A data representation method using distance correlation

doi:10.1007/s11704-023-3396-y

Front. Comput. Sci.

2025, Vol. 19

Issue (1) : 191303 https://doi.org/10.1007/s11704-023-3396-y

Artificial Intelligence

A data representation method using distance correlation

Xinyan LIANG¹, Yuhua QIAN^1,²(

), Qian GUO^3,⁴, 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

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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.

Keywords association representation distance correlation classification

Corresponding Author(s): Yuhua QIAN

Just Accepted Date: 01 November 2023 Issue Date: 12 March 2024

Cite this article:

Xinyan LIANG,Yuhua QIAN,Qian GUO, et al. A data representation method using distance correlation[J]. Front. Comput. Sci., 2025, 19(1): 191303.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-023-3396-y
https://academic.hep.com.cn/fcs/EN/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 Characteristics of the first group of datasets whose sample sizes are larger than 700 (Group 1)

Data	Accuracy		Precision		Recall		F1		Kappa
Data	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 Classification performance comparison between LR

(D)

and LR

(D ′)

on benchmark datasets L1-L40

Data	Accuracy		Precision		Recall		F1		Kappa
Data	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 Classification performance comparison between LR

(D)

and LR

(D ′)

on benchmark datasets L41-L60

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 Characteristics of the second group of datasets whose the numbers are smaller than 700 (Group 2)

Data	Accuracy		Precision		Recall		F1		Kappa
Data	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 Classification performance comparison between LR

(D)

and LR

(D ′)

on benchmark datasets S1-S40

Data	Accuracy		Precision		Recall		F1		Kappa
Data	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 Classification performance comparison between LR

(D)

and LR

(D ′)

on benchmark datasets S41-S60

Data	Accuracy		Precision		Recall		F1		Kappa
Data	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
Data	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
Data	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
Data	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
Data	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 Classification performance comparison between original and association-based enhancement representation using different classifiers

Data	Benchmark	AF	AF $X$	CRAM $c$	CRAM $d$	FS $M I$	FS $L R$	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 Accuracy comparison between AssoRep with other feature enhancement methods

Evaluation metric	$F F$	Critical value $(α = 0.05)$
Accuracy	20.610	2.203

Tab.9 Summary of the Friedman statistics

F F

Fig.1 Comparison between A and B (control algorithms, A and B denote the AssoRep and the baseline algorithm CRAM

d

with the best performance, and they are remarked with red star and blue star, respectively) against other comparing algorithms with the Nemenyi test. Algorithms are not connected with A (red line) and B (blue line) in the CD diagram are considered to have significantly different performance from the control algorithm (significance level

α = 0.05

)

Data	pCor	dCor	NMI	MIC	MIC $e$
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 Computation time (s) of the different association mining methods

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