Nonconvex and discriminative transfer subspace learning for unsupervised domain adaptation

doi:10.1007/s11704-023-3228-0

Front. Comput. Sci.

2025, Vol. 19

Issue (2) : 192307 https://doi.org/10.1007/s11704-023-3228-0

Artificial Intelligence

Nonconvex and discriminative transfer subspace learning for unsupervised domain adaptation

Yueying LIU, Tingjin LUO(

)

College of Science, National University of Defense Technology, Changsha 410073, China

Download: PDF(15936 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Unsupervised transfer subspace learning is one of the challenging and important topics in domain adaptation, which aims to classify unlabeled target data by using source domain information. The traditional transfer subspace learning methods often impose low-rank constraints, i.e., trace norm, to preserve data structural information of different domains. However, trace norm is only the convex surrogate to approximate the ideal low-rank constraints and may make their solutions seriously deviate from the original optimums. In addition, the traditional methods directly use the strict labels of source domain, which is difficult to deal with label noise. To solve these problems, we propose a novel nonconvex and discriminative transfer subspace learning method named NDTSL by incorporating Schatten- $p$ norm and soft label matrix. Specifically, Schatten- $p$ norm can be imposed to approximate the low-rank constraints and obtain a better low-rank representation. Then, we design and adopt soft label matrix in source domain to learn a more flexible classifier and enhance the discriminative ability of target data. Besides, due to the nonconvexity of Schatten- $p$ norm, we design an efficient alternative algorithm IALM to solve it. Finally, experimental results on several public transfer tasks demonstrate the effectiveness of NDTSL compared with several state-of-the-art methods.

Keywords transfer subspace learning unsupervised domain adaptation low-rank modeling nonconvex optimization

Corresponding Author(s): Tingjin LUO

About author: Li Liu and Yanqing Liu contributed equally to this work.

Just Accepted Date: 19 December 2023 Issue Date: 22 April 2024

Cite this article:

Yueying LIU,Tingjin LUO. Nonconvex and discriminative transfer subspace learning for unsupervised domain adaptation[J]. Front. Comput. Sci., 2025, 19(2): 192307.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-023-3228-0
https://academic.hep.com.cn/fcs/EN/Y2025/V19/I2/192307

Fig.1 A framework of NDTSL method. Schatten-

p

norm is used to impose a low-rank constraint on

Z

for preserving the original data structure;

l 1

norm is adopted to make noise matrix

E

sparsity and ensure the robustness of our model

Description	Formula
Frobenius norm	$‖ A ‖ F = ∑ i σ i (A) 2$
$l 1$ norm	$‖ A ‖ 1 = ∑ i, j \| A i j \|$
Trace norm	$‖ A ‖ ∗ = ∑ i σ i (A)$
Schatten- $p$ norm	$‖ A ‖ S p p = ∑ i = 1 m i n {m, n} σ i p (A)$

Tab.1 The formula of various norm

Tab.2 Basic description of datasets

Dataset	Measures	NN	TCA	JDA	W-BDA	JPDA	GFK	DTSL	FSSP	JLRFS	PAS	LRRCA	NDTSL
	Accuracy	.3523 $±$ .0180 $?$	.3752 $±$ .0297 $?$	.3747 $±$ .0290 $?$	.4200 $±$ .0302 $?$	.3911 $±$ .0302 $?$	.3833 $±$ .0235 $?$	.5189 $±$ .0204 $?$	.2660 $±$ .0207 $?$	.4894 $±$ .0178 $?$	.4512 $±$ .0251 $?$	.5193 $±$ .0205 $?$	.5278 $±$ .0190
C $→$ A	Precision	.3465 $±$ .0246 $?$	.3862 $±$ .0313 $?$	.3792 $±$ .0282 $?$	.4139 $±$ .0301 $?$	.3971 $±$ .0317 $?$	.4040 $±$ .0208 $?$	.5307 $±$ .0235 $?$	.2872 $±$ .0240 $?$	.4945 $±$ .0197 $?$	.4923 $±$ .0280 $?$	.5302 $±$ .0246 $?$	.5404 $±$ .0233
	Recall	.3563 $±$ .0183 $?$	.3814 $±$ .0300 $?$	.3817 $±$ .0229 $?$	.4250 $±$ .0270 $?$	.3970 $±$ .0285 $?$	.3912 $±$ .0248 $?$	.5211 $±$ .0222 $?$	.2656 $±$ .0233 $?$	.4905 $±$ .0172 $?$	.4512 $±$ .0226 $?$	.5217 $±$ .0228 $?$	.5302 $±$ .0219
	Macro-F1	.3382 $±$ .0209 $?$	.3764 $±$ .0298 $?$	.3724 $±$ .0254 $?$	.4137 $±$ .0283 $?$	.3867 $±$ .0287 $?$	.3882 $±$ .0218 $?$	.5114 $±$ .0212 $?$	.2633 $±$ .0219 $?$	.4791 $±$ .0176 $?$	.4363 $±$ .0247 $?$	.5113 $±$ .0217 $?$	.5200 $±$ .0207
	Accuracy	.3022 $±$ .0432 $?$	.2639 $±$ .0464 $?$	.3250 $±$ .0391 $?$	.3117 $±$ .0424 $?$	.2361 $±$ .0239 $?$	.2539 $±$ .0323 $?$	.3689 $±$ .0406 $?$	.2467 $±$ .0439 $?$	.3856 $±$ .0408 $⊙$	.3728 $±$ .0350 $⊙$	.3661 $±$ .0412 $?$	.3717 $±$ .0435
C $→$ W	Precision	.2882 $±$ .0422 $?$	.2736 $±$ .0556 $?$	.3269 $±$ .0444 $?$	.3157 $±$ .0446 $?$	.2263 $±$ .0359 $?$	.2990 $±$ .0407 $?$	.3910 $±$ .0477 $?$	.2546 $±$ .0491 $?$	.4157 $±$ .0495 $∘$	.4431 $±$ .0345 $∘$	.3895 $±$ .0481 $?$	.3926 $±$ .0497
	Recall	.3125 $±$ .0362 $?$	.2501 $±$ .0549 $?$	.3242 $±$ .0413 $?$	.3238 $±$ .0469 $?$	.2352 $±$ .0379 $?$	.2450 $±$ .0320 $?$	.3766 $±$ .0392 $?$	.2626 $±$ .0434 $?$	.3957 $±$ .0421 $⊙$	.3780 $±$ .0359 $⊙$	.3738 $±$ .0389 $?$	.3791 $±$ .0416
	Macro-F1	.2790 $±$ .0337 $?$	.2501 $±$ .0515 $?$	.3079 $±$ .0415 $?$	.3055 $±$ .0427 $?$	.2187 $±$ .0316 $?$	.2537 $±$ .0327 $?$	.3613 $±$ .0366 $?$	.2456 $±$ .0428 $?$	.3896 $±$ .0416 $∘$	.3907 $±$ .0318 $∘$	.3594 $±$ .0366 $?$	.3632 $±$ .0388
	Accuracy	.3448 $±$ .0714 $?$	.2833 $±$ .0571 $?$	.2708 $±$ .0487 $?$	.3510 $±$ .0660 $?$	.3510 $±$ .0649 $?$	.2958 $±$ .0403 $?$	.4719 $±$ .0602 $⊙$	.2896 $±$ .0589 $?$	.4479 $±$ .0739 $⊙$	.3865 $±$ .0646 $?$	.4729 $±$ .0597 $⊙$	.4719 $±$ .0602
C $→$ D	Precision	.2899 $±$ .0656 $?$	.2935 $±$ .0613 $?$	.2688 $±$ .0498 $?$	.3251 $±$ .0672 $?$	.3312 $±$ .0838 $?$	.2858 $±$ .0464 $?$	.4224 $±$ .0801 $⊙$	.2784 $±$ .0514 $?$	.4415 $±$ .0776 $⊙$	.3989 $±$ .0741 $⊙$	.4215 $±$ .0802 $⊙$	.4224 $±$ .0801
	Recall	.3161 $±$ .0782 $?$	.2701 $±$ .0621 $?$	.2646 $±$ .0743 $?$	.3400 $±$ .0827 $?$	.3228 $±$ .0766 $?$	.2878 $±$ .0581 $?$	.4713 $±$ .0685 $⊙$	.2592 $±$ .0672 $?$	.4481 $±$ .0686 $⊙$	.3743 $±$ .0647 $?$	.4742 $±$ .0694 $⊙$	.4713 $±$ .0685
	Macro-F1	.2791 $±$ .0590 $?$	.2528 $±$ .0563 $?$	.2439 $±$ .0534 $?$	.3113 $±$ .0630 $?$	.3071 $±$ .0710 $?$	.2640 $±$ .0448 $?$	.4180 $±$ .0649 $⊙$	.2485 $±$ .0517 $?$	.4142 $±$ .0607 $⊙$	.3459 $±$ .0545 $?$	.4192 $±$ .0648 $⊙$	.4180 $±$ .0649
	Accuracy	.3201 $±$ .0229 $?$	.3345 $±$ .0205 $?$	.3249 $±$ .0187 $?$	.3643 $±$ .0164 $?$	.3808 $±$ .0192 $?$	.3407 $±$ .0232 $?$	.4269 $±$ .0191 $⊙$	.2353 $±$ .0185 $?$	.4157 $±$ .0215 $?$	.3725 $±$ .0205 $?$	.4392 $±$ .0170 $∘$	.4327 $±$ .0202
A $→$ C	Precision	.3290 $±$ .0246 $?$	.3534 $±$ .0233 $?$	.3319 $±$ .0194 $?$	.3569 $±$ .0172 $?$	.3827 $±$ .0169 $?$	.3589 $±$ .0230 $?$	.4451 $±$ .0193 $?$	.2511 $±$ .0235 $?$	.4226 $±$ .0228 $?$	.4084 $±$ .0349 $?$	.4550 $±$ .0199 $⊙$	.4565 $±$ .0254
	Recall	.3167 $±$ .0225 $?$	.3258 $±$ .0188 $?$	.3238 $±$ .0228 $?$	.3615 $±$ .0187 $?$	.3714 $±$ .0180 $?$	.3326 $±$ .0223 $?$	.4171 $±$ .0191 $?$	.2300 $±$ .0195 $?$	.4091 $±$ .0225 $?$	.3648 $±$ .0228 $?$	.4311 $±$ .0174 $⊙$	.4274 $±$ .0213
	Macro-F1	.3144 $±$ .0223 $?$	.3239 $±$ .0189 $?$	.3175 $±$ .0192 $?$	.3532 $±$ .0165 $?$	.3669 $±$ .0157 $?$	.3313 $±$ .0210 $?$	.4133 $±$ .0163 $?$	.2263 $±$ .0188 $?$	.4081 $±$ .0205 $?$	.3414 $±$ .0206 $?$	.4271 $±$ .0157 $⊙$	.4232 $±$ .0207
	Accuracy	.3072 $±$ .0323 $?$	.2806 $±$ .0396 $?$	.2367 $±$ .0344 $?$	.2811 $±$ .0455 $?$	.2222 $±$ .0484 $?$	.2606 $±$ .0401 $?$	.3656 $±$ .0459 $∘$	.2022 $±$ .0394 $?$	.3517 $±$ .0359 $⊙$	.3700 $±$ .0434 $⊙$	.3633 $±$ .0398 $∘$	.3511 $±$ .0435
A $→$ W	Precision	.2871 $±$ .0354 $?$	.2954 $±$ .0463 $?$	.2468 $±$ .0349 $?$	.2892 $±$ .0447 $?$	.2023 $±$ .0339 $?$	.3316 $±$ .0430 $?$	.3954 $±$ .0400 $⊙$	.2201 $±$ .0511 $?$	.3588 $±$ .0425 $?$	.4533 $±$ .0464 $∘$	.4043 $±$ .0501 $∘$	.3835 $±$ .0408
	Recall	.3137 $±$ .0390 $?$	.2906 $±$ .0479 $?$	.2691 $±$ .0296 $?$	.3145 $±$ .0342 $?$	.2180 $±$ .0415 $?$	.2757 $±$ .0365 $?$	.3909 $±$ .0497 $∘$	.1986 $±$ .0332 $?$	.3686 $±$ .0463 $⊙$	.3954 $±$ .0464 $∘$	.3812 $±$ .0483 $⊙$	.3728 $±$ .0513
	Macro-F1	.2879 $±$ .0315 $?$	.2774 $±$ .0422 $?$	.2496 $±$ .0282 $?$	.2814 $±$ .0349 $?$	.2010 $±$ .0360 $?$	.2914 $±$ .0378 $?$	.3682 $±$ .0415 $∘$	.1887 $±$ .0353 $?$	.3443 $±$ .0394 $⊙$	.3969 $±$ .0413 $∘$	.3670 $±$ .0408 $∘$	.3533 $±$ .0445
	Accuracy	.2938 $±$ .0615 $?$	.3021 $±$ .0499 $?$	.3115 $±$ .0551 $?$	.4094 $±$ .0631 $⊙$	.3719 $±$ .0617 $⊙$	.3312 $±$ .0573 $?$	.3865 $±$ .0539 $⊙$	.3177 $±$ .0651 $?$	.4229 $±$ .0638 $∘$	.3823 $±$ .0613 $⊙$	.3958 $±$ .0483 $⊙$	.3906 $±$ .0553
A $→$ D	Precision	.3067 $±$ .0716 $?$	.2918 $±$ .0478 $?$	.2692 $±$ .0524 $?$	.3625 $±$ .0433 $⊙$	.2985 $±$ .0522 $?$	.3456 $±$ .0481 $?$	.3699 $±$ .0573 $⊙$	.3280 $±$ .0776 $?$	.4445 $±$ .0753 $∘$	.4043 $±$ .0642 $⊙$	.4073 $±$ .0775 $⊙$	.3872 $±$ .0651
	Recall	.3143 $±$ .0653 $?$	.3193 $±$ .0517 $?$	.3121 $±$ .0663 $?$	.3955 $±$ .0604 $?$	.3604 $±$ .0418 $?$	.3277 $±$ .0517 $?$	.4162 $±$ .0697 $⊙$	.3621 $±$ .0732 $?$	.4399 $±$ .0775 $⊙$	.3869 $±$ .0553 $?$	.4337 $±$ .0549 $⊙$	.4287 $±$ .0632
	Macro-F1	.2804 $±$ .0613 $?$	.2799 $±$ .0349 $?$	.2703 $±$ .0483 $?$	.3499 $±$ .0456 $⊙$	.3001 $±$ .0373 $?$	.3167 $±$ .0410 $?$	.3614 $±$ .0486 $⊙$	.3130 $±$ .0699 $?$	.4069 $±$ .0686 $∘$	.3628 $±$ .0519 $⊙$	.3785 $±$ .0534 $⊙$	.3687 $±$ .0531
	Accuracy	.2493 $±$ .0142 $?$	.2678 $±$ .0210 $?$	.2692 $±$ .0192 $?$	.2997 $±$ .0175 $?$	.3012 $±$ .0210 $?$	.2695 $±$ .0227 $?$	.3081 $±$ .0205 $?$	.2509 $±$ .0204 $?$	.3027 $±$ .0186 $?$	.2200 $±$ .0168 $?$	.3127 $±$ .0187 $?$	.3172 $±$ .0190
W $→$ C	Precision	.2376 $±$ .0131 $?$	.2412 $±$ .0194 $?$	.2441 $±$ .0183 $?$	.2778 $±$ .0191 $?$	.2788 $±$ .0207 $?$	.2566 $±$ .0232 $?$	.2971 $±$ .0207 $⊙$	.2268 $±$ .0200 $?$	.2743 $±$ .0192 $?$	.2663 $±$ .0188 $?$	.2937 $±$ .0174 $?$	.2995 $±$ .0188
	Recall	.2510 $±$ .0134 $?$	.2580 $±$ .0168 $?$	.2589 $±$ .0146 $?$	.2917 $±$ .0166 $?$	.2937 $±$ .0186 $?$	.2621 $±$ .0220 $?$	.3021 $±$ .0192 $?$	.2374 $±$ .0166 $?$	.2948 $±$ .0155 $?$	.2179 $±$ .0157 $?$	.3061 $±$ .0162 $?$	.3110 $±$ .0162
	Macro-F1	.2261 $±$ .0122 $?$	.2423 $±$ .0178 $?$	.2453 $±$ .0163 $?$	.2778 $±$ .0169 $?$	.2777 $±$ .0184 $?$	.2533 $±$ .0226 $?$	.2894 $±$ .0197 $?$	.2249 $±$ .0178 $?$	.2742 $±$ .0165 $?$	.1981 $±$ .0118 $?$	.2893 $±$ .0163 $?$	.2942 $±$ .0171
	Accuracy	.3106 $±$ .0223 $?$	.2873 $±$ .0202 $?$	.2924 $±$ .0216 $?$	.3382 $±$ .0239 $?$	.3469 $±$ .0222 $⊙$	.3148 $±$ .0271 $?$	.3465 $±$ .0232 $?$	.3040 $±$ .0241 $?$	.3493 $±$ .0215 $?$	.3328 $±$ .0193 $?$	.3399 $±$ .0207 $?$	.3531 $±$ .0217
W $→$ A	Precision	.2908 $±$ .0227 $?$	.2808 $±$ .0152 $?$	.2820 $±$ .0166 $?$	.3241 $±$ .0260 $?$	.3312 $±$ .0211 $?$	.3262 $±$ .0267 $?$	.3490 $±$ .0258 $⊙$	.2719 $±$ .0193 $?$	.3390 $±$ .0227 $?$	.3666 $±$ .0198 $∘$	.3539 $±$ .0166 $⊙$	.3446 $±$ .0278
	Recall	.3140 $±$ .0221 $?$	.2920 $±$ .0157 $?$	.2980 $±$ .0153 $?$	.3486 $±$ .0190 $?$	.3552 $±$ .0190 $⊙$	.3206 $±$ .0210 $?$	.3516 $±$ .0204 $?$	.3109 $±$ .0210 $?$	.3540 $±$ .0173 $?$	.3315 $±$ .0199 $?$	.3427 $±$ .0183 $?$	.3583 $±$ .0199
	Macro-F1	.2864 $±$ .0203 $?$	.2781 $±$ .0155 $?$	.2798 $±$ .0161 $?$	.3285 $±$ .0207 $?$	.3379 $±$ .0183 $⊙$	.3134 $±$ .0216 $?$	.3393 $±$ .0192 $⊙$	.2820 $±$ .0184 $?$	.3361 $±$ .0172 $⊙$	.3128 $±$ .0187 $?$	.3354 $±$ .0179 $⊙$	.3394 $±$ .0191
	Accuracy	.8271 $±$ .0478 $?$	.6823 $±$ .0363 $?$	.7010 $±$ .0559 $?$	.7094 $±$ .0466 $?$	.7156 $±$ .0516 $?$	.6823 $±$ .0405 $?$	.8260 $±$ .0396 $?$	.6906 $±$ .0628 $?$	.8438 $±$ .0391 $?$	.8063 $±$ .0444 $?$	.8396 $±$ .0371 $?$	.8719 $±$ .0434
W $→$ D	Precision	.8082 $±$ .0680 $?$	.6755 $±$ .0627 $?$	.6884 $±$ .0828 $?$	.6763 $±$ .0806 $?$	.7022 $±$ .0686 $?$	.6542 $±$ .0716 $?$	.8267 $±$ .0521 $?$	.7034 $±$ .0767 $?$	.8419 $±$ .0519 $?$	.8166 $±$ .0682 $?$	.8515 $±$ .0420 $?$	.8875 $±$ .0533
	Recall	.8316 $±$ .0597 $?$	.6690 $±$ .0377 $?$	.7113 $±$ .0578 $?$	.7128 $±$ .0488 $?$	.7199 $±$ .0561 $?$	.6736 $±$ .0544 $?$	.8239 $±$ .0585 $?$	.7121 $±$ .0787 $?$	.8474 $±$ .0594 $?$	.8261 $±$ .0481 $?$	.8456 $±$ .0484 $?$	.8825 $±$ .0660
	Macro-F1	.7982 $±$ .0683 $?$	.6394 $±$ .0431 $?$	.6792 $±$ .0669 $?$	.6712 $±$ .0596 $?$	.6824 $±$ .0614 $?$	.6427 $±$ .0637 $?$	.8104 $±$ .0534 $?$	.6896 $±$ .0733 $?$	.8264 $±$ .0558 $?$	.8038 $±$ .0614 $?$	.8270 $±$ .0443 $?$	.8707 $±$ .0597
	Accuracy	.2839 $±$ .0208 $?$	.2775 $±$ .0164 $?$	.2769 $±$ .0176 $?$	.2831 $±$ .0157 $?$	.2947 $±$ .0155 $?$	.2799 $±$ .0222 $?$	.3250 $±$ .0216 $?$	.2581 $±$ .0221 $?$	.3226 $±$ .0225 $?$	.2456 $±$ .0160 $?$	.3272 $±$ .0219 $?$	.3315 $±$ .0222
D $→$ C	Precision	.2512 $±$ .0205 $?$	.2710 $±$ .0130 $?$	.2723 $±$ .0130 $?$	.2716 $±$ .0146 $?$	.2650 $±$ .0190 $?$	.2820 $±$ .0243 $?$	.3160 $±$ .0298 $?$	.2407 $±$ .0259 $?$	.3165 $±$ .0299 $?$	.2654 $±$ .0289 $?$	.3206 $±$ .0288 $?$	.3299 $±$ .0309
	Recall	.2711 $±$ .0150 $?$	.2666 $±$ .0155 $?$	.2663 $±$ .0164 $?$	.2717 $±$ .0139 $?$	.2838 $±$ .0122 $?$	.2746 $±$ .0174 $?$	.3103 $±$ .0212 $?$	.2408 $±$ .0193 $?$	.3054 $±$ .0199 $?$	.2316 $±$ .0137 $?$	.3132 $±$ .0213 $?$	.3192 $±$ .0227
	Macro-F1	.2501 $±$ .0174 $?$	.2614 $±$ .0138 $?$	.2614 $±$ .0145 $?$	.2636 $±$ .0131 $?$	.2647 $±$ .0142 $?$	.2637 $±$ .0176 $?$	.2867 $±$ .0237 $?$	.2322 $±$ .0177 $?$	.2878 $±$ .0222 $?$	.1879 $±$ .0150 $?$	.2911 $±$ .0235 $?$	.2948 $±$ .0246
	Accuracy	.3120 $±$ .0243 $?$	.3031 $±$ .0172 $?$	.2983 $±$ .0187 $?$	.3155 $±$ .0248 $?$	.3297 $±$ .0251 $?$	.2955 $±$ .0201 $?$	.3455 $±$ .0235 $?$	.2925 $±$ .0196 $?$	.3715 $±$ .0212 $∘$	.2826 $±$ .0182 $?$	.3519 $±$ .0214 $?$	.3608 $±$ .0228
D $→$ A	Precision	.2946 $±$ .0255 $?$	.2769 $±$ .0108 $?$	.2620 $±$ .0118 $?$	.2907 $±$ .0176 $?$	.3105 $±$ .0313 $?$	.3013 $±$ .0237 $?$	.3467 $±$ .0273 $⊙$	.2824 $±$ .0215 $?$	.3582 $±$ .0279 $⊙$	.2917 $±$ .0157 $?$	.3549 $±$ .0306 $⊙$	.3508 $±$ .0283
	Recall	.3181 $±$ .0183 $?$	.3067 $±$ .0145 $?$	.3017 $±$ .0144 $?$	.3198 $±$ .0176 $?$	.3354 $±$ .0205 $?$	.2999 $±$ .0154 $?$	.3471 $±$ .0218 $?$	.2963 $±$ .0196 $?$	.3725 $±$ .0203 $∘$	.2850 $±$ .0121 $?$	.3528 $±$ .0200 $?$	.3620 $±$ .0212
	Macro-F1	.2912 $±$ .0209 $?$	.2843 $±$ .0114 $?$	.2736 $±$ .0115 $?$	.2955 $±$ .0164 $?$	.3133 $±$ .0221 $?$	.2846 $±$ .0152 $?$	.3286 $±$ .0215 $?$	.2786 $±$ .0174 $?$	.3476 $±$ .0201 $∘$	.2546 $±$ .0096 $?$	.3302 $±$ .0198 $?$	.3391 $±$ .0207
	Accuracy	.6394 $±$ .0490 $?$	.6111 $±$ .0390 $?$	.7539 $±$ .0365 $⊙$	.6961 $±$ .0473 $?$	.6650 $±$ .0366 $?$	.6256 $±$ .0387 $?$	.7600 $±$ .0435 $⊙$	.6389 $±$ .0561 $?$	.7672 $±$ .0365 $⊙$	.7078 $±$ .0312 $?$	.7461 $±$ .0387 $?$	.7667 $±$ .0390
D $→$ W	Precision	.7202 $±$ .0487 $?$	.6644 $±$ .0503 $?$	.7905 $±$ .0358 $⊙$	.7256 $±$ .0500 $?$	.7209 $±$ .0444 $?$	.6972 $±$ .0366 $?$	.7870 $±$ .0422 $?$	.6618 $±$ .0558 $?$	.8115 $±$ .0372 $⊙$	.8024 $±$ .0361 $⊙$	.7773 $±$ .0381 $?$	.8012 $±$ .0373
	Recall	.6504 $±$ .0533 $?$	.6147 $±$ .0427 $?$	.7543 $±$ .0395 $?$	.6912 $±$ .0552 $?$	.6616 $±$ .0448 $?$	.6256 $±$ .0499 $?$	.7634 $±$ .0457 $⊙$	.6286 $±$ .0637 $?$	.7695 $±$ .0413 $⊙$	.7085 $±$ .0329 $?$	.7513 $±$ .0390 $?$	.7746 $±$ .0348
	Macro-F1	.6432 $±$ .0523 $?$	.6109 $±$ .0436 $?$	.7601 $±$ .0362 $⊙$	.6936 $±$ .0528 $?$	.6637 $±$ .0440 $?$	.6264 $±$ .0461 $?$	.7607 $±$ .0438 $⊙$	.6288 $±$ .0619 $?$	.7632 $±$ .0414 $⊙$	.7156 $±$ .0348 $?$	.7498 $±$ .0381 $?$	.7715 $±$ .0344
win/tie/loss		48/0/0	48/0/0	45/3/0	45/3/0	44/4/0	48/0/0	28/17/3	48/0/0	24/16/8	34/8/6	29/15/4	?

Tab.3 Four evaluation metrics: Accuracy, Precision, Recall, and Macro-F1 of different methods on Office+Caltech10 by NN classifier. The best results on each row are bolded, and

? / ⊙ / ∘

means that the NDTSL method is better/tied/worse than other methods. (pairwise single-tailed t-test at 95% confidence level)

Dataset	Measures	NN	TCA	JDA	W-BDA	JPDA	GFK	DTSL	FSSP	JLRFS	PAS	LRRCA	NDTSL
	Accuracy	.6297 $±$ .0144 $?$	.5314 $±$ .0143 $?$	.5591 $±$ .0170 $?$	.5728 $±$ .0113 $?$	.5530 $±$ .0095 $?$	.5814 $±$ .0092 $?$	.6740 $±$ .0094 $⊙$	.5743 $±$ .0146 $?$	.6699 $±$ .0121 $?$	.5615 $±$ .0151 $?$	.6746 $±$ .0125 $?$	.6769 $±$ .0113
V $→$ S	Precision	.4131 $±$ .0125 $?$	.3831 $±$ .0128 $?$	.3856 $±$ .0130 $?$	.3836 $±$ .0087 $?$	.3801 $±$ .0098 $?$	.4004 $±$ .0085 $?$	.4774 $±$ .0194 $⊙$	.3804 $±$ .0130 $?$	.4882 $±$ .0411 $⊙$	.4547 $±$ .0176 $?$	.4812 $±$ .0271 $?$	.4837 $±$ .0270
	Recall	.4584 $±$ .0303 $?$	.4078 $±$ .0450 $?$	.4064 $±$ .0442 $?$	.3937 $±$ .0272 $?$	.4189 $±$ .0408 $?$	.4681 $±$ .0361 $?$	.5908 $±$ .0496 $⊙$	.4198 $±$ .0296 $?$	.5332 $±$ .0619 $?$	.5890 $±$ .0347 $⊙$	.5808 $±$ .0634 $?$	.5830 $±$ .0636
	Macro-F1	.4154 $±$ .0158 $?$	.3629 $±$ .0131 $?$	.3743 $±$ .0159 $?$	.3759 $±$ .0117 $?$	.3741 $±$ .0143 $?$	.3995 $±$ .0121 $?$	.4954 $±$ .0230 $⊙$	.3825 $±$ .0170 $?$	.4914 $±$ .0374 $⊙$	.3920 $±$ .0215 $?$	.4957 $±$ .0312 $?$	.4985 $±$ .0310
	Accuracy	.5469 $±$ .0193 $?$	.4446 $±$ .0158 $?$	.5086 $±$ .0177 $?$	.5171 $±$ .0139 $?$	.5528 $±$ .0130 $?$	.5297 $±$ .0156 $?$	.5716 $±$ .0143 $⊙$	.4810 $±$ .0191 $?$	.5698 $±$ .0164 $⊙$	.4063 $±$ .0185 $?$	.5709 $±$ .0143 $⊙$	.5735 $±$ .0142
V $→$ L	Precision	.4915 $±$ .0280 $⊙$	.2741 $±$ .0096 $?$	.3281 $±$ .0298 $?$	.3920 $±$ .0409 $?$	.3742 $±$ .0279 $?$	.3996 $±$ .0232 $?$	.4874 $±$ .0268 $⊙$	.3313 $±$ .0344 $?$	.5042 $±$ .0238 $∘$	.4039 $±$ .0466 $?$	.4869 $±$ .0268 $⊙$	.4891 $±$ .0216
	Recall	.4314 $±$ .0318 $?$	.3168 $±$ .0175 $?$	.3581 $±$ .0361 $?$	.3734 $±$ .0387 $?$	.3863 $±$ .0311 $?$	.3993 $±$ .0386 $?$	.4762 $±$ .0294 $?$	.3338 $±$ .0363 $?$	.4789 $±$ .0267 $?$	.4361 $±$ .0327 $?$	.4759 $±$ .0294 $?$	.4861 $±$ .0307
	Macro-F1	.4231 $±$ .0261 $?$	.2646 $±$ .0109 $?$	.3296 $±$ .0295 $?$	.3575 $±$ .0358 $?$	.3673 $±$ .0279 $?$	.3766 $±$ .0267 $?$	.4477 $±$ .0246 $⊙$	.3036 $±$ .0333 $?$	.4615 $±$ .0206 $⊙$	.2961 $±$ .0247 $?$	.4473 $±$ .0245 $⊙$	.4564 $±$ .0221
	Accuracy	.5341 $±$ .0133 $?$	.5219 $±$ .0142 $?$	.5422 $±$ .0159 $?$	.5414 $±$ .0148 $?$	.5339 $±$ .0157 $?$	.5498 $±$ .0156 $?$	.5541 $±$ .0154 $?$	.6321 $±$ .0167 $∘$	.5470 $±$ .0119 $?$	.3681 $±$ .0114 $?$	.5575 $±$ .0153 $⊙$	.5614 $±$ .0143
S $→$ V	Precision	.5382 $±$ .0340 $⊙$	.4276 $±$ .0498 $?$	.4269 $±$ .0360 $?$	.4076 $±$ .0482 $?$	.4442 $±$ .0455 $?$	.5502 $±$ .0345 $⊙$	.5915 $±$ .0531 $∘$	.6527 $±$ .0177 $∘$	.5148 $±$ .1309 $⊙$	.4335 $±$ .0116 $?$	.5884 $±$ .0537 $∘$	.5543 $±$ .0295
	Recall	.4387 $±$ .0139 $?$	.3967 $±$ .0098 $?$	.4171 $±$ .0111 $?$	.4011 $±$ .0112 $?$	.4020 $±$ .0121 $?$	.4313 $±$ .0152 $?$	.4237 $±$ .0113 $?$	.5629 $±$ .0188 $∘$	.4052 $±$ .0076 $?$	.4448 $±$ .0123 $⊙$	.4269 $±$ .0108 $?$	.4474 $±$ .0135
	Macro-F1	.4226 $±$ .0195 $?$	.3560 $±$ .0112 $?$	.3731 $±$ .0114 $?$	.3667 $±$ .0109 $?$	.3723 $±$ .0145 $?$	.4226 $±$ .0180 $?$	.3990 $±$ .0143 $?$	.5833 $±$ .0189 $∘$	.3597 $±$ .0094 $?$	.3917 $±$ .0109 $?$	.4019 $±$ .0143 $?$	.4362 $±$ .0166
	Accuracy	.5128 $±$ .0144 $?$	.5044 $±$ .0213 $?$	.5169 $±$ .0165 $?$	.5367 $±$ .0157 $?$	.5361 $±$ .0180 $?$	.5214 $±$ .0147 $?$	.5724 $±$ .0156 $⊙$	.5052 $±$ .0167 $?$	.5652 $±$ .0208 $?$	.2672 $±$ .0105 $?$	.5719 $±$ .0164 $⊙$	.5739 $±$ .0169
S $→$ L	Precision	.3446 $±$ .0834 $?$	.2781 $±$ .0353 $?$	.2966 $±$ .0411 $?$	.3114 $±$ .0630 $?$	.3754 $±$ .0810 $⊙$	.3839 $±$ .0985 $⊙$	.4385 $±$ .1490 $⊙$	.2469 $±$ .0283 $?$	.4184 $±$ .1566 $⊙$	.2979 $±$ .0121 $?$	.4387 $±$ .1493 $⊙$	.4136 $±$ .1350
	Recall	.2705 $±$ .0201 $?$	.2800 $±$ .0275 $⊙$	.2597 $±$ .0167 $?$	.2619 $±$ .0159 $?$	.2909 $±$ .0175 $⊙$	.2912 $±$ .0279 $⊙$	.2842 $±$ .0133 $?$	.2524 $±$ .0185 $?$	.2910 $±$ .0209 $⊙$	.1894 $±$ .0203 $?$	.2840 $±$ .0135 $⊙$	.2907 $±$ .0153
	Macro-F1	.2466 $±$ .0255 $?$	.2594 $±$ .0227 $?$	.2491 $±$ .0154 $?$	.2467 $±$ .0123 $?$	.2642 $±$ .0158 $?$	.2767 $±$ .0304 $⊙$	.2764 $±$ .0198 $⊙$	.2296 $±$ .0160 $?$	.2793 $±$ .0268 $⊙$	.2007 $±$ .0103 $?$	.2764 $±$ .0201 $⊙$	.2820 $±$ .0222
	Accuracy	.5478 $±$ .0126 $?$	.4606 $±$ .0147 $?$	.5118 $±$ .0134 $?$	.5348 $±$ .0153 $?$	.4733 $±$ .0148 $?$	.5452 $±$ .0147 $?$	.5479 $±$ .0141 $?$	.5247 $±$ .0124 $?$	.5355 $±$ .0162 $?$	.1850 $±$ .0109 $?$	.5448 $±$ .0145 $?$	.5568 $±$ .0141
L $→$ V	Precision	.5286 $±$ .0147 $?$	.3793 $±$ .0260 $?$	.4347 $±$ .0157 $?$	.4444 $±$ .0178 $?$	.4508 $±$ .0228 $?$	.4841 $±$ .0140 $?$	.5366 $±$ .0178 $?$	.4778 $±$ .0167 $?$	.3546 $±$ .0151 $?$	.3143 $±$ .0119 $?$	.5380 $±$ .0177 $?$	.5444 $±$ .0176
	Recall	.4947 $±$ .0100 $∘$	.3302 $±$ .0118 $?$	.4365 $±$ .0144 $?$	.4085 $±$ .0087 $?$	.3988 $±$ .0124 $?$	.4806 $±$ .0134 $⊙$	.4740 $±$ .0132 $?$	.4791 $±$ .0156 $⊙$	.4281 $±$ .0106 $?$	.2866 $±$ .0080 $?$	.4647 $±$ .0135 $?$	.4813 $±$ .0159
	Macro-F1	.4824 $±$ .0104 $⊙$	.3109 $±$ .0136 $?$	.4306 $±$ .0148 $?$	.4022 $±$ .0104 $?$	.3861 $±$ .0145 $?$	.4787 $±$ .0134 $⊙$	.4820 $±$ .0135 $⊙$	.4773 $±$ .0154 $⊙$	.3788 $±$ .0107 $?$	.2093 $±$ .0093 $?$	.4707 $±$ .0139 $?$	.4815 $±$ .0158
	Accuracy	.4402 $±$ .0118 $?$	.3980 $±$ .0151 $?$	.4512 $±$ .0186 $?$	.4700 $±$ .0131 $?$	.4499 $±$ .0122 $?$	.4684 $±$ .0134 $?$	.4899 $±$ .0152 $?$	.4672 $±$ .0154 $?$	.4337 $±$ .0121 $?$	.3864 $±$ .0150 $?$	.4902 $±$ .0144 $?$	.5034 $±$ .0136
L $→$ S	Precision	.3320 $±$ .0175 $?$	.2755 $±$ .0146 $?$	.3232 $±$ .0147 $?$	.3318 $±$ .0079 $?$	.3332 $±$ .0116 $?$	.3477 $±$ .0129 $?$	.3500 $±$ .0226 $?$	.3345 $±$ .0129 $?$	.3805 $±$ .0267 $∘$	.3342 $±$ .0170 $?$	.3505 $±$ .0231 $?$	.3599 $±$ .0219
	Recall	.3553 $±$ .0483 $?$	.2590 $±$ .0293 $?$	.3213 $±$ .0353 $?$	.3383 $±$ .0266 $?$	.3642 $±$ .0609 $?$	.4003 $±$ .0412 $⊙$	.3659 $±$ .0399 $?$	.3281 $±$ .0328 $?$	.3389 $±$ .0487 $?$	.4401 $±$ .0280 $∘$	.3661 $±$ .0393 $?$	.3963 $±$ .0357
	Macro-F1	.3000 $±$ .0197	.2322 $±$ .0141 $?$	.2986 $±$ .0172 $?$	.3106 $±$ .0097 $?$	.2986 $±$ .0122 $?$	.3231 $±$ .0143 $?$	.3325 $±$ .0196 $?$	.3071 $±$ .0164 $?$	.2606 $±$ .0190 $?$	.2417 $±$ .0107 $?$	.3328 $±$ .0200 $?$	.3509 $±$ .0211
win/tie/loss		20/3/1	23/1/0	24/0/0	24/0/0	22/2/0	18/6/0	12/11/1	18/2/4	14/8/2	21/2/1	15/8/1	?

Tab.4 Four evaluation metrics: Accuracy, Precision, Recall, and Macro-F1 of different methods on VSL by NN classifier. The best results on each row are bolded, and

? / ⊙ / ∘

means that the NDTSL method is better/tied/worse than other methods. (pairwise single-tailed t-test at 95% confidence level)

Dataset	Measures	SVM	TCA	JDA	W-BDA	JPDA	GFK	DTSL	FSSP	JLRFS	PAS	LRRCA	NDTSL
	Accuracy	.5033 $±$ .0157 $?$	.4453 $±$ .0210 $?$	.4347 $±$ .0223 $?$	.4668 $±$ .0179 $?$	.4627 $±$ .0211 $?$	.4545 $±$ .0216 $?$	.5161 $±$ .0204 $?$	.3203 $±$ .0178 $?$	.5128 $±$ .0264 $?$	.4512 $±$ .0215 $?$	.5224 $±$ .0241 $?$	.5403 $±$ .0223
C $→$ A	Precision	.5302 $±$ .0226 $?$	.4382 $±$ .0304 $?$	.4298 $±$ .0287 $?$	.4757 $±$ .0258 $?$	.4742 $±$ .0310 $?$	.4640 $±$ .0238 $?$	.5435 $±$ .0204 $?$	.3718 $±$ .0263 $?$	.5262 $±$ .0271 $?$	.4923 $±$ .0280 $?$	.5408 $±$ .0249 $?$	.5560 $±$ .0240
	Recall	.5065 $±$ .0186 $?$	.4486 $±$ .0218 $?$	.4363 $±$ .0223 $?$	.4715 $±$ .0202 $?$	.4676 $±$ .0228 $?$	.4608 $±$ .0232 $?$	.5184 $±$ .0206 $?$	.3218 $±$ .0186 $?$	.5150 $±$ .0258 $?$	.4512 $±$ .0226 $?$	.5255 $±$ .0227 $?$	.5434 $±$ .0223
	Macro-F1	.4953 $±$ .0183 $?$	.4186 $±$ .0220 $?$	.4105 $±$ .0224 $?$	.4531 $±$ .0216 $?$	.4480 $±$ .0242 $?$	.4456 $±$ .0225 $?$	.5070 $±$ .0196 $?$	.3064 $±$ .0180 $?$	.5030 $±$ .0256 $?$	.4363 $±$ .0247 $?$	.5146 $±$ .0224 $?$	.5303 $±$ .0243
	Accuracy	.3361 $±$ .0362 $?$	.3472 $±$ .0381 $?$	.3672 $±$ .0377 $?$	.3694 $±$ .0391 $?$	.2944 $±$ .0352 $?$	.2672 $±$ .0379 $?$	.3917 $±$ .0474 $?$	.3350 $±$ .0462 $?$	.3850 $±$ .0387 $?$	.3728 $±$ .0350 $?$	.4239 $±$ .0462 $?$	.4411 $±$ .0364
C $→$ W	Precision	.3803 $±$ .0318 $?$	.3162 $±$ .0542 $?$	.3126 $±$ .0458 $?$	.3487 $±$ .0510 $?$	.3124 $±$ .0268 $?$	.2980 $±$ .0443 $?$	.4414 $±$ .0400 $?$	.3862 $±$ .0498 $?$	.4136 $±$ .0508 $?$	.4431 $±$ .0345 $⊙$	.3952 $±$ .0404 $?$	.4746 $±$ .0579
	Recall	.3494 $±$ .0453 $?$	.3613 $±$ .0281 $?$	.3815 $±$ .0229 $?$	.3683 $±$ .0334 $?$	.2986 $±$ .0225 $?$	.2759 $±$ .0396 $?$	.3943 $±$ .0418 $?$	.3399 $±$ .0349 $?$	.3929 $±$ .0408 $?$	.3780 $±$ .0359 $?$	.4204 $±$ .0402 $?$	.4407 $±$ .0330
	Macro-F1	.3458 $±$ .0352 $?$	.2987 $±$ .0313 $?$	.3090 $±$ .0265 $?$	.3191 $±$ .0313 $?$	.2891 $±$ .0217 $?$	.2757 $±$ .0402 $?$	.4001 $±$ .0407 $?$	.3347 $±$ .0394 $?$	.3849 $±$ .0405 $?$	.3907 $±$ .0318 $?$	.3900 $±$ .0371 $?$	.4347 $±$ .0377
	Accuracy	.3948 $±$ .0461 $?$	.3865 $±$ .0606 $?$	.3510 $±$ .0575 $?$	.4750 $±$ .0664 $?$	.4281 $±$ .0636 $?$	.3813 $±$ .0478 $?$	.4719 $±$ .0617 $?$	.4365 $±$ .0681 $?$	.4688 $±$ .0543 $?$	.3865 $±$ .0646 $?$	.5312 $±$ .0751 $⊙$	.5146 $±$ .0612
C $→$ D	Precision	.3509 $±$ .0592 $?$	.2755 $±$ .0516 $?$	.2453 $±$ .0453 $?$	.4079 $±$ .0742 $⊙$	.3662 $±$ .0739 $⊙$	.3139 $±$ .0531 $?$	.4324 $±$ .0836 $∘$	.3503 $±$ .0566 $?$	.3969 $±$ .0525 $⊙$	.3989 $±$ .0741 $⊙$	.4404 $±$ .0695 $∘$	.3824 $±$ .0497
	Recall	.3811 $±$ .0469 $?$	.3288 $±$ .0546 $?$	.3004 $±$ .0564 $?$	.4532 $±$ .0829 $⊙$	.4035 $±$ .0647 $?$	.3560 $±$ .0498 $?$	.4626 $±$ .0640 $⊙$	.3869 $±$ .0658 $?$	.4137 $±$ 0308 $?$	.3743 $±$ .0647 $?$	.5069 $±$ .0526 $∘$	.4838 $±$ .0514
	Macro-F1	.3421 $±$ .0470 $?$	.2763 $±$ .0474 $?$	.2540 $±$ .0461 $?$	.4010 $±$ .0691 $⊙$	.3600 $±$ .0617 $?$	.3141 $±$ .0470 $?$	.4193 $±$ .0678 $⊙$	.3418 $±$ .0577 $?$	.3902 $±$ .0400 $?$	.3459 $±$ .0545 $?$	.4428 $±$ .0552 $∘$	.4075 $±$ .0462
	Accuracy	.4382 $±$ .0154 $?$	.3654 $±$ .0176 $?$	.3849 $±$ .0222 $?$	.3981 $±$ .0184 $?$	.4093 $±$ .0139 $?$	.3754 $±$ .0186 $?$	.4365 $±$ .0137 $?$	.2994 $±$ .0232 $?$	.4357 $±$ .0189 $?$	.3725 $±$ .0205 $?$	.4388 $±$ .0151 $?$	.4490 $±$ .0148
A $→$ C	Precision	.4812 $±$ .0172 $⊙$	.4094 $±$ .0190 $?$	.4028 $±$ .0204 $?$	.4186 $±$ .0186 $?$	.4471 $±$ .0142 $?$	.4225 $±$ .0211 $?$	.4494 $±$ .0172 $?$	.3310 $±$ .0295 $?$	.4742 $±$ .0237 $?$	.4084 $±$ .0349 $?$	.4530 $±$ .0181 $?$	.4844 $±$ .0235
	Recall	.4295 $±$ .0154 $?$	.3592 $±$ .0200 $?$	.3822 $±$ .0242 $?$	.3913 $±$ .0208 $?$	.3988 $±$ .0152 $?$	.3675 $±$ .0203 $?$	.4272 $±$ .0141 $?$	.2852 $±$ .0241 $?$	.4246 $±$ .0188 $?$	.3648 $±$ .0228 $?$	.4292 $±$ .0141 $?$	.4399 $±$ .0159
	Macro-F1	.4288 $±$ .0148 $⊙$	.3559 $±$ .0191 $?$	.3806 $±$ .0213 $?$	.3925 $±$ .0182 $?$	.4086 $±$ .0132 $?$	.3685 $±$ .0185 $?$	.4200 $±$ .0142 $?$	.2802 $±$ .0229 $?$	.4213 $±$ .0177 $?$	.3414 $±$ .0206 $?$	.4223 $±$ .0152 $?$	.4350 $±$ .0150
	Accuracy	.3433 $±$ .0388 $?$	.2683 $±$ .0405 $?$	.3061 $±$ .0381 $?$	.3044 $±$ .0377 $?$	.2200 $±$ .0376 $?$	.3200 $±$ .0442 $?$	.3756 $±$ .0430 $?$	.2583 $±$ .0481 $?$	.3489 $±$ .0446 $?$	.3700 $±$ .0434 $?$	.3956 $±$ .0439 $?$	.4089 $±$ .0401
A $→$ W	Precision	.4072 $±$ .0475 $⊙$	.3081 $±$ .0624 $?$	.3136 $±$ .0345 $?$	.2823 $±$ .0359 $?$	.2651 $±$ .0468 $?$	.3804 $±$ .0523 $⊙$	.3790 $±$ .0520 $?$	.3347 $±$ .0459 $?$	.3509 $±$ .0472 $?$	.4533 $±$ .0464 $∘$	.4039 $±$ .0494 $⊙$	.4088 $±$ .0468
	Recall	.3596 $±$ .0387 $?$	.2837 $±$ .0443 $?$	.3423 $±$ .0379 $?$	.3518 $±$ .0337 $?$	.2350 $±$ .0406 $?$	.3529 $±$ .0503 $?$	.4061 $±$ .0463 $?$	.2905 $±$ .0489 $?$	.3832 $±$ .0518 $?$	.3954 $±$ .0464 $?$	.4271 $±$ .0468 $?$	.4433 $±$ .0416
	Macro-F1	.3592 $±$ .0399 $?$	.2658 $±$ .0454 $?$	.3177 $±$ .0324 $?$	.3003 $±$ .0342 $?$	.2308 $±$ .0404 $?$	.3324 $±$ .0558 $?$	.3763 $±$ .0373 $?$	.2670 $±$ .0492 $?$	.3542 $±$ .0438 $?$	.3969 $±$ .0413 $⊙$	.3983 $±$ .0388 $?$	.4074 $±$ .0369
	Accuracy	.3979 $±$ .0585 $?$	.3135 $±$ .0530 $?$	.3625 $±$ .0723 $?$	.4427 $±$ .0630 $⊙$	.3750 $±$ .0561 $?$	.3260 $±$ .0621 $?$	.3875 $±$ .0639 $?$	.3458 $±$ .0538 $?$	.4083 $±$ .0657 $⊙$	.3823 $±$ .0613 $?$	.3760 $±$ .0567 $?$	.4240 $±$ .0493
A $→$ D	Precision	.3959 $±$ .0930 $⊙$	.3181 $±$ .0503 $?$	.3180 $±$ .0582 $?$	.4368 $±$ .0856 $⊙$	.3152 $±$ .0359 $?$	.3409 $±$ .0626 $?$	.3635 $±$ .0785 $?$	.4329 $±$ .0413 $⊙$	.4075 $±$ .0567 $⊙$	.4043 $±$ .0642 $⊙$	.3996 $±$ .0738 $⊙$	.4055 $±$ .0651
	Recall	.4208 $±$ .0828 $?$	.3285 $±$ .0569 $?$	.3704 $±$ .0589 $?$	.4434 $±$ .0552 $⊙$	.3705 $±$ .0432 $?$	.3523 $±$ .0611 $?$	.4260 $±$ .0649 $?$	.3818 $±$ .0664 $?$	.4328 $±$ .0699 $?$	.3869 $±$ .0553 $?$	.4174 $±$ .0634 $?$	.4618 $±$ .0490
	Macro-F1	.3737 $±$ .0703 $⊙$	.2859 $±$ .0474 $?$	.3192 $±$ .0526 $?$	.4101 $±$ .0623 $⊙$	.3208 $±$ .0333 $?$	.3176 $±$ .0548 $?$	.3477 $±$ .0499 $?$	.3689 $±$ .0522 $⊙$	.3838 $±$ .0612 $⊙$	.3628 $±$ .0519 $?$	.3698 $±$ .0589 $?$	.3906 $±$ .0476
	Accuracy	.3061 $±$ .0199 $?$	.2533 $±$ .0200 $?$	.2672 $±$ .0184 $?$	.3135 $±$ .0208 $?$	.3194 $±$ .0217 $?$	.2865 $±$ .0218 $?$	.2999 $±$ .0170 $?$	.2845 $±$ .0231 $?$	.3157 $±$ .0219 $?$	.2200 $±$ .0168 $?$	.3037 $±$ .0171 $?$	.3268 $±$ .0189
W $→$ C	Precision	.2851 $±$ .0243 $?$	.2554 $±$ .0247 $?$	.2625 $±$ .0208 $?$	.2763 $±$ .0361 $?$	3029 $±$ .0217 $⊙$	.2983 $±$ .0396 $⊙$	.2917 $±$ .0169 $?$	.2549 $±$ .0226 $?$	.2887 $±$ .0196 $?$	.2663 $±$ .0188 $?$	.2871 $±$ .0162 $?$	.3053 $±$ .0163
	Recall	.3024 $±$ .0195 $?$	.2509 $±$ .0191 $?$	.2666 $±$ .0171 $?$	.3086 $±$ .0190 $?$	3117 $±$ .0191 $?$	.2844 $±$ .0208 $?$	.2955 $±$ .0156 $?$	.2709 $±$ .0230 $?$	.3076 $±$ .0177 $?$	.2179 $±$ .0157 $?$	.2975 $±$ .0142 $?$	.3196 $±$ .0142
	Macro-F1	.2801 $±$ .0187 $?$	.2361 $±$ .0191 $?$	.2542 $±$ .0171 $?$	.2698 $±$ .0189 $?$	2994 $±$ .0197 $⊙$	.2597 $±$ .0197 $?$	.2856 $±$ .0145 $?$	.2568 $±$ .0217 $?$	.2861 $±$ .0187 $?$	.1981 $±$ .0118 $?$	.2825 $±$ .0144 $?$	.3004 $±$ .0144
	Accuracy	.3106 $±$ .0215 $?$	.2944 $±$ .0229 $?$	.2509 $±$ .0218 $?$	.3701 $±$ .0222 $⊙$	.3903 $±$ .0213 $∘$	.2988 $±$ .0219 $?$	.3405 $±$ .0200 $?$	.3148 $±$ .0272 $?$	.3411 $±$ .0219 $?$	.3328 $±$ .0193 $?$	.3505 $±$ .0195 $?$	.3665 $±$ .0208
W $→$ A	Precision	.3345 $±$ .0194 $?$	.2940 $±$ .0187 $?$	.2460 $±$ .0202 $?$	.3455 $±$ .0189 $?$	.3888 $±$ .0231 $⊙$	.3177 $±$ .0223 $?$	.3501 $±$ .0225 $?$	.3025 $±$ .0272 $?$	.3294 $±$ .0229 $?$	.3666 $±$ .0198 $⊙$	.3583 $±$ .0250 $?$	.3772 $±$ .0264
	Recall	.3140 $±$ .0157 $?$	.2991 $±$ .0169 $?$	.2496 $±$ .0200 $?$	.3816 $±$ .0195 $∘$	.3991 $±$ .0167 $∘$	.3053 $±$ .0140 $?$	.3441 $±$ .0154 $?$	.3192 $±$ .0196 $?$	.3469 $±$ .0176 $?$	.3315 $±$ .0199 $?$	.3563 $±$ .0150 $?$	.3703 $±$ .0159
	Macro-F1	.3096 $±$ .0163 $?$	.2908 $±$ .0161 $?$	.2414 $±$ .0174 $?$	.3572 $±$ .0180 $⊙$	.3851 $±$ .0180 $∘$	.2986 $±$ .0140 $?$	.3369 $±$ .0160 $?$	.3013 $±$ .0213 $?$	.3291 $±$ .0173 $?$	.3128 $±$ .0187 $?$	.3450 $±$ .0156 $?$	.3596 $±$ .0159
	Accuracy	.8167 $±$ .0392 $?$	.6625 $±$ .0535 $?$	.6229 $±$ .0510 $?$	.7021 $±$ .0483 $?$	.7292 $±$ .0388 $?$	.6365 $±$ .0575 $?$	.8427 $±$ .0534 $?$	.7083 $±$ .0627 $?$	.8542 $±$ .0473 $?$	.8063 $±$ .0444 $?$	.8625 $±$ .0460 $⊙$	.8635 $±$ .0499
W $→$ D	Precision	.8203 $±$ .0688 $?$	.6582 $±$ .0684 $?$	.6297 $±$ .0740 $?$	.6819 $±$ .0892 $?$	.7280 $±$ .0543 $?$	.6350 $±$ .0970 $?$	.8480 $±$ .0729 $?$	.6890 $±$ .0848 $?$	.8664 $±$ .0645 $⊙$	.8166 $±$ .0682 $?$	.8731 $±$ .0562 $⊙$	.8718 $±$ .0637
	Recall	.8024 $±$ .0697 $?$	.6515 $±$ .0673 $?$	.6576 $±$ .0545 $?$	.6866 $±$ .0734 $?$	.7338 $±$ .0446 $?$	.6356 $±$ .0587 $?$	.8483 $±$ .0840 $?$	.6971 $±$ .0679 $?$	.8587 $±$ .0696 $?$	.8261 $±$ .0481 $?$	.8782 $±$ .0579 $⊙$	.8684 $±$ .0724
	Macro-F1	.7925 $±$ .0707 $?$	.6197 $±$ .0627 $?$	.6102 $±$ .0589 $?$	.6563 $±$ .0783 $?$	.6952 $±$ .0458 $?$	.5984 $±$ .0715 $?$	.8307 $±$ .0805 $?$	.6690 $±$ .0755 $?$	.8441 $±$ .0691 $?$	.8038 $±$ .0614 $?$	.8588 $±$ .0602 $⊙$	.8543 $±$ .0698
	Accuracy	.3041 $±$ .0197 $?$	.2757 $±$ .0199 $?$	.2839 $±$ .0200 $?$	.3084 $±$ .0149 $?$	.3070 $±$ .0154 $?$	.2794 $±$ .0231 $?$	.3018 $±$ .0222 $?$	.2811 $±$ .0196 $?$	.3203 $±$ .0225 $?$	.2456 $±$ .0160 $?$	.3050 $±$ .0225 $?$	.3274 $±$ .0205
D $→$ C	Precision	.2931 $±$ .0276 $?$	.2457 $±$ .0198 $?$	.2443 $±$ .0182 $?$	.2530 $±$ .0161 $?$	.2559 $±$ .0197 $?$	.2815 $±$ .0407 $?$	.2940 $±$ .0262 $?$	.2813 $±$ .0279 $?$	.2970 $±$ .0251 $?$	.2654 $±$ .0289 $?$	.2941 $±$ .0259 $?$	.3161 $±$ .0270
	Recall	.2888 $±$ .0178 $?$	.2693 $±$ .0167 $?$	.2772 $±$ .0159 $?$	.2975 $±$ .0116 $?$	.2958 $±$ .0133 $?$	.2631 $±$ .0176 $?$	.2875 $±$ .0178 $?$	.2601 $±$ .0185 $?$	.3051 $±$ .0196 $?$	.2316 $±$ .0137 $?$	.2909 $±$ .0195 $?$	.3139 $±$ .0167
	Macro-F1	.2653 $±$ .0185 $?$	.2414 $±$ .0169 $?$	.2405 $±$ .0155 $?$	.2518 $±$ .0117 $?$	.2514 $±$ .0140 $?$	.2427 $±$ .0187 $?$	.2706 $±$ .0211 $?$	.2504 $±$ .0187 $?$	.2876 $±$ .0212 $⊙$	.1879 $±$ .0150 $?$	.2726 $±$ .0215 $?$	.2850 $±$ .0196
	Accuracy	.3378 $±$ .0223 $?$	.3128 $±$ .0245 $?$	.2760 $±$ .0196 $?$	.3358 $±$ .0243 $?$	.3512 $±$ .0188 $?$	.2983 $±$ .0261 $?$	.3436 $±$ .0213 $?$	.3201 $±$ .0228 $?$	.3642 $±$ .0251 $⊙$	.2826 $±$ .0182 $?$	.3549 $±$ .0224 $?$	.3653 $±$ .0231
D $→$ A	Precision	.3561 $±$ .0326 $⊙$	.3163 $±$ .0408 $?$	.2359 $±$ .0111 $?$	.3129 $±$ .0201 $?$	.3220 $±$ .0153 $?$	.3215 $±$ .0377 $?$	.3412 $±$ .0314 $?$	.3092 $±$ .0248 $?$	.3494 $±$ .0284 $⊙$	.2917 $±$ .0157 $?$	.3631 $±$ .0302 $∘$	.3552 $±$ .0279
	Recall	.3373 $±$ .0183 $?$	.3188 $±$ .0168 $?$	.2823 $±$ .0145 $?$	.3405 $±$ .0155 $?$	.3562 $±$ .0178 $⊙$	.3022 $±$ .0201 $?$	.3438 $±$ .0199 $?$	.3240 $±$ .0211 $?$	.3654 $±$ .0219 $⊙$	.2850 $±$ .0121 $?$	.3549 $±$ .0207 $?$	.3658 $±$ .0220
	Macro-F1	.3120 $±$ .0194 $?$	.2781 $±$ .0165 $?$	.2477 $±$ .0105 $?$	.3111 $±$ .0166 $?$	.3333 $±$ .0153 $?$	.2803 $±$ .0201 $?$	.3219 $±$ .0210 $?$	.3076 $±$ .0215 $?$	.3418 $±$ .0227 $⊙$	.2546 $±$ .0096 $?$	.3354 $±$ .0202 $?$	.3430 $±$ .0208
	Accuracy	.6711 $±$ .0492 $?$	.5172 $±$ .0432 $?$	.5783 $±$ .0455 $?$	.6511 $±$ .0446 $?$	.6339 $±$ .0372 $?$	.4700 $±$ .0486 $?$	.7344 $±$ .0419 $?$	.6928 $±$ .0439 $?$	.7639 $±$ .0371 $⊙$	.7078 $±$ .0312 $?$	.7417 $±$ .0395 $?$	.7606 $±$ .0384
D $→$ W	Precision	.7521 $±$ .0426 $?$	.5582 $±$ .0894 $?$	.6184 $±$ .0451 $?$	.7133 $±$ .0513 $?$	.6811 $±$ .0379 $?$	.5669 $±$ .0661 $?$	.7720 $±$ .0378 $?$	.6913 $±$ .0539 $?$	.8090 $±$ .0376 $∘$	.8024 $±$ .0361 $⊙$	.7761 $±$ .0379 $?$	.7977 $±$ .0368
	Recall	.6738 $±$ .0489 $?$	.5181 $±$ .0368 $?$	.5757 $±$ .0423 $?$	.6489 $±$ .0455 $?$	.6563 $±$ .0417 $?$	.4780 $±$ .0462 $?$	.7383 $±$ .0449 $?$	.6933 $±$ .0423 $?$	.7669 $±$ .0411 $⊙$	.7085 $±$ .0329 $?$	.7429 $±$ .0412 $?$	.7669 $±$ .0371
	Macro-F1	.6720 $±$ .0519 $?$	.4632 $±$ .0363 $?$	.5617 $±$ .0385 $?$	.6524 $±$ .0473 $?$	.6430 $±$ .0417 $?$	.4557 $±$ .0473 $?$	.7367 $±$ .0405 $?$	.6773 $±$ .0473 $?$	.7602 $±$ .0411 $⊙$	.7156 $±$ .0348 $?$	.7452 $±$ .0378 $?$	.7641 $±$ .0357
win/tie/loss		42/6/0	48/0/0	48/0/0	38/9/1	40/5/3	46/2/0	45/2/1	46/2/0	34/13/1	41/6/1	37/7/4	?

Tab.5 Four evaluation metrics: Accuracy, Precision, Recall, and Macro-F1 of different methods on Office+Caltech10 by SVM classifier. The best results on each row are bolded, and

? / ⊙ / ∘

means that the NDTSL method is better/tied/worse than other methods. (pairwise single-tailed t-test at 95% confidence level)

Dataset	Measures	NN	TCA	JDA	W-BDA	JPDA	GFK	DTSL	FSSP	JLRFS	PAS	LRRCA	NDTSL
	Accuracy	.6888 $±$ .0117 $⊙$	.6426 $±$ .0131 $?$	.7013 $±$ .0133 $?$	.6804 $±$ .0126 $?$	.6781 $±$ .0148 $?$	.6936 $±$ .0127 $?$	.7140 $±$ .0111 $?$	.6822 $±$ .0132 $?$	.7199 $±$ .0132 $⊙$	.5615 $±$ .0151 $?$	.7170 $±$ .0096 $?$	.7209 $±$ .0105
V $→$ S	Precision	.5022 $±$ .0392 $?$	.4533 $±$ .0096 $?$	.4612 $±$ .0143 $?$	.4507 $±$ .0150 $?$	.4644 $±$ .0205 $?$	.4907 $±$ .0250 $?$	.5696 $±$ .0616 $⊙$	.5036 $±$ .0948 $?$	.5718 $±$ .0866 $⊙$	.4547 $±$ .0176 $?$	.5441 $±$ .0505 $?$	.5714 $±$ .0566
	Recall	.5410 $±$ .0680 $?$	.5638 $±$ .0260 $⊙$	.5336 $±$ .0324 $?$	.4543 $±$ .0232 $?$	.5580 $±$ .0478 $⊙$	.5881 $±$ .0356 $⊙$	.5896 $±$ .0561 $⊙$	.5614 $±$ .0479 $⊙$	.5402 $±$ .0652 $?$	.5890 $±$ .0347 $⊙$	.5982 $±$ .0552 $∘$	.5785 $±$ .0623
	Macro-F1	.4980 $±$ .0355 $?$	.4286 $±$ .0121 $?$	.4661 $±$ .0191 $?$	.4408 $±$ .0155 $?$	.4675 $±$ .0223 $?$	.4812 $±$ .0216 $?$	.5355 $±$ .0385 $?$	.4692 $±$ .0308 $?$	.5305 $±$ .0499 $⊙$	.3920 $±$ .0215 $?$	.5323 $±$ .0351 $?$	.5440 $±$ .0349
	Accuracy	.5825 $±$ .0136 $?$	.5595 $±$ .0140 $?$	.5857 $±$ .0200 $?$	.6109 $±$ .0108 $?$	.6471 $±$ .0129 $∘$	.5937 $±$ .0148 $?$	.6209 $±$ .0162 $?$	.6074 $±$ .0157 $?$	.6207 $±$ .0109 $?$	.4063 $±$ .0185 $?$	.6335 $±$ .0139 $?$	.6382 $±$ .0134
V $→$ L	Precision	.5613 $±$ .0352 $?$	.2974 $±$ .0068 $?$	.3157 $±$ .0175 $?$	.3442 $±$ .0149 $?$	.3918 $±$ .0309 $?$	.4168 $±$ .0388 $?$	.2512 $±$ .0062 $?$	.4970 $±$ .1010 $?$	.6971 $±$ .1001 $∘$	.4039 $±$ .0466 $?$	.5623 $±$ .0955 $?$	.6005 $±$ .0717
	Recall	.4781 $±$ .0305 $∘$	.3931 $±$ .0147 $?$	.3717 $±$ .0207 $?$	.4159 $±$ .0184 $⊙$	.4138 $±$ .0201 $⊙$	.4207 $±$ .0249 $⊙$	.2706 $±$ .0061 $?$	.3979 $±$ .0243 $?$	.4056 $±$ .0243 $⊙$	.4361 $±$ .0327 $∘$	.3121 $±$ .0146 $?$	.4158 $±$ .0331
	Macro-F1	.4719 $±$ .0272 $⊙$	.2920 $±$ .0089 $?$	.3241 $±$ .0184 $?$	.3661 $±$ .0154 $?$	.3978 $±$ .0200 $?$	.3975 $±$ .0210 $?$	.2591 $±$ .0062 $?$	.4110 $±$ .0255 $?$	.4509 $±$ .0287 $⊙$	.2961 $±$ .0247 $?$	.3284 $±$ .0236 $?$	.4526 $±$ .0371
	Accuracy	.5650 $±$ .0133 $?$	.6118 $±$ .0135 $?$	.6227 $±$ .0147 $⊙$	.6071 $±$ .0129 $?$	.6138 $±$ .0150 $?$	.5848 $±$ .0147 $?$	.5845 $±$ .0142 $?$	.6366 $±$ .0152 $∘$	.5906 $±$ .0117 $?$	.3681 $±$ .0114 $?$	.5846 $±$ .0143 $?$	.6230 $±$ .0153
S $→$ V	Precision	.5058 $±$ .1321 $?$	.3782 $±$ .0082 $?$	.3919 $±$ .0086 $?$	.3720 $±$ .0084 $?$	.3978 $±$ .0081 $?$	.4067 $±$ .0073 $?$	.3969 $±$ .0079 $?$	.4287 $±$ .0071 $?$	.6595 $±$ .1049 $⊙$	.4335 $±$ .0116 $?$	.3965 $±$ .0083 $?$	.6723 $±$ .0340
	Recall	.4176 $±$ .0084 $?$	.4551 $±$ .0084 $?$	.4594 $±$ .0094 $?$	.4413 $±$ .0086 $?$	.4427 $±$ .0091 $?$	.4062 $±$ .0090 $?$	.4104 $±$ .0083 $?$	.4505 $±$ .0074 $?$	.4517 $±$ .0104 $?$	.4448 $±$ .0123 $?$	.4107 $±$ .0084 $?$	.4858 $±$ .0157
	Macro-F1	.3791 $±$ .0105 $?$	.4109 $±$ .0074 $?$	.4205 $±$ .0083 $?$	.4009 $±$ .0074 $?$	.4138 $±$ .0080 $?$	.3883 $±$ .0082 $?$	.3869 $±$ .0081 $?$	.4299 $±$ .0071 $?$	.4321 $±$ .0132 $?$	.3917 $±$ .0109 $?$	.3871 $±$ .0083 $?$	.4955 $±$ .0191
	Accuracy	.5774 $±$ .0146 $?$	.5435 $±$ .0157 $?$	.5765 $±$ .0156 $?$	.5951 $±$ .0154 $∘$	.4606 $±$ .0152 $?$	.5558 $±$ .0166 $?$	.5744 $±$ .0142 $?$	.5231 $±$ .0150 $?$	.5764 $±$ .0142 $?$	.2672 $±$ .0105 $?$	.5805 $±$ .0154 $⊙$	.5821 $±$ .0128
S $→$ L	Precision	.3839 $±$ .1248 $?$	.2637 $±$ .0065 $?$	.2797 $±$ .0210 $?$	.2762 $±$ .0186 $?$	.2437 $±$ .0073 $?$	.2520 $±$ .0132 $?$	.3889 $±$ .1056 $⊙$	.2623 $±$ .0212 $?$	.4315 $±$ .1334 $⊙$	.2979 $±$ .0121 $?$	.3925 $±$ .1089 $⊙$	.4101 $±$ .1553
	Recall	.2831 $±$ .0145 $∘$	.2826 $±$ .0123 $⊙$	.2678 $±$ .0106 $?$	.2737 $±$ .0100 $⊙$	.2330 $±$ .0112 $?$	.2568 $±$ .0104 $?$	.2846 $±$ .0141 $⊙$	.2447 $±$ .0085 $?$	.2838 $±$ .0153 $⊙$	.1894 $±$ .0203 $?$	.2864 $±$ .0155 $⊙$	.2818 $±$ .0238
	Macro-F1	.2738 $±$ .0202 $?$	.2598 $±$ .0064 $?$	.2540 $±$ .0141 $?$	.2614 $±$ .0125 $?$	.2251 $±$ .0063 $?$	.2403 $±$ .0125 $?$	.2755 $±$ .0208 $⊙$	.2207 $±$ .0120 $?$	.2767 $±$ .0233 $⊙$	.2007 $±$ .0103 $?$	.2801 $±$ .0230 $⊙$	.2784 $±$ .0336
	Accuracy	.5677 $±$ .0120 $?$	.4375 $±$ .0121 $?$	.5376 $±$ .0159 $?$	.5874 $±$ .0141 $?$	.5599 $±$ .0136 $?$	.5683 $±$ .0160 $?$	.6196 $±$ .0138 $?$	.6669 $±$ .0148 $∘$	.6000 $±$ .0124 $?$	.1850 $±$ .0109 $?$	.6206 $±$ .0144 $?$	.6497 $±$ .0150
L $→$ V	Precision	.5673 $±$ .0237 $?$	.1734 $±$ .0050 $?$	.2145 $±$ .0055 $?$	.3555 $±$ .0112 $?$	.3194 $±$ .0102 $?$	.3189 $±$ .0093 $?$	.6705 $±$ .0928 $⊙$	.5738 $±$ .0110 $?$	.5718 $±$ .0164 $?$	.3143 $±$ .0119 $?$	.6534 $±$ .0915 $⊙$	.6507 $±$ .0303
	Recall	.4635 $±$ .0118 $?$	.2776 $±$ .0058 $?$	.3293 $±$ .0042 $?$	.4286 $±$ .0107 $?$	.4320 $±$ .0086 $?$	.4585 $±$ .0096 $?$	.4706 $±$ .0096 $?$	.5625 $±$ .0133 $∘$	.5533 $±$ .0137 $∘$	.2866 $±$ .0080 $?$	.4726 $±$ .0099 $?$	.5438 $±$ .0205
	Macro-F1	.4437 $±$ .0143 $?$	.2077 $±$ .0046 $?$	.2597 $±$ .0046 $?$	.3812 $±$ .0100 $?$	.3617 $±$ .0084 $?$	.3720 $±$ .0094 $?$	.4298 $±$ .0098 $?$	.5570 $±$ .0121 $⊙$	.5490 $±$ .0137 $⊙$	.2093 $±$ .0093 $?$	.4355 $±$ .0113 $?$	.5513 $±$ .0237
	Accuracy	.4709 $±$ .0149 $?$	.4656 $±$ .0147 $?$	.4736 $±$ .0143 $?$	.4638 $±$ .0145 $?$	.4855 $±$ .0144 $?$	.4565 $±$ .0150 $?$	.4872 $±$ .0107 $?$	.4568 $±$ .0154 $?$	.5065 $±$ .0133 $?$	.3864 $±$ .0150 $?$	.4877 $±$ .0112 $?$	.5279 $±$ .0113
L $→$ S	Precision	.4751 $±$ .0959 $?$	.1857 $±$ .0063 $?$	.1882 $±$ .0056 $?$	.2217 $±$ .0367 $?$	.1984 $±$ .0061 $?$	.2056 $±$ .0173 $?$	.3900 $±$ .0243 $?$	.2420 $±$ .0074 $?$	.4267 $±$ .0534 $?$	.3342 $±$ .0170 $?$	.3898 $±$ .0241 $?$	.4862 $±$ .0889
	Recall	.3752 $±$ .0445 $?$	.2677 $±$ .0059 $?$	.2835 $±$ .0058 $?$	.2970 $±$ .0320 $?$	.2824 $±$ .0070 $?$	.3477 $±$ .0523 $?$	.4530 $±$ .0475 $?$	.2539 $±$ .0044 $?$	.4349 $±$ .0423 $⊙$	.4401 $±$ .0280 $⊙$	.4531 $±$ .0474 $∘$	.4301 $±$ .0430
	Macro-F1	.3238 $±$ .0338 $?$	.2153 $±$ .0060 $?$	.2260 $±$ .0056 $?$	.2441 $±$ .0283 $?$	.2294 $±$ .0063 $?$	.2509 $±$ .0203 $?$	.3828 $±$ .0247 $?$	.2082 $±$ .0063 $?$	.3890 $±$ .0265 $⊙$	.2417 $±$ .0107 $?$	.3830 $±$ .0246 $?$	.4040 $±$ .0321
win/tie/loss		20/2/2	22/2/0	23/1/0	21/2/1	22/2/0	22/2/0	18/6/0	19/2/3	10/12/2	21/2/1	17/5/2	?

Tab.6 Four evaluation metrics: Accuracy, Precision, Recall, and Macro-F1 of different methods on VSL by SVM classifier. The best results on each row are bolded, and

? / ⊙ / ∘

means that the NDTSL method is better/tied/worse than other methods. (pairwise single-tailed t-test at 95% confidence level)

Fig.2 The curves of four evaluation metrics for different methods on transfer tasks: A→W, A→D, and V→L by SVM classifier. (a) A→W; (b) A→W; (c) A→W; (d) A→W; (e) A→D; (f) A→D; (g) A→D; (h) A→D; (i) V→L; (i) V→L; (k) V→L; (l) V→L

Fig.3 The curves of four evaluation metrics for different methods on transfer tasks V→L by NN classifier. (a) accuracy; (b) precision; (c) recall; (d) macro-F1

Fig.4 The convergence of objective function values and classification accuracy curves on four transfer tasks. (a) A→C; (b) D→A; (c) S→V; (d) L→S

Tab.7 The computation cost of transfer subspace learning methods on four transfer tasks by NN classifier

Fig.5 The influence of hyperparameters

α

and

β

for accuracy on four transfer tasks by NN classifier. (a) A→C; (b) D→A; (c) S→V; (d) L→S

Fig.6 The accuracy curves vary with the hyperparameters

λ

and

p

on four transfer tasks by NN classifier. (a) λ; (b) p

Dataset	C $→$ A	C $→$ W	C $→$ D	A $→$ C	A $→$ W	A $→$ D
Low-rank	.5280 $±$ .0226	.3961 $±$ .0463	.4719 $±$ .0617	.4380 $±$ .0140	.3867 $±$ .0438	.3688 $±$ .0570
Strict label	.5229 $±$ .0221	.4139 $±$ .0332	.4594 $±$ .0571	.4280 $±$ .0153	.3694 $±$ .0401	.3854 $±$ .0543
NDTSL	$.5403 ± .0223$	$.4411 ± .0364$	$.5146 ± .0612$	$.4490 ± .0148$	$.4089 ± .0401$	$.4240 ± .0493$

Dataset	W $→$ C	W $→$ A	W $→$ D	D $→$ C	D $→$ A	D $→$ W
Low-rank	.3111 $±$ .0200	.3497 $±$ .0192	.8583 $±$ .0486	.3077 $±$ .0216	.3564 $±$ .0227	.7383 $±$ .0448
Strict label	.3034 $±$ .0198	.3589 $±$ .0199	.8240 $±$ .0490	.3155 $±$ .0227	.3608 $±$ .0207	.7456 $±$ .0395
NDTSL	$.3268 ± .0189$	$.3665 ± .0208$	$.8635 ± .0499$	$.3274 ± .0205$	$.3653 ± .0231$	$.7606 ± .0384$

Tab.8 Accuracy of different methods on Office+Caltech10 by SVM classifier

1	A Margolis . A literature review of domain adaptation with unlabeled data. Washington: University of Washington, 2011, 1−42
2	You K, Long M, Cao Z, Wang J, Jordan M I. Universal domain adaptation. In: Proceedings of IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2019, 2715−2724
3	W M, Kouw M Loog . A review of domain adaptation without target labels. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021, 43( 3): 766–785
4	A, Farahani S, Voghoei K, Rasheed H R Arabnia . A brief review of domain adaptation. In: Stahlbock R, Weiss G M, Abou-Nasr M, Yang C Y, Arabnia H R, Deligiannidis L, eds. Advances in Data Science and Information Engineering. Cham: Springer, 2021, 877−894
5	V M, Patel R, Gopalan R, Li R Chellappa . Visual domain adaptation: a survey of recent advances. IEEE Signal Processing Magazine, 2015, 32( 3): 53–69
6	G Csurka . Domain Adaptation in Computer Vision Applications. Cham: Springer, 2017
7	J Jiang . Domain adaptation in natural language processing. University of Illinois at Urbana-Champaign, Dissertation, 2008
8	C S, Perone P, Ballester R C, Barros J Cohen-Adad . Unsupervised domain adaptation for medical imaging segmentation with self-ensembling. NeuroImage, 2019, 194: 1–11
9	Y, Zhang Y, Wei Q, Wu P, Zhao S, Niu J, Huang M Tan . Collaborative unsupervised domain adaptation for medical image diagnosis. IEEE Transactions on Image Processing, 2020, 29: 7834–7844
10	H, Guan M Liu . Domain adaptation for medical image analysis: a survey. IEEE Transactions on Biomedical Engineering, 2022, 69( 3): 1173–1185
11	S J, Pan I W, Tsang J T, Kwok Q Yang . Domain adaptation via transfer component analysis. IEEE Transactions on Neural Networks, 2011, 22( 2): 199–210
12	M, Long J, Wang G, Ding J, Sun P S Yu . Transfer feature learning with joint distribution adaptation. In: Proceedings of the IEEE International Conference on Computer Vision. 2013, 2200−2207
13	J, Wang Y, Chen S, Hao W, Feng Z Shen . Balanced distribution adaptation for transfer learning. In: Proceedings of the IEEE International Conference on Data Mining. 2017, 1129−1134
14	Zhang W, Wu D. Discriminative joint probability maximum mean discrepancy (DJP-MMD) for domain adaptation. In: Proceedings of IEEE International Joint Conference on Neural Networks. 2020, 1−8
15	W, Wang H, Li Z, Ding F, Nie J, Chen X, Dong Z Wang . Rethinking maximum mean discrepancy for visual domain adaptation. IEEE Transactions on Neural Networks and Learning Systems, 2023, 34( 1): 264–277
16	A, Gretton K M, Borgwardt M J, Rasch B, Schölkopf A Smola . A kernel two-sample test. The Journal of Machine Learning Research, 2012, 13: 723–773
17	Fernando B, Habrard A, Sebban M, Tuytelaars T. Unsupervised visual domain adaptation using subspace alignment. In: Proceedings of IEEE International Conference on Computer Vision. 2013, 2960−2967
18	B, Sun K Saenko . Subspace distribution alignment for unsupervised domain adaptation. In: Proceedings of the British Machine Vision Conference. 2015, 24.1−24.10
19	Sun B, Feng J, Saenko K. Return of frustratingly easy domain adaptation. In: Proceedings of the 30th AAAI Conference on Artificial Intelligence. 2016, 2058−2065
20	Gopalan R, Li R, Chellappa R. Domain adaptation for object recognition: an unsupervised approach. In: Proceedings of IEEE International Conference on Computer Vision. 2011, 999−1006
21	Gong B, Shi Y, Sha F, Grauman K. Geodesic flow kernel for unsupervised domain adaptation. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2012, 2066−2073
22	M, Shao D, Kit Y Fu . Generalized transfer subspace learning through low-rank constraint. International Journal of Computer Vision, 2014, 109( 1−2): 74–93
23	Y, Xu X, Fang J, Wu X, Li D Zhang . Discriminative transfer subspace learning via low-rank and sparse representation. IEEE Transactions on Image Processing, 2016, 25( 2): 850–863
24	Li J, Zhao J, Lu K. Joint feature selection and structure preservation for domain adaptation. In: Proceedings of the 25th International Joint Conference on Artificial Intelligence. 2016, 1697−1703
25	Z, Lin Z, Zhao T, Luo W, Yang Y, Zhang Y Tang . Non-convex transfer subspace learning for unsupervised domain adaptation. In: Proceedings of the IEEE International Conference on Multimedia and Expo. 2019, 1468−1473
26	L, Yang Q Zhou . Transfer subspace learning joint low-rank representation and feature selection. Multimedia Tools and Applications, 2022, 81( 27): 38353–38373
27	W, Li S Chen . Unsupervised domain adaptation with progressive adaptation of subspaces. Pattern Recognition, 2022, 132: 108918
28	P, Razzaghi P, Razzaghi K Abbasi . Transfer subspace learning via low-rank and discriminative reconstruction matrix. Knowledge-Based Systems, 2019, 163: 174–185
29	T, Xiao P, Liu W, Zhao H, Liu X Tang . Structure preservation and distribution alignment in discriminative transfer subspace learning. Neurocomputing, 2019, 337: 218–234
30	H, Xia T, Jing Z Ding . Maximum structural generation discrepancy for unsupervised domain adaptation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023, 45( 3): 3434–3445
31	Y, Madadi V, Seydi R Hosseini . Multi-source domain adaptation-based low-rank representation and correlation alignment. International Journal of Computers and Applications, 2022, 44( 7): 670–677
32	L, Yang B, Lu Q, Zhou P Su . Unsupervised domain adaptation via re-weighted transfer subspace learning with inter-class sparsity. Knowledge-Based Systems, 2023, 263: 110277
33	G, Liu Z, Lin S, Yan J, Sun Y, Yu Y Ma . Robust recovery of subspace structures by low-rank representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35( 1): 171–184
34	Fazel M, Hindi H, Boyd S P. A rank minimization heuristic with application to minimum order system approximation. In: Proceedings of IEEE American Control Conference. 2001, 4734−4739
35	X, Fang Y, Xu X, Li Z, Lai W K, Wong B Fang . Regularized label relaxation linear regression. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29( 4): 1006–1018
36	Y, Wang W, Yin J Zeng . Global convergence of ADMM in nonconvex nonsmooth optimization. Journal of Scientific Computing, 2019, 78( 1): 29–63
37	Nie F, Wang H, Cai X, Huang H, Ding C. Robust matrix completion via joint schatten p-Norm and lp-norm minimization. In: Proceedings of the 12th IEEE International Conference on Data Mining. 2012, 566−574
38	Z, Lin M, Chen L, Wu Y Ma . The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. Urbana: Coordinated Science Laboratory, 2009
39	K, Saenko B, Kulis M, Fritz T Darrell . Adapting visual category models to new domains. In: Proceedings of the 11th European Conference on Computer Vision. 2010, 213−226
40	G, Griffin A, Holub P Perona . Caltech-256 object category dataset. Pasadena: California Institute of Technology, 2007
41	M, Everingham Gool L, Van C K I, Williams J, Winn A Zisserman . The PASCAL visual object classes (VOC) challenge. International Journal of Computer Vision, 2010, 88( 2): 303–338
42	B C, Russell A, Torralba K P, Murphy W T Freeman . LabelMe: a database and web-based tool for image annotation. International Journal of Computer Vision, 2008, 77( 1−3): 157–173
43	Choi M J, Lim J J, Torralba A, Willsky A S. Exploiting hierarchical context on a large database of object categories. In: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2010, 129−136
44	H, Bay T, Tuytelaars Gool L Van . SURF: speeded up robust features. In: Proceedings of the 9th European Conference on Computer Vision. 2006, 404−417
45	J, Donahue Y, Jia O, Vinyals J, Hoffman N, Zhang E, Tzeng T Darrell . DeCAF: a deep convolutional activation feature for generic visual recognition. In: Proceedings of the 31st International Conference on Machine Learning. 2014, I-647−I-655

[1]

FCS-23228-OF-YL_suppl_1

Download

[1]	Yi ZHU, Xindong WU, Jipeng QIANG, Yunhao YUAN, Yun LI. Representation learning via an integrated autoencoder for unsupervised domain adaptation[J]. Front. Comput. Sci., 2023, 17(5): 175334-.
[2]	Yunyun WANG, Chao WANG, Hui XUE, Songcan CHEN. Self-corrected unsupervised domain adaptation[J]. Front. Comput. Sci., 2022, 16(5): 165323-.
[3]	Xuejun WANG, Feilong CAO, Wenjian WANG. Adaptive sparse and dense hybrid representation with nonconvex optimization[J]. Front. Comput. Sci., 2020, 14(4): 144306-.

Viewed

Full text

Abstract

Cited

Shared

Discussed