8560488 0.831397729 0.633947515 0.857128234 0.790396427 0.788172343 0.820165643 0.827033315 0.846780197 0.799990694 0.817606551 0.774055462
UWaveGestureLibraryY 0.807686581 0.808030895 0.797031454 0.78323097 0.662125442 0.766192071 0.775041876 0.789456542 0.754680811 0.770630932 0.783398567 0.767215708 0.668220733 0.783631119 0.67585148 0.714824121 0.74491904 0.764628699 0.788023451 0.721877908 0.725823562 0.694369998
UWaveGestureLibraryZ 0.81652708 0.818220733 0.809826912 0.79580309 0.695495999 0.776214405 0.78884236 0.803294249 0.77514424 0.773208636 0.800325633 0.767383212 0.66352131 0.795831007 0.751386562 0.736376326 0.772473479 0.783696259 0.791178113 0.73340778 0.754820398 0.710580681
Wafer 0.999718797 0.999735021 0.999675535 0.998583171 0.998907636 0.998940082 0.999605235 1 0.999859399 0.998621025 0.998978033 0.996144279 0.995354748 0.998648064 0.998880597 0.999042829 0.999978369 0.999837768 0.998923859 0.996593121 0.999913476 0.998929267
Wine 0.92037037 0.916666667 0.92654321 0.922839506 0.892592593 0.878395062 0.874074074 0.924691358 0.891975309 0.886419753 0.927777633 0.85617284 0.870987654 0.914197531 0.85617284 0.89382716 0.885802469 0.888888889 0.898148148 0.862345679 0.930246914 0.877777778
WordSynonyms 0.78615465 0.787251829 0.77215256 0.758777429 0.658411703 0.68631139 0.695245559 0.766196447 0.693155695 0.751776385 0.767554867 0.77816092 0.591640543 0.764420063 0.613322884 0.737565308 0.623040752 0.755485893 0.793678161 0.647910136 0.712748171 0.667816092
Worms 0.72987013 0.729437229 0.729004329 0.714718615 0.725541126 0.708225108 0.748484848 0.758008658 0.716450216 0.77965368 0.7294375 0.693073593 0.686580087 0.72034632 0.758874459 0.717316017 0.733333333 0.741991342 0.768398268 0.612121212 0.778354978 0.662337662
WormsTwoClass 0.796536797 0.791341991 0.798268398 0.774458874 0.807792208 0.798701298 0.803463203 0.805194805 0.78961039 0.803463203 0.7926409 0.769264069 0.785281385 0.78961039 0.767965368 0.807792208 0.785281385 0.815151515 0.786147186 0.693506494 0.8004329 0.790909091
Yoga 0.931877778 0.932011111 0.9251 0.912255556 0.910155556 0.874255555 0.8898 0.930033333 0.912433333 0.912311111 0.918688933 0.887444444 0.8372 0.913844444 0.877211111 0.915055556 0.879988889 0.928633333 0.872633333 0.8658 0.892377778 0.912122222

Here are the results for some MultiRocket variants on the full 128 UCR datasets.

Here are the results for some MultiRocket variants on 30 resamples of 109 UCR datasets.

Acknowledgement

We would like to thank Professor Eamonn Keogh, Professor Tony Bagnall and their team who have provided the UCR time series classification archive and making a comprehensive benchmark results widely available. We also appreciate the open source code to draw the critical difference diagrams from Hassan Fawaz.

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Multiple pooling operators and transformations for fast and effective time series classification

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