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Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

CN 10-1014/TP

邮发代号 80-970

2019 Impact Factor: 1.275

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Frontiers of Computer Science  2025, Vol. 19 Issue (1): 191303   https://doi.org/10.1007/s11704-023-3396-y
  本期目录
A data representation method using distance correlation
Xinyan LIANG1, Yuhua QIAN1,2(), Qian GUO3,4, Keyin ZHENG1
1. Institute of Big Data Science and Industry, Shanxi University, Taiyuan 030006, China
2. Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan 030006, China
3. School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan 030024, China
4. Shanxi Key Laboratory of Big Data Analysis and Parallel Computing, Taiyuan University of Science and Technology, Taiyuan 030024, China
 全文: PDF(1511 KB)   HTML
Abstract：

Association in-between features has been demonstrated to improve the representation ability of data. However, the original association data reconstruction method may face two issues: the dimension of reconstructed data is undoubtedly higher than that of original data, and adopted association measure method does not well balance effectiveness and efficiency. To address above two issues, this paper proposes a novel association-based representation improvement method, named as AssoRep. AssoRep first obtains the association between features via distance correlation method that has some advantages than Pearson’s correlation coefficient. Then an improved matrix is formed via stacking the association value of any two features. Next, an improved feature representation is obtained by aggregating the original feature with the enhancement matrix. Finally, the improved feature representation is mapped to a low-dimensional space via principal component analysis. The effectiveness of AssoRep is validated on 120 datasets and the fruits further prefect our previous work on the association data reconstruction.
Key words： association    representation    distance correlation    classification
收稿日期: 2023-05-10      出版日期: 2024-03-12
Corresponding Author(s): Yuhua QIAN   
 引用本文:   
. [J]. Frontiers of Computer Science, 2025, 19(1): 191303.
Xinyan LIANG, Yuhua QIAN, Qian GUO, Keyin ZHENG. A data representation method using distance correlation. Front. Comput. Sci., 2025, 19(1): 191303.
 链接本文:  
https://academic.hep.com.cn/fcs/CN/10.1007/s11704-023-3396-y
https://academic.hep.com.cn/fcs/CN/Y2025/V19/I1/191303
ID Dataset n d L ID Dataset n d L ID Dataset n d L
L1 abalone 4177 8 3 L2 adult 48842 14 2 L3 annealing 798 38 6
L4 bank 4521 17 2 L5 blood 748 4 2 L6 car 1728 6 4
L7 ctg-10classes 2126 21 10 L8 ctg-3classes 2126 21 3 L9 chess-krvk 28056 6 18
L10 chess-krvkp 3196 36 2 L11 connect-4 67557 42 2 L12 contrac 1473 9 3
L13 energy-y1 768 8 3 L14 wav-mfcc 15352 80 1215 L15 led-display 1000 7 10
L16 letter 20000 16 26 L17 magic 19020 10 2 L18 mammographic 961 5 2
L19 molec-biol-splice 3190 60 3 L20 monks-3 3190 6 2 L21 mushroom 8124 21 2
L22 musk-2 6598 166 2 L23 nursery 12960 8 5 L24 oocMerl2F 1022 25 3
L25 oocMerl4D 1022 41 2 L26 oocTris2F 912 25 2 L27 oocTris5B 912 32 3
L28 optical 3823 62 10 L29 ozone 2536 72 2 L30 page-blocks 5473 10 5
L31 pendigits 7494 16 10 L32 pima 768 5 2 L33 plant-margin 1600 64 100
L34 plant-shape 1600 64 100 L35 plant-texture 1600 36 100 L89 ringnorm 7400 20 2
L37 semeion 1593 256 10 L38 spambase 4601 57 2 L39 st-german-credit 1000 24 2
L40 st-image 2310 18 7 L41 st-landsat 4435 36 6 L42 st-shuttle 43500 9 7
L43 st-vehicle 846 18 4 L44 steel-plates 1941 27 7 L45 thyroid 3772 21 3
L46 tic-tac-toe 958 9 2 L47 titanic 2201 3 2 L48 twonorm 7400 20 2
L49 wall-following 5456 24 4 L50 waveform 5000 21 3 L51 wine-quality-red 1599 11 6
L52 wine-quality-white 4898 11 7 L53 yeast 1484 8 10 L54 robotnavigation 5456 25 4
L55 AWArgsift-hist 3048 2000 10 L56 UJIndoorLoc 21048 520 5 L57 MM-IMDB-T 7799 600 2
L58 MM-IMDB-I 7799 2048 2 L59 YouTubeFaces4 5074 838 31 L60 Gesture-R 4977 2048 83
Tab.1  
DataAccuracyPrecisionRecallF1Kappa
LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)
L1 0.647±0.020 0.662±0.021? 0.636±0.021 0.652±0.022? 0.642±0.020 0.658±0.021? 0.636±0.021 0.653±0.021? 0.469±0.031 0.492±0.031?
L2 0.843±0.007 0.852±0.007? 0.796±0.010 0.809±0.012? 0.738±0.016 0.757±0.014? 0.759±0.014 0.777±0.013? 0.521±0.028 0.557±0.025?
L3 0.873±0.027 0.951±0.014? 0.792±0.116 0.924±0.077? 0.641±0.111 0.888±0.080? 0.678±0.113 0.901±0.077? 0.620±0.087 0.871±0.040?
L4 0.895±0.007 0.897±0.005∘ 0.761±0.040 0.760±0.022∘ 0.612±0.030 0.641±0.029? 0.644±0.035 0.675±0.027? 0.301±0.066 0.357±0.052?
L5 0.772±0.015 0.786±0.019∘ 0.705±0.099 0.713±0.054∘ 0.549±0.023 0.608±0.033? 0.535±0.036 0.621±0.040? 0.135±0.059 0.267±0.074?
L6 0.794±0.027 0.881±0.026? 0.577±0.123 0.809±0.090? 0.444±0.062 0.630±0.068? 0.470±0.079 0.667±0.075? 0.498±0.072 0.737±0.060?
L7 0.768±0.032 0.834±0.027? 0.762±0.054 0.837±0.041? 0.639±0.039 0.782±0.039? 0.668±0.042 0.796±0.035? 0.720±0.039 0.802±0.033?
L8 0.894±0.018 0.912±0.018? 0.827±0.048 0.861±0.044? 0.775±0.046 0.827±0.035? 0.796±0.042 0.841±0.035? 0.701±0.054 0.754±0.053?
L9 0.282±0.008 0.351±0.010? 0.242±0.038 0.337±0.041? 0.203±0.011 0.299±0.018? 0.188±0.010 0.294±0.021? 0.179±0.009 0.264±0.012?
L10 0.970±0.012 0.971±0.014∘ 0.970±0.013 0.971±0.014∘ 0.970±0.012 0.971±0.014∘ 0.970±0.012 0.971±0.014∘ 0.940±0.025 0.941±0.027∘
L11 0.754±0.000 0.830±0.004? 0.720±0.091 0.784±0.006? 0.502±0.001 0.728±0.006? 0.434±0.002 0.748±0.006? 0.005±0.002 0.499±0.012?
L12 0.507±0.042 0.568±0.055? 0.491±0.053 0.550±0.066? 0.472±0.044 0.531±0.055? 0.474±0.047 0.533±0.058? 0.221±0.067 0.318±0.085?
L13 0.874±0.013 0.881±0.012∘ 0.847±0.026 0.862±0.022∘ 0.786±0.020 0.796±0.020∘ 0.795±0.023 0.807±0.024∘ 0.792±0.021 0.804±0.020∘
L14 0.231±0.011 0.281±0.007? 0.137±0.009 0.164±0.007? 0.166±0.010 0.209±0.008? 0.142±0.009 0.174±0.007? 0.229±0.011 0.280±0.007?
L15 0.735±0.040 0.735±0.040∘ 0.745±0.039 0.745±0.039∘ 0.736±0.040 0.736±0.040∘ 0.731±0.038 0.731±0.038∘ 0.705±0.045 0.705±0.045∘
L16 0.723±0.013 0.846±0.009? 0.725±0.013 0.849±0.009? 0.721±0.013 0.845±0.009? 0.720±0.013 0.846±0.009? 0.712±0.014 0.840±0.010?
L17 0.791±0.006 0.850±0.008? 0.782±0.009 0.845±0.009? 0.745±0.007 0.820±0.011? 0.756±0.007 0.829±0.010? 0.517±0.014 0.660±0.019?
L18 0.823±0.035 0.832±0.035∘ 0.825±0.035 0.834±0.034∘ 0.823±0.035 0.831±0.034∘ 0.822±0.035 0.831±0.035∘ 0.645±0.070 0.663±0.069∘
L19 0.835±0.018 0.951±0.013? 0.819±0.020 0.942±0.014? 0.831±0.021 0.949±0.012? 0.824±0.020 0.945±0.013? 0.735±0.029 0.920±0.021?
L20 0.761±0.123 0.930±0.067? 0.777±0.127 0.937±0.063? 0.761±0.124 0.930±0.067? 0.757±0.125 0.929±0.068? 0.521±0.246 0.859±0.135?
L21 0.947±0.009 1.000±0.000? 0.947±0.009 1.000±0.000? 0.946±0.009 1.000±0.000? 0.947±0.009 1.000±0.000? 0.893±0.018 1.000±0.000?
L22 0.949±0.005 0.945±0.005∘ 0.921±0.011 0.921±0.012∘ 0.878±0.015 0.858±0.016∘ 0.898±0.011 0.885±0.012∘ 0.795±0.021 0.771±0.023∘
L23 0.899±0.007 0.916±0.007? 0.649±0.056 0.660±0.056? 0.664±0.057 0.676±0.057? 0.656±0.056 0.668±0.056? 0.851±0.010 0.876±0.010?
L24 0.918±0.021 0.930±0.021∘ 0.881±0.046 0.923±0.034? 0.893±0.054 0.919±0.038∘ 0.883±0.045 0.919±0.032? 0.823±0.045 0.847±0.047∘
L25 0.796±0.036 0.837±0.020? 0.788±0.051 0.819±0.038? 0.731±0.045 0.803±0.028? 0.746±0.047 0.809±0.030? 0.499±0.092 0.619±0.061?
L26 0.797±0.030 0.836±0.030? 0.800±0.033 0.834±0.029? 0.787±0.031 0.829±0.035? 0.789±0.031 0.830±0.032? 0.580±0.061 0.661±0.064?
L27 0.924±0.021 0.930±0.024∘ 0.866±0.151 0.915±0.109∘ 0.828±0.140 0.897±0.109∘ 0.840±0.141 0.900±0.107∘ 0.846±0.044 0.858±0.050∘
L28 0.964±0.016 0.968±0.013∘ 0.965±0.016 0.969±0.013∘ 0.964±0.016 0.968±0.013∘ 0.964±0.016 0.968±0.013∘ 0.960±0.018 0.965±0.015∘
L29 0.969±0.008 0.966±0.011∘ 0.570±0.173 0.743±0.176? 0.533±0.074 0.584±0.045? 0.542±0.104 0.611±0.060? 0.092±0.205 0.226±0.120?
L30 0.954±0.003 0.959±0.004∘ 0.862±0.043 0.842±0.049∘ 0.659±0.039 0.701±0.029? 0.725±0.044 0.753±0.030? 0.720±0.023 0.763±0.024?
L31 0.943±0.010 0.983±0.004? 0.943±0.010 0.983±0.005? 0.943±0.010 0.983±0.004? 0.942±0.010 0.983±0.005? 0.937±0.011 0.981±0.005?
L32 0.779±0.029 0.779±0.029∘ 0.768±0.039 0.768±0.039∘ 0.734±0.029 0.734±0.029∘ 0.743±0.031 0.743±0.031∘ 0.490±0.062 0.490±0.062∘
L33 0.747±0.025 0.798±0.022? 0.724±0.025 0.779±0.019? 0.750±0.025 0.796±0.022? 0.714±0.023 0.767±0.020? 0.745±0.026 0.796±0.023?
L34 0.509±0.032 0.564±0.038? 0.444±0.033 0.502±0.045? 0.518±0.030 0.569±0.035? 0.446±0.033 0.501±0.042? 0.504±0.032 0.560±0.038?
L35 0.809±0.018 0.839±0.028? 0.789±0.028 0.823±0.047? 0.810±0.022 0.841±0.033? 0.776±0.025 0.811±0.040? 0.807±0.018 0.837±0.028?
L36 0.760±0.016 0.986±0.005? 0.763±0.015 0.986±0.005? 0.760±0.016 0.986±0.005? 0.759±0.016 0.986±0.005? 0.520±0.032 0.972±0.010?
L37 0.890±0.031 0.927±0.019? 0.896±0.032 0.932±0.018? 0.889±0.031 0.927±0.019? 0.889±0.032 0.927±0.019? 0.878±0.035 0.919±0.021?
L38 0.925±0.011 0.932±0.008? 0.925±0.012 0.931±0.010? 0.919±0.012 0.927±0.008? 0.921±0.012 0.929±0.009? 0.843±0.023 0.857±0.018?
L39 0.761±0.040 0.771±0.040∘ 0.716±0.053 0.733±0.054? 0.684±0.060 0.685±0.062∘ 0.691±0.062 0.695±0.065∘ 0.389±0.117 0.400±0.122∘
L40 0.913±0.019 0.929±0.014? 0.917±0.016 0.930±0.013? 0.913±0.019 0.929±0.014? 0.913±0.018 0.928±0.013? 0.898±0.022 0.917±0.016?
Tab.2  
DataAccuracyPrecisionRecallF1Kappa
LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)
L41 0.838±0.009 0.887±0.009? 0.803±0.029 0.867±0.012? 0.757±0.009 0.858±0.008? 0.751±0.011 0.861±0.009? 0.797±0.011 0.860±0.011?
L42 0.930±0.002 0.992±0.001? 0.522±0.079 0.780±0.116? 0.488±0.078 0.633±0.093? 0.501±0.078 0.653±0.087? 0.783±0.008 0.978±0.003?
L43 0.792±0.024 0.819±0.024? 0.790±0.029 0.821±0.024? 0.794±0.025 0.821±0.024? 0.786±0.027 0.819±0.025? 0.723±0.032 0.759±0.032?
L44 0.706±0.026 0.744±0.023? 0.731±0.049 0.773±0.028? 0.695±0.042 0.756±0.043? 0.702±0.048 0.758±0.033? 0.619±0.033 0.671±0.029?
L45 0.950±0.004 0.960±0.010? 0.876±0.063 0.897±0.074∘ 0.664±0.041 0.705±0.088∘ 0.672±0.025 0.763±0.083? 0.528±0.005 0.644±0.099?
L46 0.983±0.016 0.983±0.016∘ 0.988±0.012 0.988±0.012∘ 0.976±0.023 0.976±0.023∘ 0.981±0.018 0.981±0.018∘ 0.962±0.037 0.962±0.037∘
L47 0.776±0.019 0.778±0.019∘ 0.760±0.025 0.763±0.025∘ 0.700±0.029 0.703±0.028∘ 0.714±0.030 0.718±0.030∘ 0.437±0.056 0.444±0.055∘
L48 0.979±0.006 0.979±0.006∘ 0.979±0.006 0.979±0.006∘ 0.979±0.006 0.979±0.006∘ 0.979±0.006 0.979±0.006∘ 0.957±0.012 0.957±0.012∘
L49 0.688±0.013 0.922±0.011? 0.690±0.036 0.921±0.016? 0.593±0.023 0.918±0.019? 0.622±0.027 0.919±0.016? 0.514±0.021 0.882±0.017?
L50 0.869±0.015 0.869±0.015∘ 0.869±0.015 0.869±0.015∘ 0.869±0.015 0.869±0.015∘ 0.868±0.015 0.868±0.015∘ 0.803±0.023 0.803±0.023∘
L51 0.592±0.030 0.604±0.044∘ 0.277±0.043 0.296±0.034∘ 0.253±0.017 0.280±0.028? 0.246±0.022 0.281±0.031? 0.316±0.052 0.351±0.073∘
L52 0.537±0.014 0.541±0.018∘ 0.289±0.047 0.365±0.157∘ 0.228±0.018 0.257±0.049? 0.221±0.018 0.264±0.064? 0.234±0.026 0.260±0.029?
L53 0.588±0.044 0.611±0.030? 0.568±0.092 0.552±0.065∘ 0.485±0.059 0.533±0.050? 0.499±0.064 0.529±0.054∘ 0.458±0.059 0.493±0.041?
L54 0.688±0.013 0.900±0.014? 0.690±0.036 0.903±0.021? 0.593±0.023 0.893±0.019? 0.622±0.027 0.897±0.018? 0.514±0.021 0.849±0.022?
L55 0.137±0.011 0.192±0.019? 0.109±0.014 0.154±0.017? 0.109±0.010 0.157±0.017? 0.103±0.009 0.149±0.015? 0.113±0.012 0.170±0.020?
L56 0.930±0.005 0.981±0.002? 0.933±0.005 0.983±0.003? 0.932±0.007 0.982±0.003? 0.932±0.005 0.982±0.003? 0.909±0.007 0.976±0.003?
L57 0.709±0.021 0.725±0.018? 0.708±0.022 0.725±0.018? 0.707±0.022 0.722±0.019? 0.707±0.022 0.722±0.019? 0.415±0.043 0.445±0.037?
L58 0.612±0.021 0.644±0.014? 0.610±0.021 0.645±0.014? 0.608±0.021 0.638±0.014? 0.608±0.021 0.637±0.014? 0.218±0.042 0.279±0.028?
L59 0.470±0.026 0.496±0.020? 0.492±0.032 0.515±0.024? 0.443±0.031 0.479±0.018? 0.453±0.030 0.486±0.018? 0.412±0.030 0.441±0.020?
L60 0.928±0.005 0.936±0.007? 0.937±0.005 0.943±0.006? 0.928±0.006 0.936±0.007? 0.928±0.005 0.935±0.007? 0.928±0.006 0.935±0.007?
Tab.3  
ID Dataset n d L ID Dataset n d L ID Dataset n d L
S1 ac-inflam 120 6 2 S2 acute-nephritis 120 6 2 S3 arrhythmia 452 262 13
S4 audiology-std 226 59 18 S5 balance-scale 625 4 3 S6 balloons 16 4 2
S7 breast-cancer 286 9 2 S8 conn-bench-sonar 208 60 2 S9 conn-bench-vowel 528 11 11
S10 credit-approval 690 15 2 S11 cylinder-bands 512 35 2 S12 dermatology 366 34 6
S13 echocardiogram 131 10 2 S14 ecoli 336 7 8 S15 fertility 100 9 2
S16 flag 194 28 8 S17 glass 214 9 6 S18 haberman-survival 306 3 2
S19 hayes-roth 132 3 3 S20 heart-cleveland 303 13 5 S21 heart-hungarian 294 12 2
S22 heart-switzerland 123 12 2 S23 heart-va 200 12 5 S24 hepatitis 155 19 2
S25 hill-valley 606 100 2 S26 horse-colic 300 25 2 S27 ilpd-indian-liver 583 9 2
S28 image-segmentation 210 19 7 S29 ionosphere 351 33 2 S30 iris 150 4 3
S31 lenses 24 4 3 S32 low-res-spect 531 100 9 S33 lung-cancer 32 56 3
S34 lymphography 148 18 4 S35 molec-biol-promoter 106 57 2 S36 monks-1 124 6 2
S37 monks-2 169 6 2 S38 musk-1 476 166 2 S39 parkinsons 195 22 2
S40 pb-MATERIAL 106 4 3 S41 pb-REL-L 103 4 3 S42 pb-SPAN 92 4 3
S43 pb-T-OR-D 102 4 3 S44 pb-TYPE 105 4 3 S45 planning 182 12 2
S46 post-operative 90 8 3 S47 primary-tumor 330 17 15 S48 seeds 210 7 3
S49 soybean 307 35 18 S50 spect 80 22 2 S51 spectf 80 44 2
S52 st-australian-credit 690 14 2 S53 st-heart 270 13 2 S54 synthetic-control 600 60 6
S55 teaching 151 5 3 S56 trains 10 28 2 S57 vc-2classes 310 6 2
S58 vc-3classes 310 6 3 S59 wine 179 13 3 S60 zoo 101 16 7
Tab.4  
DataAccuracyPrecisionRecallF1Kappa
LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)
S1 1.000±0.000 1.000±0.000∘ 1.000±0.000 1.000±0.000∘ 1.000±0.000 1.000±0.000∘ 1.000±0.000 1.000±0.000∘ 1.000±0.000 1.000±0.000∘
S2 1.000±0.000 1.000±0.000∘ 1.000±0.000 1.000±0.000∘ 1.000±0.000 1.000±0.000∘ 1.000±0.000 1.000±0.000∘ 1.000±0.000 1.000±0.000∘
S3 0.661±0.048 0.695±0.037∘ 0.427±0.084 0.452±0.071∘ 0.384±0.083 0.415±0.058 ∘ 0.389±0.080 0.414±0.054∘ 0.457±0.082 0.494±0.066∘
S4 0.696±0.032 0.789±0.029? 0.493±0.047 0.542±0.061∘ 0.490±0.067 0.582±0.082∘ 0.473±0.045 0.549±0.067∘ 0.648±0.038 0.750±0.035?
S5 0.862±0.028 0.922±0.005? 0.580±0.016 0.615±0.003? 0.624±0.021 0.667±0.000? 0.599±0.019 0.640±0.002? 0.745±0.052 0.855±0.008?
S6 0.619±0.048 0.730±0.159∘ 0.480±0.195 0.601±0.315∘ 0.588±0.088 0.688±0.188∘ 0.515±0.152 0.623±0.260∘ 0.171±0.171 0.385±0.385∘
S7 0.711±0.036 0.727±0.031∘ 0.630±0.090 0.671±0.057∘ 0.575±0.049 0.613±0.034? 0.569±0.067 0.619±0.039∘ 0.175±0.116 0.257±0.076∘
S8 0.773±0.027 0.788±0.023∘ 0.775±0.027 0.792±0.025∘ 0.770±0.027 0.785±0.023∘ 0.770±0.027 0.786±0.023∘ 0.542±0.054 0.573±0.046∘
S9 0.557±0.046 0.801±0.019? 0.552±0.066 0.816±0.013? 0.556±0.050 0.801±0.019? 0.537±0.058 0.797±0.019? 0.512±0.051 0.781±0.021?
S10 0.858±0.041 0.861±0.040∘ 0.861±0.038 0.864±0.037∘ 0.863±0.038 0.867±0.038∘ 0.857±0.041 0.861±0.039∘ 0.717±0.080 0.723±0.078∘
S11 0.733±0.056 0.748±0.053∘ 0.730±0.068 0.742±0.058∘ 0.702±0.061 0.727±0.057∘ 0.705±0.066 0.729±0.057∘ 0.418±0.125 0.462±0.113∘
S12 0.978±0.027 0.978±0.027∘ 0.981±0.022 0.981±0.022∘ 0.976±0.030 0.976±0.030∘ 0.975±0.030 0.975±0.030∘ 0.972±0.034 0.972±0.034∘
S13 0.812±0.063 0.818±0.052∘ 0.819±0.097 0.828±0.079∘ 0.749±0.069 0.755±0.058∘ 0.766±0.075 0.773±0.063∘ 0.540±0.149 0.5353±0.124∘
S14 0.868±0.015 0.872±0.016∘ 0.642±0.030 0.646±0.029∘ 0.637±0.019 0.643±0.018 0.633±0.032 0.639±0.032∘ 0.817±0.021 0.822±0.023∘
S15 0.854±0.047 0.850±0.053∘ 0.438±0.012 0.438±0.013∘ 0.485±0.026 0.483±0.029∘ 0.460±0.014 0.459±0.016∘ ?0.030±0.048 -0.035±0.052∘
S16 0.487±0.061 0.530±0.085∘ 0.289±0.042 0.340±0.078∘ 0.310±0.051 0.363±0.076∘ 0.290±0.042 0.341±0.076∘ 0.351±0.078 0.412±0.104∘
S17 0.620±0.054 0.660±0.051∘ 0.484±0.093 0.532±0.084∘ 0.483±0.075 0.542±0.078∘ 0.472±0.076 0.525±0.076∘ 0.462±0.076 0.520±0.069∘
S18 0.737±0.016 0.751±0.033∘ 0.679±0.105 0.687±0.081∘ 0.548±0.029 0.597±0.032∘ 0.527±0.050 0.603±0.040∘ 0.120±0.065 0.233±0.078∘
S19 0.544±0.062 0.844±0.032? 0.554±0.061 0.881±0.027? 0.584±0.069 0.856±0.035? 0.546±0.060 0.860±0.032? 0.302±0.099 0.759±0.050?
S20 0.583±0.028 0.589±0.030∘ 0.303±0.054 0.329±0.078∘ 0.310±0.042 0.318±0.040∘ 0.301±0.046 0.314±0.048∘ 0.306±0.049 0.311±0.054∘
S21 0.824±0.039 0.839±0.034∘ 0.813±0.041 0.829±0.035∘ 0.800±0.048 0.819±0.043∘ 0.804±0.045 0.822±0.040∘ 0.6100±0.090 0.645±0.079∘
S22 0.371±0.050 0.392±0.048∘ 0.231±0.021 0.232±0.032∘ 0.241±0.030 0.241±0.030∘ 0.232±0.026 0.226±0.031∘ 0.090±0.067 0.094±0.069∘
S23 0.326±0.058 0.336±0.071∘ 0.255±0.064 0.303±0.082∘ 0.272±0.059 0.303±0.067∘ 0.256±0.058 0.294±0.071∘ 0.111±0.078 0.127±0.093∘
S24 0.810±0.039 0.840±0.032∘ 0.711±0.066 0.765±0.053∘ 0.723±0.085 0.728±0.069∘ 0.713±0.073 0.736±0.067∘ 0.428±0.146 0.476±0.125∘
S25 0.660±0.032 0.700±0.030? 0.775±0.011 0.787±0.029∘ 0.656±0.032 0.696±0.030? 0.615±0.050 0.672±0.040? 0.314±0.065 0.395±0.061?
S26 0.798±0.035 0.827±0.024? 0.786±0.044 0.822±0.028? 0.777±0.034 0.800±0.031? 0.780±0.036 0.807±0.029? 0.560±0.073 0.616±0.057?
S27 0.716±0.011 0.725±0.010∘ 0.626±0.028 0.653±0.034? 0.563±0.018 0.558±0.015∘ 0.557±0.024 0.545±0.023∘ 0.154±0.040 0.147±0.037∘
S28 0.864±0.016 0.872±0.029∘ 0.872±0.022 0.875±0.030∘ 0.864±0.016 0.872±0.029∘ 0.860±0.018 0.870±0.030∘ 0.841±0.019 0.851±0.034∘
S29 0.880±0.046 0.920±0.042? 0.891±0.048 0.935±0.040? 0.851±0.055 0.894±0.052? 0.863±0.053 0.908±0.049? 0.729±0.104 0.818±0.096?
S30 0.907±0.053 0.973±0.033? 0.924±0.041 0.978±0.027? 0.907±0.053 0.973±0.033? 0.904±0.058 0.973±0.033? 0.860±0.080 0.960±0.049?
S31 0.764±0.057 0.792±0.080∘ 0.717±0.125 0.782±0.085∘ 0.716±0.116 0.774±0.107∘ 0.671±0.108 0.743±0.094∘ 0.574±0.103 0.637±0.131∘
S32 0.712±0.034 0.737±0.023∘ 0.735±0.039 0.775±0.021? 0.712±0.034 0.737±0.023∘ 0.701±0.037 0.731±0.025∘ 0.691±0.037 0.718±0.025∘
S33 0.434±0.121 0.488±0.081∘ 0.446±0.140 0.538±0.103? 0.455±0.115 0.496±0.082∘ 0.430±0.123 0.489±0.081∘ 0.157±0.172 0.219±0.122∘
S34 0.823±0.039 0.849±0.025∘ 0.677±0.079 0.676±0.012∘ 0.675±0.081 0.674±0.015∘ 0.672±0.078 0.673±0.014∘ 0.661±0.076 0.707±0.050∘
S35 0.781±0.042 0.834±0.034? 0.786±0.044 0.836±0.035? 0.781±0.043 0.834±0.033? 0.780±0.043 0.834±0.033? 0.562±0.085 0.668±0.067?
S36 0.669±0.070 0.726±0.068∘ 0.674±0.074 0.742±0.070∘ 0.669±0.071 0.725±0.070∘ 0.666±0.071 0.718±0.080∘ 0.337±0.141 0.450±0.141∘
S37 0.550±0.072 0.561±0.096∘ 0.407±0.133 0.448±0.160∘ 0.459±0.066 0.481±0.100∘ 0.403±0.073 0.445±0.118∘ ?0.089±0.145 -0.043±0.219∘
S38 0.857±0.088 0.891±0.039∘ 0.858±0.052 0.891±0.039∘ 0.857±0.088 0.894±0.038∘ 0.855±0.055 0.890±0.039∘ 0.711±0.108 0.780±0.078∘
S39 0.852±0.055 0.882±0.056? 0.822±0.080 0.855±0.076? 0.780±0.061 0.830±0.066? 0.794±0.068 0.839±0.069? 0.591±0.136 0.678±0.137?
S40 0.853±0.039 0.859±0.035∘ 0.556±0.097 0.542±0.055∘ 0.597±0.070 0.619±0.049∘ 0.566±0.070 0.573±0.049∘ 0.610±0.090 0.625±0.077∘
Tab.5  
DataAccuracyPrecisionRecallF1Kappa
LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)LR(D)LR(D′)
S41 0.652±0.075 0.675±0.081∘ 0.485±0.089 0.475±0.066∘ 0.508±0.071 0.516±0.068∘ 0.487±0.077 0.486±0.067∘ 0.371±0.138 0.402±0.151∘
S42 0.693±0.063 0.713±0.050∘ 0.730±0.091 0.725±0.073∘ 0.645±0.044 0.653 ±0.068∘ 0.652±0.053 0.664±0.067 ∘ 0.481±0.086 0.506±0.094∘
S43 0.868±0.037 0.882±0.052∘ 0.683±0.202 0.759±0.170∘ 0.615±0.100 0.706±0.140∘ 0.625±0.124 0.712±0.137∘ 0.270±0.230 0.431±0.269∘
S44 0.590±0.037 0.644±0.035? 0.414±0.075 0.579±0.055? 0.432±0.043 0.530±0.043? 0.404±0.046 0.524±0.039? 0.422±0.048 0.513±0.048?
S45 0.709±0.021 0.715±0.015∘ 0.356±0.008 0.357±0.008∘ 0.496±0.012 0.500±0.000∘ 0.415±0.007 0.417±0.005∘ ?0.010±0.031 0.000±0.000∘
S46 0.680±0.079 0.680±0.079∘ 0.334±0.078 0.334±0.078∘ 0.450±0.081 0.450±0.081∘ 0.382±0.077 0.382±0.077∘ ?0.040±0.110 ?0.040±0.110∘
S47 0.503±0.100 0.509±0.041∘ 0.341±0.118 0.331±0.081∘ 0.370±0.117 0.383±0.081∘ 0.335±0.114 0.337±0.082∘ 0.428±0.118 0.439±0.076∘
S48 0.933±0.044 0.971±0.032? 0.939±0.042 0.976±0.026? 0.933±0.044 0.971±0.032? 0.932±0.044 0.971±0.032? 0.900±0.065 0.957±0.047?
S49 0.892±0.065 0.892±0.056∘ 0.907±0.078 0.900±0.048∘ 0.913±0.064 0.906±0.048∘ 0.901±0.072 0.895±0.050∘ 0.881±0.072 0.881±0.061∘
S50 0.645±0.057 0.686±0.043? 0.581±0.073 0.636±0.064? 0.571±0.064 0.592±0.042∘ 0.570±0.070 0.589±0.052? 0.149±0.134 0.204±0.093?
S51 0.752±0.055 0.785±0.064∘ 0.766±0.057 0.801±0.070∘ 0.751±0.056 0.784±0.065∘ 0.748±0.058 0.782±0.066∘ 0.503±0.111 0.569±0.129∘
S52 0.667±0.011 0.668±0.012∘ 0.458±0.085 0.562±0.044∘ 0.497±0.008 0.522±0.015∘ 0.418±0.012 0.484±0.025∘ ?0.018±0.021 0.054±0.038∘
S53 0.839±0.054 0.850±0.051∘ 0.842±0.057 0.854±0.051∘ 0.836±0.055 0.845±0.052∘ 0.836±0.056 0.847±0.053∘ 0.673±0.111 0.694±0.104∘
S54 0.940±0.024 0.960±0.021∘ 0.946±0.022 0.965±0.019∘ 0.940±0.024 0.960±0.021∘ 0.938±0.025 0.960±0.021∘ 0.928±0.029 0.952±0.026∘
S55 0.506±0.048 0.511±0.025∘ 0.508±0.049 0.518±0.027∘ 0.509±0.049 0.513±0.025∘ 0.497±0.047 0.509±0.024∘ 0.261±0.072 0.268±0.038∘
S56 0.774±0.180 0.900±0.134∘ 0.775±0.210 0.933±0.088∘ 0.742±0.188 0.900±0.128∘ 0.716±0.204 0.891±0.144∘ 0.470±0.383 0.799±0.258∘
S57 0.842±0.042 0.848±0.058∘ 0.824±0.049 0.829±0.064∘ 0.823±0.058 0.828±0.078∘ 0.819±0.050 0.825±0.071∘ 0.639±0.101 0.651±0.141∘
S58 0.852±0.050 0.858±0.050∘ 0.815±0.071 0.826±0.071∘ 0.803±0.069 0.813±0.069∘ 0.804±0.070 0.814±0.070∘ 0.761±0.082 0.772±0.082∘
S59 0.983±0.026 0.994±0.017∘ 0.983±0.026 0.994±0.017∘ 0.986±0.021 0.995±0.014∘ 0.983±0.025 0.994±0.017∘ 0.974±0.039 0.992±0.025∘
S60 0.951±0.022 0.954±0.015∘ 0.940±0.034 0.916±0.052∘ 0.891±0.041 0.901±0.038∘ 0.896±0.045 0.892±0.044∘ 0.935±0.029 0.940±0.020∘
Tab.6  
DataAccuracyPrecisionRecallF1Kappa
SVM(D)SVM(D′)SVM(D)SVM(D′)SVM(D)SVM(D′)SVM(D)SVM(D′)SVM(D)SVM(D′)
Iris 0.967±0.054 0.980±0.031 0.972±0.047 0.983±0.025 0.967±0.054 0.980±0.031 0.966±0.055 0.980±0.031 0.950±0.081 0.970±0.046
oocMer4D 0.787±0.033 0.832±0.028 0.787±0.062 0.821±0.036 0.718±0.032 0.803±0.029 0.734±0.036 0.806±0.029 0.476±0.073 0.615±0.057
Contrac 0.519±0.030 0.557±0.024 0.505±0.036 0.545±0.030 0.494±0.036 0.530±0.026 0.494±0.037 0.531±0.028 0.249±0.049 0.309±0.037
Abalone 0.642±0.025 0.654±0.023 0.644±0.029 0.653±0.030 0.640±0.025 0.651±0.023 0.635±0.026 0.647±0.026 0.464±0.038 0.481±0.034
Magic 0.792±0.005 0.852±0.005 0.781±0.005 0.851±0.006 0.748±0.007 0.818±0.006 0.759±0.006 0.830±0.005 0.520±0.012 0.662±0.011
Mean values 0.741 0.775 (↑3.4%) 0.738 0.771 (↑3.3%) 0.713 0.756 (↑4.3%) 0.718 0.759 (↑4.1%) 0.532 0.607 (↑7.5%)
Data Accuracy Precision Recall F1 Kappa
kNN(D) kNN(D′) kNN(D) kNN(D′) kNN(D) kNN(D′) kNN(D) kNN(D′) kNN(D) kNN(D′)
Iris 0.953±0.052 0.960±0.044 0.960±0.045 0.964±0.042 0.953±0.052 0.960±0.044 0.953±0.053 0.960±0.044 0.930±0.078 0.940±0.066
oocMer4D 0.739±0.055 0.793±0.038 0.734±0.036 0.806±0.029 0.773±0.050 0.728±0.048 0.698±0.058 0.768±0.046 0.399±0.114 0.537±0.093
Contrac 0.489±0.024 0.501±0.023 0.470±0.028 0.485±0.025 0.467±0.026 0.485±0.025 0.465±0.026 0.482±0.024 0.203±0.035 0.227±0.035
Abalone 0.601±0.027 0.616±0.023 0.598±0.030 0.616±0.031 0.599±0.027 0.615±0.024 0.595±0.030 0.611±0.027 0.402±0.040 0.425±0.035
Magic 0.840±0.008 0.851±0.008 0.846±0.011 0.860±0.008 0.798±0.009 0.810±0.010 0.814±0.009 0.827±0.010 0.630±0.018 0.656±0.019
Mean values 0.724 0.744 (↑2.0%) 0.722 0.746 (↑2.4%) 0.718 0.720 (↑0.2%) 0.705 0.730 (↑2.5%) 0.513 0.557 (↑4.4%)
Data Accuracy Precision Recall F1 Kappa
RF(D) RF(D′) RF(D) RF(D′) RF(D) RF(D′) RF(D) RF(D′) RF(D) RF(D′)
Iris 0.947±0.058 0.953±0.052 0.953±0.056 0.964±0.038 0.947±0.058 0.953±0.052 0.946±0.059 0.953±0.052 0.920±0.087 0.930±0.078
oocMer4D 0.761±0.034 0.787±0.032 0.730±0.039 0.764±0.040 0.728±0.048 0.747±0.037 0.728±0.043 0.753±0.036 0.456±0.086 0.507±0.073
Contrac 0.511±0.016 0.517±0.036 0.489±0.022 0.500±0.036 0.481±0.020 0.491±0.034 0.480±0.021 0.491±0.035 0.233±0.026 0.243±0.058
Abalone 0.604±0.027 0.624±0.028 0.603±0.032 0.625±0.032 0.602±0.028 0.622±0.028 0.600±0.030 0.619±0.029 0.406±0.041 0.436±0.042
Magic 0.870±0.005 0.860±0.007 0.871±0.007 0.860±0.010 0.840±0.007 0.828±0.008 0.852±0.006 0.840±0.008 0.705±0.013 0.681±0.016
Mean values 0.739 0.748 (↑0.9%) 0.729 0.743 (↑1.4%) 0.720 0.728 (↑0.8%) 0.721 0.731 (↑1.0%) 0.544 0.559 (↑1.5%)
Data Accuracy Precision Recall F1 Kappa
Percept(D) Percept(D′) Percept(D) Percept(D′) Percept(D) Percept(D′) Percept(D) Percept(D′) Percept(D) Percept(D′)
Iris 0.873±0.081 0.973±0.033 0.910±0.059 0.978±0.027 0.873±0.081 0.973±0.033 0.865±0.089 0.973±0.033 0.810±0.122 0.960±0.049
oocMer4D 0.751±0.050 0.784±0.042 0.736±0.082 0.767±0.045 0.694±0.044 0.759±0.041 0.703±0.048 0.755±0.041 0.411±0.100 0.515±0.081
Contrac 0.452±0.034 0.517±0.040 0.434±0.051 0.502±0.051 0.424±0.039 0.487±0.039 0.407±0.047 0.483±0.044 0.142±0.056 0.244±0.063
Abalone 0.604±0.054 0.594±0.042 0.589±0.078 0.596±0.050 0.598±0.056 0.592±0.040 0.574±0.072 0.564±0.050 0.404±0.083 0.392±0.062
Magic 0.745±0.023 0.776±0.019 0.735±0.026 0.757±0.022 0.700±0.022 0.746±0.017 0.704±0.022 0.749±0.018 0.418±0.038 0.500±0.036
Mean values 0.685 0.729 (↑4.4%) 0.681 0.720 (↑3.9%) 0.658 0.711 (↑5.3%) 0.651 0.705 (↑5.4%) 0.437 0.522 (↑8.5%)
Data Accuracy Precision Recall F1 Kappa
GNB(D) GNB(D′) GNB(D) GNB(D′) GNB(D) GNB(D′) GNB(D) GNB(D′) GNB(D) GNB(D′)
Iris 0.953±0.043 0.940±0.036 0.963±0.033 0.952±0.027 0.953±0.043 0.940±0.036 0.952±0.044 0.939±0.037 0.930±0.064 0.910±0.054
oocMer4D 0.593±0.052 0.675±0.080 0.599±0.040 0.680±0.060 0.610±0.045 0.696±0.070 0.580±0.049 0.663±0.076 0.193±0.083 0.353±0.133
Contrac 0.466±0.036 0.539±0.023 0.486±0.030 0.535±0.019 0.490±0.037 0.535±0.024 0.463±0.035 0.529±0.021 0.214±0.048 0.299±0.036
Abalone 0.572±0.062 0.603±0.033 0.566±0.068 0.626±0.034 0.568±0.060 0.604±0.031 0.558±0.063 0.601±0.034 0.357±0.092 0.407±0.048
Magic 0.727±0.006 0.763±0.009 0.721±0.010 0.750±0.011 0.647±0.007 0.709±0.012 0.653±0.008 0.719±0.012 0.329±0.014 0.445±0.023
Mean values 0.662 0.704 (↑4.2%) 0.667 0.709 (↑4.2%) 0.654 0.697 (↑4.3%) 0.641 0.690 (↑4.9%) 0.405 0.483 (↑7.8%)
Tab.7  
Data Benchmark AF AFX CRAMc CRAMd FSMI FSLR AssoRep
Iris 0.907±0.053 0.927±0.055 0.953±0.043 0.953±0.043 0.953±0.043 0.947±0.050 0.940±0.055 0.973±0.033
oocMer4D 0.796±0.036 0.751±0.023 0.811±0.035 0.820±0.028 0.822±0.028 0.797±0.028 0.800±0.035 0.837±0.020
Contrac 0.507±0.042 0.568±0.052 0.566±0.058 0.519±0.035 0.517±0.035 0.507±0.030 0.519±0.041 0.568±0.055
Abalone 0.647±0.020 0.640±0.023 0.659±0.022 0.650±0.015 0.651±0.017 0.647±0.019 0.635±0.012 0.662±0.021
Magic 0.791±0.006 0.837±0.007 0.844±0.008 0.845±0.008 0.844±0.008 0.791±0.007 0.787±0.008 0.850±0.008
Annealing 0.873±0.027 0.893±0.017 0.910±0.024 0.910±0.024 0.911±0.021 0.880±0.024 0.863±0.017 0.951±0.014
ctg-10classes 0.768±0.032 0.802±0.030 0.800±0.026 0.817±0.023 0.813±0.023 0.771±0.027 0.751±0.030 0.834±0.027
oocTris2F 0.797±0.030 0.815±0.036 0.815±0.031 0.828±0.043 0.829±0.040 0.795±0.031 0.785±0.031 0.836±0.030
Mean values 0.7608 (↑5.31%) 0.7791 (↑3.48%) 0.7948 (↑1.91%) 0.7927 (↑2.012%) 0.7925 (↑2.14%) 0.7669 (↑4.70%) 0.7600 (↑5.39%) 0.8139
Avg. rank 6.813 5.250 3.563 3.125 3.063 6.188 6.938 1.063
Tab.8  
Evaluation metric FF Critical value (α=0.05)
Accuracy 20.610 2.203
Tab.9  
Fig.1  
Data pCor dCor NMI MIC MICe
Iris 0.16 0.05 1.01 0.30 0.29
oocMer4D 0.36 5.90 75.37 71.23 70.37
Contrac 0.22 0.55 3.84 10.05 7.16
Abalone 0.26 1.24 3.71 10.82 11.08
Magic 1.02 7.50 7.07 58.84 59.11
AWArgsift-hist 178.90 618.08 3124.94 9956.50 15541.76
Tab.10  
  
  
  
  
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