Boosting Transferability and Discriminability for Time Series Domain Adaptation

Authors: mingyang  liu
xinyang  chen
yang  shu
xiucheng  li
weili  guan
liqiang  nie
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-11 05:36:44

Abstract: Unsupervised domain adaptation excels in transferring knowledge from a labeled source domain to an unlabeled target domain, playing a critical role in time series applications. Existing time series domain adaptation methods either ignore frequency features or treat temporal and frequency features equally, which makes it challenging to fully exploit the advantages of both types of features. In this paper, we delve into transferability and discriminability, two crucial properties in transferable representation learning. It's insightful to note that frequency features are more discriminative within a specific domain, while temporal features show better transferability across domains. Based on the findings, we propose **A**dversarial **CO**-learning **N**etworks (**ACON**), to enhance transferable representation learning through a collaborative learning manner in three aspects: (1) Considering the multi-periodicity in time series, multi-period frequency feature learning is proposed to enhance the discriminability of frequency features; (2) Temporal-frequency domain mutual learning is proposed to enhance the discriminability of temporal features in the source domain and improve the transferability of frequency features in the target domain; (3) Domain adversarial learning is conducted in the correlation subspaces of temporal-frequency features instead of original feature spaces to further enhance the transferability of both features. Extensive experiments conducted on a wide range of time series datasets and five common applications demonstrate the state-of-the-art performance of ACON. Code is available at <https://github.com/mingyangliu1024/ACON>.

Main paper: 
 introduction: 
 Time series classification has achieved significant success in the deep learning era by leveraging discriminative features learned from extensive labeled data [18] . However, the presence of distribution shift may arise when deploying the model, potentially impeding the generalization ability of deep models [31] . Unsupervised domain adaptation [13] , offering the potential to transfer knowledge from a labeled source domain to an unlabeled target domain, emerges as a promising solution.Existing domain adaptation methods tailored for time series primarily focus on learning domaininvariant temporal features [30, 41, 29] , yielding promising results. Recently, the significance of frequency features for enhancing domain-invariant representation has also been recognized [16] . However, frequency features and temporal features are treated equally, and their distinct properties are overlooked, leading to the inability to fully leverage both types of features to boost transfer learning.In this paper, we analyze the two most important properties of features in transfer learning: transferability and discriminability, to investigate the characteristics of the frequency features and temporal features. We find that under the premise of adopting advanced backbones in state-of-the-art works [31, 16] , frequency features are more discriminative within a specific domain, while temporal features show better transferability across domains.Based on the findings, we propose Adversarial CO-learning Networks (ACON) to maximize the potential of temporal features and frequency features in terms of both transferability and discriminability in a collaborative learning manner. Firstly, to fully leverage the properties of multi-periodicity in time series, we propose multi-period frequency feature learning to further enhance the discriminability of frequency features. Secondly, we propose temporal-frequency domain mutual learning to enhance the discriminability of temporal features in the source domain and improve the transferability of frequency features in the target domain. Specifically, to harness the potent discriminability of frequency features within the domain, we enable the transfer of knowledge from frequency features to temporal features within the source domain via knowledge distillation. To leverage the strong transferability of temporal features across domains, we facilitate the transfer of knowledge from temporal features to frequency features in the target domain through knowledge distillation. Thirdly, we propose to learn transferable representations via domain adversarial learning in temporal-frequency correlation subspace instead of the original temporal feature space. The temporal-frequency correlation subspace not only possesses the properties of the original temporal feature space and original frequency feature space but also incorporates the correlation between the two types of features. Learning transferable representations in the temporal-frequency correlation subspace can further enhance the transferability of features. Our main contributions can be summarized as follows:• We uncover the characteristics wherein temporal features and frequency features cannot be equally treated in transfer learning. Specifically, we observe that frequency features are more discriminative within a specific domain, while temporal features show better transferability across domains through empirical findings.• We design ACON, which enhances UDA in three key aspects: a multi-period feature learning module to enhance the discriminability of frequency features, a temporal-frequency domain mutual learning module to enhance the discriminability of temporal features in the source domain and improve the transferability of frequency features in the target domain, and a domain adversarial learning module in temporal-frequency correlation subspace to further enhance transferability of features.• Experiments conducted on a wide range of time series datasets and five common applications verify the effectiveness of ACON. 
related work: 
 General Unsupervised Domain Adaptation Methods Unsupervised domain adaptation leverages the labeled source domain to predict the labels of a different but related, unlabeled target domain. It finds wide applications in computer vision [46, 15, 8] and natural language processing [40, 39, 44] .Existing UDA methods can be classified into three categories: (1) Methods based on adversarial training aim to learn domain-invariant representations via the game between the feature extractor and the domain discriminator. Widely used methods include DANN [13] , CDAN [26] and DIRT-T [34] .(2) Methods based on statistical divergence aim to reduce the domain discrepancy by minimizing domain discrepancy in a latent feature space. Widely used methods include DAN [25] , DeepCoral [36] and HoMM [5] .(3) Methods based on self-training produce pseudo-labels on unlabeled data and use confident pseudo-labels together with the labeled data to train the model. Widely used methods include PFAN [6] , CST [22] and AdaMatch [2] . However, these methods are generally designed and do not fully leverage the properties of time series. Although these methods can be applied to time series through tailored feature extractors, they often obtain suboptimal performance and UDA algorithm specially designed for time series is needed.To date, a few methods have been tailored to unsupervised domain adaptation for time series data. VRADA [30] is the first UDA method for multivariate time series that uses adversarial learning for reducing domain discrepancy. In VRADA, a variational recurrent neural network (VRNN) [10] is trained in an adversarial way to learn domain-invariant temporal features. CoDATS [41] builds upon VRADA but uses a convolutional neural network for the feature extractor, proposing a solution for multi-source domain adaptation in time series classification. SASA [3] adopts LSTM [33] as feature extractors to capture the domaininvariant association, and aligns sparse associative structure between source and target domain via the minimization of maximum mean discrepancy (MMD) [38] . AdvSKM [23] modifies MMD to make it more suitable for time series data. CLUDA [29] learns contextual representation via contrastive learning, and aligns features between source and target domain via adversarial training. RAINCOAT [16] is the first to introduce frequency features into domain adaptation, aligning temporal features and frequency features respectively via Sinkhorn divergence.Research gap In general, in terms of representation learning, most methods only focus on the temporal domain or assume that the temporal domain and the frequency domain are independent of each other, hindering the full utilization of two types of features. In terms of feature adaptation, existing works only focus on aligning temporal features or adopting simple statistical divergence to align frequency features, ignoring the different properties of the temporal features and frequency features in transfer learning. In terms of evaluation, the existing evaluations are conducted on several datasets of limited scale in a few specific tasks, and more general evaluations are needed.3 Transferability and Discriminability in Time Series 
problem setup: 
 In this paper, we study the UDA problem for time series classification. In time series classification problem, the model receives a set of n labeled samples {(x i , y i )} n i=1 , where i-th sample x i ∈ R C×T contains observation of C variates over T time steps. We allow for both univariate and multivariate time series. In UDA setup, we are given n s labeled samples from a source domain P = {(x s i , y s i )} ns i=1 and n t unlabeled samples from a target domain Q = {(x t i )} nt i=1 , which are sampled from different distributions P and Q. Superscripts s and t are adopted to distinguish the source domain and the target domain. UDA for time series aims to learn a time series classification model with labeled source data P and unlabeled target data Q, which can make accurate predictions on the target domain.In addition to the source domain and target domain in UDA, time series naturally can be represented in the temporal domain and frequency domain. By Fast Fourier Transform (FFT), the raw time series input x i in the temporal domain can be transformed to corresponding frequency input v i in the frequency domain:EQUATIONwhere the complex variable v i ∈ C C×⌊ T 2 ⌋ contains observation of C variates over ⌊ T 2 ⌋ different frequencies. Due to the conjugacy of frequency domain, we only consider the frequencies within {1, ..., ⌊ T 2 ⌋}. As Figure 1 (a) presented, compared to the uniform distribution of temporal data for different classes, the frequency data for different classes shows distinct differences in the dominant frequencies and peaks, which holds more discriminative information. To further investigate the discriminability of frequency features, we perform the single data domain classification task in the frequency domain and temporal domain respectively on all five data domains of the CAP [37, 14] dataset.In order to minimize the impact of specific model structures, we adopt 3-layer 1D-CNN, a generic structure as the temporal feature extractor, and 1-layer linear as the frequency feature extractor, which have both widely validated for their effectiveness in existing time series analysis methods [23, 16, 42, 43] . We only retain the low-frequency data to ensure that the temporal feature extractor and the frequency feature extractor have comparable parameter quantities. For the classifiers, we uniformly use 1-layer linear. As Figure 1 (b) shown, with a simple feature extractor, the frequency classification outperforms the temporal classification, demonstrating that the frequency features have better discriminability. More analysis results on different datasets are included in Appendix C.1.Another key criterion that characterizes the performance of domain adaptation is transferability [7] .Transferability indicates the ability to learn invariant features across domains. Since the frequency features have better discriminability within the source domain, it is natural to raise the question: Will the frequency features also have better discriminability in the target domain?We investigate this problem starting with the comparison of four methods: The above analysis reveals two insights for time series domain adaptation: With better discriminability but worse transferability, domain adaptation in the frequency domain obtains suboptimal performance; while with better transferability, domain adaptation in the temporal domain has the potential to achieve superior performance under the guidance of more discriminative information. 
approach: 
 Based on the above observations, our motivation is to simultaneously leverage the strong discriminability of frequency features and the strong transferability of temporal features to enhance domain adaptation. This inspires us to learn domain-invariant temporal and frequency features in a collaborative learning manner.Figure 2 illustrates the overall structure of our Adversarial CO-learning Networks (ACON). To avoid confusion, subscripts T and F are adopted to distinguish the temporal domain and the frequency domain. Specifically, in the temporal domain, we have a temporal feature extractor with temporal input f = ψ T (x) and a temporal classifier ŷT = g T (f ); while in the frequency domain, we have a frequency feature extractor with frequency input z = ψ F (v) and a frequency classifier ŷF = g F (z).Additionally, we have a domain discriminator g D , which is trained to distinguish the source feature and the target feature. In the following, we will introduce three main contributions in ACON: multi-period frequency feature learning in Section 4.1, temporal-frequency domain mutual learning in Section 4.2, and domain adversarial learning in temporal-frequency correlation subspace in Section 4.3.The real-world time series usually present multi-periodicity, which is reflected in the frequency domain as the presence of a few dominant frequencies with significantly larger amplitudes. Data from different periods can have different discriminative patterns. Based on this, before performing FFT, we segment the raw time series according to the top-k significant periods, enhancing the B C c = " > A A A C A X i c b V D L S s N A F J 3 U V 6 2 v q B v B T b A I r k o i U l 0 W B X F Z w T 6 g i W E y n b R D J 5 M w M x H C E D f + i h s X i r j 1 L 9 z 5 N 0 7 a L L T 1 w I X D O f d y 7 z 1 B Q o m Q t v 1 t V J a W V 1 b X q u u 1 j c 2 t 7 R 1 z d 6 8 r 4 p Q j 3 E E x j X k / g A J T w n B H E k l x P + E Y R g H F v W B y V f i 9 B 8 w F i d m d z B L s R X D E S E g Q l F r y z Q N 3 D K V y I y j H Q a i y P L 9 X I v f V d e 6 b d b t h T 2 E t E q c k d V C i 7 Z t f 7 j B G a Y S Z R B Q K M X D s R H o K c k k Q x X n N T Q V O I J r A E R 5 o y m C E h a e m H + T W s V a G V h h z X U x a U / X 3 h I K R E F k U 6 M 7 i V D H v F e J / 3 i C V 4 Y W n C E t S i R m a L Q p T a s n Y K u K w h o R j J G m m C U S c 6 F s t N I Y c I q l D q + k Q n P m X F 0 n 3 t O E 0 GM S q E 1 K N g k v 0 D T c C O 4 l C G o U C 2 + H k f u 6 3 n 1 B p H s u m m S Y Y R H Q k + Z A z a q z k j / p Z c 9 Y v V 9 y q u w B Z J 1 5 O K p C j 0 S 9 / 9 Q Y x S y O U h g m q d d d z E x N k V B n O B M 5 K v V R j Q t m E j r B r q a Q R 6 i B b H D s j F 1 Y Z k G G s b E l D F u r v i Y x G W k + j 0 H Z G 1 I z 1 q j c X / / O 6 q R n e B h m X S W p Q s u W i Y S q I i c n 8 c z L g C p k R U 0 s o U 9 z e S t i Y K s q M z a d k Q / B W X 1 4 n r a u q V 6 v W H q 8 rU i T j R V J D F o V H C k Y 5 Q 3 g I a M k m J 5 j N D M J H M Z E V k g i U m 2 n R V M S W 4 y 1 / + S z q n d b d R b 9 y d 1 Z q X R R 1 l O I Q j O A E X z q E J N 9 C C N h B I 4A l e 4 N V 6 t J 6 t N + t 9 M V q y i p 0 D + A X r 4 x s T n 5 N h < / l a t e x i t > To capture the overall multi-periodicity, before training, we randomly sample mini-batches from the training set to perform FFT and select the frequencies with the top-k amplitudes {f 1 , . . . , f k }. Given the frequency f j , the corresponding period is p j = ⌈ T fj ⌉. For each selected period p j in {p 1 , . . . , p k } and frequency f j in the corresponding {f 1 , . . . , f k }, we perform the following transform on input x i :K I e Q L v H h Q x K u f 5 M 2 / c Z L s Q R M L G o q q b r q 7 g k R w b V z 3 2 8 m t r W 9 s b u W 3 C z u 7 e / s H x c O j p o 5 T x b D B Y h G r d k A 1 C i 6 x Y b g R 2 E 4 U 0 i g Q 2 A p G t z O / 9 Y R K 8 1 g + m H G C f k Q H k o e c U W O l + l 2 v W H L L 7 h x k l X g Z K U G G W q / 4 1 e 3 H L I 1 Q G i a o 1 h 3 P T Y w / o c p w J n B a 6 K Y a E 8 p G d I A d S y W N U P u T + a F T c m a V P g l j Z U s a M l d / T 0 x o p P U 4 C m x n R M 1 Q L 3 s z 8 T + v k 5 r w 2 p 9 w m a Q G J V s s C l N B T E x m X 5 M + V 8 i M G F t C m e L 2 V s K G V F F m b D Y F G 4 K 3 / P I q a V 6 U v U q 5 U r 8 s V W + y O P J w A q d w D h 5 c Q R X u o Q Y N Y I D+ g f H j U N n G q G W + x W M a 6 E 1 D D p V C 8 h Q I l 7 y S a 0 y i Q / C E Y 3 8 7 8 h y e u j Y h V E y c J 9 y M 6 V C I U j K K V O r 3 E i H 7 W n P b L F b f q z k F W i Z e T C u R o 9 M t f v U H M 0 o g r Z J I a 0 / X c B P 2 M a h R M 8 m m p l x q e U D a m Q 9 6 1 V N G I G z + b 3 z s l Z 1 Y Z k D D W t h S S u f p 7 I q O R M Z M o s J 0 R x Z F Z 9 m b i f 1 4 3 x f D a z 4 R K U u S K L R a F q S Q Y k 9 n z Z C A 0 Z y g n l l C m h b 2 V s B H V l K G N q G R D 8 J Z f X i X t i 6 p X q 9 b u L y v 1 m z y O I p z A K Z y D B 1 d Q h z t o Q A s Y S H i G V 3 h z H p 0 X 5 9 3 5 W L Q W n H z m G P 7 A + f w B S + W Q K A = = < / l a t e x i t > T < l a t e x i t s h a 1 _ b a s e 6 4 = " 4 7 v l j z 0 m C 1 F C H U E a D i m j 5 s Z M e s I = " > A A A B 7 3 i c b V B N S 8 N A E J 3 4 W e t X 1 a O X x S J 4 K o l I 9 V g U x G M F + w F t K J v t p F 2 6 2 c T d j V B C / 4 Q X D 4 p 4 9 e 9 4 8 9 + 4 b X P Q 1 g c D j / d m m J k X J I J r 4 7 r f z s r q 2 v r G Z m G r u L 2 z u 7 d f O j h s 6 j h V D B s s F r F q B 1 S j 4 B I b h h u B 7 U Q h j Q K B r W B 0 M / V b T 6 g 0 j + W D G S f o R 3 Q g e c g Z N V Z q d x P N e 9 n t p F c q u x V 3 B r J M v J y U I U e 9 V / r q 9 m O W R i g N E 1 T r j u c m x s + o M p w J n B S 7 q c a E s h E d Y M d S S S P U f j a 7 d 0 J O r d I n Y a x s S U N m 6 u + J j E Z a j 6 P A d k b U D P W i N x X / 8 z q p C a / 8 j M s k N S j Z f F G Y C m J i M n 2 e 9 L l C Z s T Y E s o U t 7 c S N q S K M m M j K t o Q v M W X l 0 n z v O J V K 9 X 7 i 3 L t O o + j A M d w A m f g w S X U 4 A 7 q 0 A A G A p 7 h F d 6 c R + f F e X c + 5 q 0 r T j 5 z B H / g f P 4 A N p + Q G g = = < / l a t e x i t > F < l a t e x i t s h a 1 _ b a s e 6 4 = " r l 1 j u B J j 2 r 9 k 7 O x P 6 Q F L + 0 0 P X S 8 = " > A A A C A X i c b V D L S s N A F J 3 U V 6 2 v q B v B T b A I r k o i U l 0 W B X F Z w T 6 g i W E y n b R D J w 9 m b o Q Q 4 s Z f c e N C E b f + h T v / xC F Z F N 5 B G l M n w K O Q + Y x g U J K r H 9 h j D J k d Y B h 7 f p b m + X 0 G u Z t d 5 6 5 e N x v m F M Y i s U p S R y X a r v 5 l D y O S B D Q E w r G U A 8 u M w c m w A E Y 4 z W t 2 I m m M y Q S P 6 E D R E A d U O t n 0 g 9 w 4 V s r Q 8 C O h K g R j q v 6 e y H A g Z R p 4 q r M 4 V c 5 7 h f i f N 0 j A v 3 A y F s Y J 0 J D M F v k J N y A y i j i M I R O U A E 8 V w U Q w d a t B x l h g A i q 0 m g r B m n 9 5 k X R P G 1 a z 0 b w 9 q 7 c u y z i q 6 B A d o R N k o X P U Q j e o j T q I o E f 0 j F 7 R m / a k v W j v 2 s e s t a K V M / v o D 7 T P H + 9 Y l 9 0 = < / l a t e x i t > ŷt F < l a t e x i t s h a 1 _ b a s e 6 4 = " K a 9 1 f d d 2 0 X G P r v n o s C z / C l C / h d w = " > A A A C A X i c b V D L S s N A F J 3 U V 6 2 v q B v B T b A I r k o i U l 0 W 3 b i s 0 B c 0 M U y m k 3 b o 5 M H M j R B C 3 P g r b l w o 4 t a / c O f f O G m z 0 N Y D F w 7 n 3 M u 9 9 3 g x Z x J M 8 1 u r r K y u r W 9 U N 2 t b 2 z u 7 e / r + Q U 9 G i S C 0 S y I e i Y G H J e U s p F 1 g w O k g F h Q H H q d 9 b 3 p T + P 0 H K i S L w g 6 k M X U C P A 6 Z z w g G J b n 6 k T 3 B k N k B h o n n Z 2 m e 3 2 e Q u 1 k n d / W 6 2 T B n M J a J V Z I 6 K t F 2 9 S 9 7 F J E k o C E Q j q U c W m Y M T o Y F M M J p X r M T S W N M p n h M h 4 q G O K D S y W Y f 5 M a p U k a G H w l V I R g z 9 f d E h g M p 0 8 B T n c W p c t E r x P + 8 Y Q L + l Z O x M E 6 A h m S + y E + 4 A Z F R x G G M m K A E e K o I J o K p W w 0 y w Q I T U K H V V A j W 4 s v L p H f e s J q N 5 t 1 F v X V d x l F F x + g E n S E L X a I W u k V t 1 E U E P a J n 9 I r e t C f t R X v X P u a t F a 2 c O U R / o H 3 + A A S t l + s = < /I c E U g U Q b D j 7 m Q = " > A A A C I 3 i c b V D J S g N B E O 1 x j X G L e v Q y G I R 4 C T M i U T w F F R H 0 E C E b J H H o 6 f Q k T X o W u m u E 0 J l / 8 e K v e P G g B C 8 e / B c 7 y 0 G T P C h 4 v F d F V T 0 3 4 k y C Z X 0 b S 8 s r q 2 v r q Y 3 0 5 t b 2 z m 5 m b 7 8 q w 1 g Q W i E h D 0 X d x Z J y F t A K M O C 0 H g m K f Z f T m t u 7 H v m 1 Z y o k C 4 M y 9 C P a 8 n E n Y B 4 j G L T k Z C 5 v H H X / k O S a X Q y q 6 W P o u p 7 q J 8 m T g s R R 5 W Q w W O z c J i d O J m v l r T H M e W J P S R Z N U X I y w 2 Y 7 J L F P A y A c S 9 m w r Q h a C g t g h N M k 3 Y w l j T D p 4 Q 5 t a B p g n 8 q W G v + Y m M d a a Z t e K H Q F Y I 7 V v x M K + 1 L 2 f V d 3 j m 6 V s 9 5 I X O Q 1 Y v A u W o o F U Q w 0 I J N F X s x N C M 1 R Y G a b C U q A 9 z X B R D B 9 q 0 m 6 W G A C O t a 0 D s G e f X m e V E / z d i F f e D z L F q + m c a T Q I T p C O W S j c 1 R E d 6 i E K o i g F / S G P t C n 8 W q 8 G 0 P j a 9 K 6 Z E x n D t A / G D + / 6 B W m 8 Q = = < / l a t e x i t > D KL (ŷ t T ||ŷ t F ) < l a t e x i t s h a 1 _ b a s e 6 4 = " o J H 7 n r r G p v + 1 / 3 R Y i d 1 i y r Q 8 D C E = " > A A A C I 3 i c b V D L S g M x F M 3 4 r P V V d e l m s A h 1 U 2 Z E q r g q K i L o o k J f 0 I 5 D J s 2 0 o Z k H S U Y o a f 7 F j b / i x o V S 3 L j w X 0 z b W W j b A x c O 5 9 z L v f d 4 M S V c W N a 3 s b S 8 s r q 2 n t n I b m 5 t 7 + z m 9 v b r P E o Y w j U U 0 Y g 1 P c g x J S G u C S I o b s Y M w 8 C j u O H 1 r 8 d + 4 x k z T q K w K g Y x d g L Y D Y l P E B R a c n O X N 6 6 8 f 1 C F d g 8 K 2 Q 6 g 6 H m + H C j 1 J L l y 5 a 0 a D h c 7 V X X i 5 v J W 0 Z r A n C d 2 S v I g R c X N j d q d C C U B D g W i k P O W b c X C k Z A J g i h W 2 X b C c Q x R H 3 Z x S 9 M Q B p g 7 c v K j M o + 1 0 j H 9 i O k K h T l R / 0 5 I G H A + C D z d O b 6 V z 3 p j c Z H X S o R / 4 U g S x o n A I Z o u 8 h N q i s g c B 2 Z 2 C M N I 0 I E m E D G i b z V R D z K I h I 4 1 q 0 O w Z 1 + e J / X T o l 0 q l h 7 P 8 u W r N I 4 M O A R H o A B s c A 7 K 4 A 5 U Q A 0 g 8 A L e w A f 4 N F 6 N d 2 N k f EEQUATION)whereX j i ∈ R C×fj ×pj , v j i ∈ C C×⌊ p j 2 ⌋ is averaged from f j dimensions by Avg(•).In other words, we perform FFT on each segment obtained by segmenting x i with period p j , and average the FFT results across segments to obtain the distribution v j i over the frequencies within {1, . . . , ⌊ pj 2 ⌋}. In this way, we obtain the overall frequency pattern for each period. To keep the discriminative patterns derived from different periods, we concatenate the different v j i , obtaining v i as the frequency input corresponding to the temporal input x i :EQUATIONWe extend the source sample set P and the target sample set Q to the frequency domain:P = {(x s i , v s i , y s i )} ns i=1 and Q = {(x t i , v t i )} nt i=1 .To learn features in both real part and imaginary part of complex frequency data, we adopt a complex-valued linear layer as the frequency feature extractor ψ F . Since the phase generally does not provide strong discriminative information, we only retain the amplitudes of each frequency to construct the frequency domain feature z i :EQUATIONwhere Amp(•) denotes the calculation of amplitude values. For multivariate time series, we convert v i into a single-channel vector by concatenating across different variates.Discriminability and transferability are two key criteria that characterize the goodness of feature representations to enable domain adaptation. In Section 3, we reveal that the frequency features are more discriminative within the source domain, while the temporal features are more transferable across domains. Based on this discovery, we propose temporal-frequency domain mutual learning, aiming to leverage the respective advantages of the temporal domain and frequency domain.The essence of domain mutual learning relies on how to transfer knowledge between the temporal domain and frequency domain. Inspired by model distillation, where the knowledge is transferred by matching the predictions between the teacher and student via the Kullback Leibler (KL) divergence [17] , we focus mutual learning on the alignment between the temporal predictions and the frequency predictions. The KL divergence between two predictions p 1 and p 2 is formulated as:EQUATION)The KL divergence is asymmetric, that is, D KL (p 1 ||p 2 ) emphasizes aligning p 2 to p 1 , while D KL (p 2 ||p 1 ) emphasizes aligning p 1 to p 2 . Based on the asymmetry, we use different alignment strategies in the source domain and target domain. Specifically, in the source domain, the frequency model serves as a more discriminative teacher, helping the temporal model make more accurate predictions; conversely, in the target domain, the temporal model acts as a more transferable teacher, assisting the frequency model in learning domain-invariant representations. We achieve temporalfrequency domain mutual learning by minimizing the KL Divergence. Formally, domain mutual learning is formulated as:EQUATIONwhere ŷs F and ŷs T refer to the frequency prediction and temporal prediction in the source domain respectively; while ŷt F and ŷt T refer to the frequency prediction and temporal prediction in the target domain respectively. By aligning ŷs T to ŷs F , the training of the temporal feature extractor and classifier is guided with more discriminative information; by aligning ŷt F to ŷt T , the transferable knowledge contained in the temporal features is transferred to frequency domain.Domain adversarial learning [13] is one of the most popular transferable representation learning methods, and it can be employed to learn transferable representation in time series. The key to the effectiveness of the method lies in how to fully utilize two types of features to learn transferable representations. Given time series in temporal domain and frequency domain, domain adversarial learning can be formulated as a minimax optimization problem with three competitive loss terms: (a) L C T on the temporal feature extractor ψ T and classifier g T , which is minimized to guarantee lower source risk of the temporal classifier; (b) L C F on the frequency feature extractor ψ F and classifier g F , which is minimized to guarantee lower source risk of the frequency classifier; (c) L D on the temporal feature extractor ψ T , the frequency feature extractor ψ F and the domain discriminator g D , which is minimized over g D but maximized over ψ T and ψ F :EQUATIONwhere ℓ denotes cross-entropy loss. Different from standard domain adversarial learning, where there is only one type of feature, domain adversarial learning in time series needs to consider the temporal features and frequency features simultaneously. A simple strategy is to concatenate the temporal feature f and the frequency feature z. However, with the concatenation strategy, the adversarial game between the domain discriminator and the feature extractors can be viewed as two independent components: the game between g D and ψ T and the game between g D and ψ F . With the worse transferability, z provides g D with rich domain-label relevant information. In this case, g D only needs to focus on the game with ψ F , ignoring the domain adversarial learning in the temporal domain.To achieve co-alignment in the temporal domain and frequency domain, we propose domain adversarial learning in temporal-frequency correlation subspace. The temporal-frequency correlation subspace not only possesses statistical characteristics of the original temporal feature subspace and original frequency feature subspace but also reflects the correlation between temporal features and frequency features. Reducing the discrepancy of the temporal-frequency correlation subspace not only reduces the discrepancy in the cross-domain temporal and frequency features but also decreases the differences in cross-domain temporal-frequency correlations.Formally, the vectors in temporal-frequency correlation subspace can be calculated as the outer product ⊗ between the temporal feature f and the frequency feature z:EQUATIONwhere z ∈ R 1×l . By adjusting the order of dimensions, z ⊗ f is equivalent to f ⊗ z. Considering the sparsity of the frequency domain and the modeling of long-length time series, the direct outer product leads to dimension explosion and the sparsity in temporal-frequency feature subspace. We address the problem by performing average pooling over z. Average pooling, which calculates the average value for the amplitudes of neighboring frequencies, yields dense frequency features with smaller dimensions. With outer product and average pooling, the adversarial loss L D is formulated as:EQUATIONwhere h(•) denotes the mapping from the inputs of the overall model to the inputs of the domain discriminator, and P (•) denotes the calculation of average pooling.During alignment, our method trains the temporal feature extractor ψ T and classifier g T by minimizing the loss L C T and trains the frequency feature extractor ψ F and classifier g F by minimizing the loss L C F using the source sample set P . Additionally, our method promotes mutual learning between the temporal domain and frequency domain by minimizing the loss L Ms on the source domain and the loss L Mt on the target domain. Meanwhile, our method aligns distributions of the source domain and target domain in the temporal-frequency correlation subspace. With two gradient reversal layers between the two feature extractors and the domain discriminator, the adversarial training is achieved by minimizing the loss L D . To simplify notation, we denote θ F as parameters containing ψ F and g F , and θ T is parameters containing ψ T and g T . The minimax optimization problem is formulated as:EQUATION5 Experiments 
setup: 
 Datasets We conduct extensive experiments using a wide range of time series datasets. (1) Experiments using benchmark datasets in sensor-based human activity recognition (HAR) task: UCIHAR [1] , HHAR [35] and WISDM [20] . For HHAR, we first split domains from the perspective of participants, denoted as HHAR-P [16, 31] dataset. Then, we split domains from the perspective of devices, denoted as HHAR-D [12] datasets. (2) Experiments using the benchmark dataset in sleep stage classification (SSC) task: CAP [14, 37] . (3) Experiments using EMG [24, 27] dataset in gesture recognition (GR) task. (4) Experiments using PCL [32, 9, 21, 19] dataset in motor imagery classification (MIC) task. ( 5) Experiments using FD [31] dataset in machine fault diagnosis (MFD) task. For each dataset, following the existing DA methods on time series [2, 16] , we randomly sample 10 source-target domain pairs for evaluation. If the dataset has less than 10 pairs, we evaluate all available domain pairs. Further details, processing and domain splits are included in Appendix A.Baselines (1) We report the performance of a model without UDA (Source-only) in the temporal domain to show the overall contribution of UDA methods. (2) We implement the following stateof-the-art baselines for UDA of time series data: CODATS [41] , AdvSKM [23] , CLUDA [29] and RAINCOAT [16] . (3) We additionally implement general unsupervised DA methods: CDAN [26] , DeepCoral [36] , AdaMatch [2] , HoMM [5] and DIRT-T [34] .Evaluation We report accuracy and Macro-F1 Score calculated using target test datasets. Accuracy is computed by dividing the number of correctly classified samples by the total number of samples. Macro-F1 Score is calculated using the unweighted mean of all the per-class F1 scores.Implementation We adopt the implementation of AdaTime [31] as a benchmarking suite for domain adaptation on time series data, using 1D-CNN as the temporal feature extractor and 1-lyer complex-valued linear as the frequency feature extractor. We use the same feature extractor across all algorithms, ensuring a fair comparison. In all experiments, we use the prediction of the temporal classifier to calculate accuracy and Macro-F1 Score. More experimental details are provided in Appendix B. Table 1 shows the average accuracy of each method on all datasets and tasks. Overall, our method has won 5 out of 5 tasks and 8 out of 8 datasets (2 metrics). Specifically, our method improves accuracy by 2.75% on GR task, 5.20% on SSC task, 1.31% on MI task, 9.86% on HAR task and 1.30% on MFD task over the advanced baseline on each dataset respectively.Due to the limited pages, we report the results for selected source-target domain pairs with metric accuracy on the representative datasets EMG (GR task), CAP (SSC task) and HHAR-P (HAR task). More accuracy results are given in Table 2 presents the results on CAP dataset. CAP contains over 40,000 samples of 3000 time steps, so adaptation on it is more challenging. Our method outperforms general DA and time series DA methods on 9 out of 10 source-target domain pairs, achieving an average improvement of 5.20% over the advanced baseline, DIRT-T. Table 3 presents the results on HHAR-P dataset. Our method significantly outperforms RAINCOAT, the state-of-the-art DA method for time series, by 10.15%. RAINCOAT: The advanced baseline that achieves suboptimal performance on the three datasets.Sensitivity Analysis It's worth noting that our total loss in Equation (10) does not include any hyperparameters. In other words, we have not tuned any trade-offs, but set them to 1 for the involved datasets in this paper, giving equal weight to all components of the total loss. In UDA setup, how to search the optimal trade-offs without access to labeled target samples is still an open problem. Considering that, we choose to set all the trade-offs to 1, as it is the most intuitive choice. Without tuning the trade-offs, our proposed ACON still achieves significant improvements. To further investigate the sensitivity of ACON to the potential trade-offs, we update Equation (10) as:EQUATIONwhere hyperparameters λ D , λ Ms and λ Mt control the contribution of each component. We investigate the sensitivity of the model to the hyperparameters λ D , λ Ms and λ Mt on the same 10 source-target domain pairs as mentioned in Section 5.1 of three different datasets. We vary the currently investigated hyperparameter in the range of 0.6 ∼ 1.4 and fix other hyperparameters at 1. ACON-λ D refers that the currently investigated hyperparameter is λ D , and others are analogous. From Figure 3 , we observe that the performance of ACON is quite stable to the hyperparameters in Equation (11) . Although setting all the trade-offs to 1 may not achieve the optimal performance, ACON still significantly outperforms the advanced baseline. It implies that without the demand for careful hyperparameter tuning, ACON has the potential to achieve superior performance on a wider range of datasets.Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?Answer • The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper. • The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions). • The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.) • The assumptions made should be given (e.g., Normally distributed errors). • It should be clear whether the error bar is the standard deviation or the standard error of the mean. • It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified. • For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates). • If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text. 
conclusion: 
 In this paper, the phenomenon is revealed--that temporal features exhibit better transferability across domains, whereas frequency features tend to be more discriminative within a specific domain. Based on the findings, Adversarial CO-learning Networks (ACON) is proposed to boost the transferability and discriminability in a collaborative learning manner. Specifically, multi-period feature learning is proposed to enhance the discriminability of frequency features; temporal-frequency domain mutual learning is proposed to enhance the discriminability of temporal features in the source domain and improve the transferability of frequency features in the target domain; domain adversarial learning in temporal-frequency correlation subspace is proposed to further enhance transferability of features. ACON achieves state-of-the-art performance on a wide range of time series datasets. 
experiments compute resources: 
 Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [Yes] Justification: All the experiments in this paper are conducted on a single NVIDIA GeForce RTX 4090 with 24GiB of memory. Guidelines:• The answer NA means that the paper does not include experiments.• The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?Answer: [Yes] Justification: All data, models, and code in the paper respect the license.Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a URL. • The name of the license (e.g., CC-BY 4.0) should be included for each asset.• For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. • If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. • For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. • If this information is not available online, the authors are encouraged to reach out to the asset's creators. 
new assets: 
 Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?Answer: [NA] Justification: The paper does not release new assets.Guidelines:• The answer NA means that the paper does not release new assets.• Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc. • The paper should discuss whether and how consent was obtained from people whose asset is used. • At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file. 
crowdsourcing and research with human subjects: 
 Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?Answer: [NA] Justification: The paper does not involve crowdsourcing nor research with human subjects.Guidelines:• The answer NA means that the paper does not involve crowdsourcing nor research with human subjects. • Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper. • We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution. • For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review. 
 
 Appendix: We conduct extensive experiments using a wide range of time series datasets. The detailed statistics for each dataset is included in Table 5 . For EMG dataset, we use the processed version released by DIVERSIFY [28] . For PCL, CAP and HHAR-D datasets, we use the processed versions released by WOODS [11] . For UCIHAR, HHAR-P, WISDM and FD datasets, we use the processed versions released by AdaTime [31] . Each domain of datasets is randomly divided into 80% training, and 20% testing. We follow [31] , apply Z-score normalization to both the training and testing splits of the data, using the following equation:EQUATIONwhere N = N s for the source domain data and N = N t for the target domain data. Note that both the training and testing splits are normalized based on the training set statistics only.The experiments were conducted on a single NVIDIA GeForce696 RTX 4090 with 24GiB of memory. As shown in Figure 3 , without tuning the trade-offs of training loss, ACON still achieves significant improvements. Here we report other key hyperparameters for ACON in Table 6 . Additional hyperparameters can be found in our code. In all experiments, we adopt 3-layer 1D-CNN as the temporal feature extractor (the specific structure is kept consistent with the existing works [31, 16] ).For frequency feature extraction, we adopt a 1-layer complex-valued linear as the frequency feature extractor. In Table 7 , we report the average accuracy of classification experiments under the setting of Section 3.2 using five different datasets: UCIAHR [1] , HHAR-P [35] , WISDM [20] , CAP [14, 37] and FD [31] . For each dataset, we collect all the domains involved in the selected 10 domain pairs as mentioned in Section 5.1, and perform the classification task on them. In Table 8 , we report the average accuracy of classification experiments under the setting of Section 3.3 using three different datasets: UCIAHR [1] , HHAR-P [35] , WISDM [20] , CAP [14, 37] and FD [31] .For each dataset, we perform the domain adaptation and classification task on the selected 10 domain pairs as mentioned in Section 5.1. We conduct ablation experiments on three datasets, UCIHAR, HHAR-P and WISDM. For each datasets, we select the same 10 source-target domain pairs as mentioned in Section 5.1. The ablation results (average accuracy of 10 domain pairs) are presented in Table 9 . We verify the effectiveness of all learning modules in the proposed method by answering the following questions.Can multi-period frequency feature learning enhance the discriminability of frequency feature?By comparing the 2nd and 3rd rows, we can observe that with multi-period frequency feature learning, the model makes more accurate predictions on the target domain. Meanwhile, compared with 1st row, even with multi-period frequency feature learning, the performance on the target domain is still inferior to the classification on the temporal domain, which is consistent with our conclusion in Section 3.3 that the temporal features have better transferability.Can aligning distributions in temporal-frequency subspace effectively learn domain-invariant features? By comparing the 1st, 3rd and 4th rows, we can observe that distribution alignment significantly improves the performance. It indicates that by aligning the distributions in the temporalfrequency subspace, the model learns more domain-invariant features.Can temporal-frequency domain mutual learning leverage the respective advantages? By comparing the 1st, 3rd and 5th rows, we can observe that the model with domain mutual learning outperforms the model using only the temporal domain or only the frequency domain. It demonstrates that via domain mutual learning, the temporal domain and frequency domain successfully transfer meaningful knowledge, leveraging their respective advantages.Can the different modules mutually promote each other? By comparing the 3rd, 4th, 5th and 6th rows, we can observe that with all modules, the model achieves the optimal performance. Specifically, with multi-period frequency feature learning, the frequency domain transfers more discriminative knowledge to the temporal domain; with aligning distribution in temporal-frequency subspace, the temporal domain transfers more transferable knowledge to the frequency domain; with aligning distribution in temporal-frequency subspace and the temporal domain as a more tranferbale teacher, both the temporal domain and frequency domain learn domain-invariant features; with domain mutual learning, the frequency domain and the temporal domain enhance each other in the transfer progress, achieving a synergistic effect.In this section, we further investigate the impact of different strategies to fuse temporal features and frequency features. We divide the training framework into three modules: feature extraction module (ψ T and ψ F ), classification module (g T and g F ), and alignment module (g D ). In the feature extraction module, ACON contains a temporal feature extractor and a frequency feature extractor.In the classification module, ACON contains a temporal feature classifier and a frequency feature classifier and adopts mutual learning to leverage the respective advantages of the temporal domain and frequency domain. In the alignment module, ACON calculates the outer product of temporal features and frequency features and performs alignment in temporal-frequency correlation subspace.With the same feature extraction module and alignment module, in classification module, we compare 3 different strategies: (1)"concat": use a classifier to perform classification on the concatenation of temporal features and frequency features (the 5th row in Table 10 ). ( 2)"2-classifiers": use two classifiers to perform classification in the temporal domain and the frequency domain respectively (the 4th row in Table 10 ). ( 3) "mutual learning": the temporal-frequency domain mutual learning used in ACON, which is based on "2-classifiers" (the 6th row in Table 10 ).With the same feature extraction module and classification module, in alignment module, we compare 2 different strategies: (1) f ⊕ z: align the concatenation of temporal features and frequency features between the source domain and target domain (the 3rd row in Table 10 ). ( 2) f ⊗ z: align the outer product of temporal features and frequency features between the source domain and target domain, i.e., the alignment in temporal-frequency correlation subspace used in ACON (the 6th row in Table 10 ).DANN-T refers to only performing alignment in the temporal domain. DANN-F refers to only performing alignment in the frequency domain. DANN-TF refers to performing alignment in both the temporal domain and the frequency domain. In the classification module, by comparing the 4th, 5th and 6th rows in Table 10 , we can observe that concatenation features do not achieve better performance. Intuitively, when we use the concatenation feature for classification, the final prediction is a simple average of the temporal prediction and the frequency prediction. Ideally, the extracted features can only maintain suboptimal discriminability and suboptimal transferability. In contrast, our mutual learning allows the frequency domain and temporal domain to become teachers with different advantages, and transfer knowledge to each other. In this way, each other's secondary quantities (e.g. the estimates of the probabilities of the next most likely classes) are transferred [17] , enhancing the discriminability and transferability.In the alignment module, by comparing the 3rd and 6th rows in Table 10 , we can observe that with the concatenation features, DANN significantly underperforms our method. Intuitively, when we use the concatenation features for alignment, f F with the worse transferability provides rich domain-label relevant information for the domain discriminator g D . In this case, g D only needs to focus on the game with ψ F in the frequency domain, ignoring the domain adversarial learning in the temporal domain. Based on the experimental performance and intuition, we discard the simple fusion and opt for co-alignment in the temporal-frequency correlation subspace.Although ACON boosts transferability and discriminability for time series Domain adaptation, like existing DA methods, it is still unstable enough in time series with relatively large variances. This is a problem that needs to be solved urgently in the future.We investigate how to boost Transferability and discriminability for domain adaptation in time series classification. We reveal that the frequency features are more discriminative, while the temporal features are more transferable. Upon this, we propose multi-period frequency feature learning, domain mutual learning, and distribution alignment in temporal-frequency feature subspace. The purpose of our research is to advance the research progress in the relevant community without any negative social impact.We present all experimental results in this section. Notably, our model achieves superior performance, yielding improvements of more than 6% in terms of accuracy and 4% in terms of Macro-F1 across 8 cross-domain time series datasets and 5 common applications on average. , with an open-source dataset or instructions for how to construct the dataset). (d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility.In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.38th Conference on Neural Information Processing Systems (NeurIPS 2024). 


Decision: Reviewers agree on acceptance based on meaningful empirical insights, effective technical solutions, and notable performance. The authors are encouraged to include discussions and results in the rebuttal to the final version.

Reviews: review: paper_summary: paper_summary: This paper uncovers an empirical insight in time series domain adaptation - frequency features are more discriminative within a specific domain, while temporal features show better transferability across domains. Based on this insight, it develops ACON (Adversarial CO-learning Networks), which achieves clear improvement over baselines.
strength_weakness: strength_weakness: - It would be better to explain (or explore) “why” behind the insight? Is it because the distinguished frequency patterns shift across domains dramatically?

- Usually, neural networks can capture some frequency patterns from time series data. Why it avoids most distinguished frequency patterns, but extracts more transferable ones?
questions: questions: See weakness.
limitations: limitations: The limitation of stability has been discussed.
paper_summary: paper_summary: The paper shows that temporal features and frequency features should not be equally treated in model training, the expression of those features are different. Frequency features show strong discriminability and temporal features show strong transferability. Then the author propose the Multi-period frequency feature learning; Temporal-frequency domain mutual learning and Domain adversarial learning in temporal-frequency correlation subspace to leverage the advantages. The proposed results are impressively good.
strength_weakness: strength_weakness: The motivation of the proposed methods should be clarified.

1. Why the alignment between the temporal predictions and the frequency predictions can leverage the respective advantages of the temporal domain and frequency domain? There is no guarantee to keep both advantages.
2. Why the Multi-period frequency feature learning can enhancing the discriminability of the frequency domain?
3. Why Domain adversarial learning can let the model learn transferable representations?
questions: questions: See weaknesses.
limitations: limitations: The authors have addressed the limitations.
paper_summary: paper_summary: This paper studies the Unsupervised Domain Adaptation (UDA) problem in time series classification. The authors first proposed an insight that temporal features enhance transferability while frequency features enhance discriminability. Based on the insight, the authors designed a model that leverages temporal and frequency features. Other techniques include but not limited to Knowledge Distillation and Domain Adversarial Learning. The evaluations show SOTA performance, and the ablation study indicates that the designed components are helpful.
strength_weakness: strength_weakness: 1.	This paper is derived from the empirical insight of temporal and frequency features. It would be better if the authors can explain a little bit about why temporal or frequency features excel in different properties. 
2.	The preliminary experiment on transferability and discriminability could use more datasets and more analysis to justify the motivation of the paper.
3.	Since there are other papers utilizing temporal and frequency features as mentioned in the related work, it would be better if the author can illustrate the differences and the advantages of the current design compared to other works.
4.	It would be helpful to improve clarity if the author can explain the “index” in figure 1.
5.	During the illustration of the model proposed, the author did not cover the design of the domain discriminator.
questions: questions: It’s a great idea to exploit the advantages of both temporal and frequency features using distillation. But I also wonder why a simple fusion of temporal and frequency features is not used and compared. Will the fused features maintain both good transferability and discriminability?
limitations: limitations: Yes
paper_summary: paper_summary: The paper introduces Adversarial CO-learning Networks (ACON) to improve unsupervised domain adaptation (UDA) for time series classification by enhancing the transferability and discriminability of temporal and frequency features. The proposed approach incorporates multi-period frequency feature learning, temporal-frequency domain mutual learning, and domain adversarial learning in temporal-frequency correlation subspaces. Extensive experiments demonstrate ACON's superior performance over existing methods on various time series datasets.
strength_weakness: strength_weakness: - Methodological Complexity: The proposed ACON framework is highly complex, involving multiple components and phases (multi-period frequency feature learning, temporal-frequency domain mutual learning, and domain adversarial learning). This complexity may hinder reproducibility and practical implementation, especially in real-world applications.
- Insufficient Scalability Analysis: The paper lacks a detailed discussion on the scalability and computational efficiency of ACON. It remains unclear how the model performs with larger datasets and whether it introduces significant computational challenges.
- Presentation and Clarity Issues: Some sections of the paper are dense and difficult to follow. Simplifying the language and providing clearer explanations would improve readability and accessibility.
- Lack of Detailed Comparative Analysis: While the paper includes experiments against various baselines, it falls short in providing a detailed comparative analysis. More in-depth discussion on why ACON outperforms other methods and the specific contributions of its individual components would strengthen the paper.
questions: questions: 1. The preliminary study assumes that low-frequency components are the most discriminative. However, the choice between phase and amplitude for frequency feature extraction can significantly impact results. Why were only the human activity recognition datasets used for this preliminary study, and how might this assumption affect other types of time series data?
2. The ablation study indicates that the domain loss contributes more significantly to the model's performance than the two KL losses. Could you explain why this is the case, and provide more insights into the individual contributions of each loss component?
3. The paper proposes domain adversarial learning to align features in both source and target domains. However, this seems to conflict with the novel aspect of different alignment strategies based on domain-specific characteristics. Could you clarify how these two approaches are reconciled in your framework?

~~4. How are classification predictions made during inference? The paper mentions a voting mechanism, but additional details on how the final prediction is derived from the individual components would be helpful.~~  

5. In Section 4.1, how is the value of k (the number of top amplitudes) determined for multi-period frequency feature learning? Is it dataset-specific, or is there a general guideline for selecting this parameter?

~~6. Can you provide more details on what the learned latent variables represent? Do they capture the essential features that define each class, and how can this be validated?~~

(The issues in Questions 4 and 6 were errors that occurred while I was switching between different pages during the review process of multiple articles. I sincerely apologize to the authors for this.)
limitations: limitations: The authors acknowledge that while ACON enhances transferability and discriminability for time series domain adaptation, it remains unstable when dealing with time series data that exhibit relatively large variances. Addressing this instability is a critical challenge that needs to be tackled in future research.

Comments: title: Response to Reviewer 5Lht
Looking forward to your feedback
Looking forward to your feedback
Response to Reviewer U97c
Response to Reviewer ggDU
Response for a deeper discussion (Part 2)
Response for a deeper discussion (Part 1)
comment: Thank you for your invaluable feedback and dedicated time to review our paper. 

We will revise our paper according to your feedback, adding more explanation on why each component works. If you have any further questions, please send them to us, we look forward to discussing with you to further improve our work.
Thanks for the explanations, I will keep my rating to 6.
Dear Reviewer 5Lht, 

Thank you for your valuable comments.

We have made an extensive effort trying to address your concerns. In our response:

- From the perspective of Knowledge Distillation, we clarify why the alignment between the temporal predictions and the frequency predictions can leverage the respective advantages.
- Based on the inherent characteristic of time series, we explain why the Multi-period frequency feature learning can enhance the discriminability of the frequency domain.
- From the intuitive perspective and the theoretical perspective, we provide explanations of why Domain adversarial learning can let the model learn transferable representations.

We hope our response can address your concerns. If you have any further concerns or questions, please do not hesitate to let us know, and we will be more than happy to address them promptly. 

All the best, 

Authors
Dear Reviewer uayq,

Thank you for your valuable comments.

We have made an extensive effort trying to address your concerns. In our response:

- From the perspective of energy, we provide an intuition behind the empirical insight.
- We further demonstrate that the mutual enhancement between the temporal domain and the frequency domain is a promising solution by comparing the sota models of temporal modeling with 1D-CNN.

We hope our response can address your concerns. If you have any further concerns or questions, please do not hesitate to let us know, and we will be more than happy to address them promptly. 

All the best, 

Authors
Thank you for the timely response and efforts in reviewing our paper. We sincerely appreciate your recommendation to accept our paper.

We will revise our paper according to your feedback and the results in the rebuttal, including adding:

- The intuition behind the empirical insight.
- More datasets for preliminary study.
- More details: a more detailed comparison with other works, the design of the domain discriminator, and the explanation of the "index".
- A comprehensive comparison of simple fusion.

Thank you again for your invaluable feedback and dedicated time to review our paper. If you have any questions, please send them to us, we look forward to discussing with you to further improve our work.
Thanks for the response. I am leaning to accept this paper and would like to maintain my positive score.
Thank you for the timely response and raising the score to 6. We are pleased to know that we have successfully addressed your concerns. We sincerely appreciate your recognition of our work as a commendable contribution that offers a fresh perspective in the field of UDA.

We will revise our paper according to your feedback and the results in the rebuttal, including adding more details about how to determine top-k periods, providing more comparisons about the evaluation scope and training speed, and discussing the enhancement between different modules.

Thank you again for your invaluable feedback and dedicated time to review our paper. If you have any questions, please send them to us, we look forward to discussing with you to further improve our work.
Thank you for your response. I have reviewed the content, and these replies effectively address my current concerns. I believe the authors have a solid understanding and insight into their research work. Additionally, they offer a fresh perspective in the field of UDA, making this a commendable contribution.

I've edited the comments and the score.
### **Feedback2: Can domain adaptation tasks be effectively completed with domain loss alone, without relying on the KL loss?**

### Subquestion 3. "Can domain loss solve domain adaptation tasks effectively?"

In subquestion 1, we know that to complete domain adaptation tasks effectively, boosting the transferability and discriminability of features is a must.

In subquestion 2, we know that domain loss is the key to improving the transferability of features.

If domain loss can solve domain adaptation tasks effectively, it means domain loss can enhance the discriminability of features. However, the training objective of domain loss is not related to the discriminability of features. Thus there is no guarantee that discriminability of features can be boosted only using domain loss.

Ref[2] reveals that adversarial learning can potentially deteriorate the discriminability since it distorts the original feature distributions when learning domain invariant features. 

Thus the answer to the subquestion 3 is: **only using domain loss cannot solve domain adaptation tasks effectively because domain loss may potentially deteriorate the discriminability of features, techniques that can boost the discriminability of features should be introduced.**





### **Feedback3: Is there any theoretical support for describing mutual learning and adversarial learning as orthogonal?**

In our rebuttal,  we state that **the alignment directions** (these words cannot be ignored) of two modules are orthogonal. Intuitively, the alignment direction of mutual learning (temporal <-> frequency) and the alignment direction of adversarial learning (source <-> target) are totally different and easy to understand.

It is quite difficult to prove the orthogonality of two learning modules theoretically, but we can prove it empirically:

Mutual learning and adversarial learning can be treated as different tasks. Following Ref [3], we analyze the individual gradients produced by adversarial learning and mutual learning in the training process. The angles between gradient vectors in mutual learning and gradient vectors in adversarial learning are calculated as in Ref [3], results are in the Table below:

|       | UCIHAR         | HHAR           | WISDM          | Average |
| ----- | -------------- | -------------- | -------------- | ------- |
| Angle | $86.16\degree$ | $84.37\degree$ | $88.22\degree$ | $86.25$ |

If the angle between two gradients are close to $90\degree$, these two tasks can be treated as orthogonal. From the above table we can find that in 3 datasets, the average angles between gradient vector in mutual learning and gradient vector are very close to  $90\degree$.

[1] Ben-David et al. "A theory of learning from different domains."  *Machine learning*, 2010.

[2] Liu et al. "Transferable Adversarial Training: A General Approach to Adapting Deep Classifiers." *ICML*, 2019.

[3] Yu et al. "Gradient Surgery for Multi-Task Learning." *NeurIPS*, 2020.



Thanks for your valuable comments. We hope our responses were able to address any remaining concerns. Please do let us know if you have any further questions as well as what would be expected for score improvement.
Thank you very much for your quick feedback. We would be delighted to engage in a deeper discussion with you.

### **Feedback1: The observation of asynchronous temporal/frequency features between the source and target domains is a valuable finding**.

Thank you very much for recognizing our empirical insight as a valuable finding. As a new finding, we believe it can provide insights to guide the design of more algorithms for future works.



### **Feedback2: Can domain adaptation tasks be effectively completed with domain loss alone, without relying on the KL loss?**

We will answer this question in 3 subquestions.

### Subquestion 1. "How to complete domain adaptation tasks effectively?"

To ensure that the reviewer fully understands our discussion, we give some detailed background knowledge in UDA here.

In domain adaptation theory [1], the generalization error $\epsilon_t$ of the target domain can be bounded by:

$\epsilon_t \leq \epsilon_s + d_{\mathcal H\Delta\mathcal H}(P,Q)+\lambda \quad (1)$

$\epsilon_s$ is the source error, $d_{\mathcal H\Delta\mathcal H}(P,Q)$ measures the divergence between the source and target feature distributions, and $\lambda$ is the error of an ideal joint hypothesis $h^*$ defined as $h^∗ = arg \min_{h\in \mathcal H }\epsilon_s(h) + \epsilon_t(h)$, such that:

$\lambda = \epsilon_s(h^*) + \epsilon_t(h^*) \quad (2)$

From Equation (1), we find that if we want to complete domain adaptation tasks effectively, we need to have three small error terms: $\epsilon_s$, $d_{\mathcal H\Delta\mathcal H}(P,Q)$ and $\lambda$. Among them, $\epsilon_s$ is the source error, considering that the model is supervised by source labeled data, $\epsilon_s$ is very small. Thus the key to achieving domain adaptation is to minimize $d_{\mathcal H\Delta\mathcal H}(P,Q)$ and $\lambda$.

$d_{\mathcal H\Delta\mathcal H}(P,Q)$ measures the divergence between the source and target feature distributions, if the features have strong transferability, the divergence between features of the source domain and target domain should be small. Thus, to minimize $d_{\mathcal H\Delta\mathcal H}(P,Q)$, boosting the transferability of features is a promising solution.

In Equation (2), $\lambda$ is the error of an ideal joint hypothesis. It means that given source features and target features, $\lambda$ is the error of the optimal classifier (e.g. linear classifier) to classify features into each class of 2 domains. Thus $\lambda$ can measure the discriminability of features. To minimize $\lambda$, boosting the discriminability of features is a good choice.

With the above background knowledge, the answer to this subquestion is: to complete domain adaptation tasks effectively, we need to minimize $d_{\mathcal H\Delta\mathcal H}(P,Q)$ and $\lambda$​, i.e. **boost transferability and discriminability of features**.







### Subquestion 2. "How does domain loss help domain adaptation?"

In our original rebuttal to the reviewer ggDU, we answer "Domain loss is the key to improving transferability" but we do not explain it in detail due to the limited space. Here we explain this answer **intuitively and theoretically**.

- Intuitively, adversarial learning is a two-player game between the domain discriminator and the feature extractor. The domain discriminator is trained to distinguish source features from target features and the feature extractor is trained simultaneously to confuse the discriminator. When the game reaches equilibrium, the domain discriminator can no longer distinguish the source features from the target features. At this point, the extracted features are invariant to the change of domains, and the transferability of features is enhanced. 

- Theoretically, according to [1], the $\mathcal{H}\Delta \mathcal{H}$-Divergence between the source feature distribution $P$ and target feature distribution $Q$ can be estimated by training the domain discriminator $D$: 

  $L_D= \max\limits_{D}\mathbb E_{f\sim P}[D(f)=0]+\mathbb E_{f\sim Q}[D(f)=1] \quad (3)$

  The objective of the feature extractor is to minimize the source error as well as the $\mathcal{H}\Delta \mathcal{H}$-Divergence bounded by Equation (3), boosting the transferability of features.

Overall, the answer to subquestion 2 is: **domain loss is the key to improving transferability of features**.
Thank you for addressing my previous concerns. I appreciate the clarifications and would like to delve deeper into a few points:

1. The observation of asynchronous temporal/frequency features between the source and target domains is quite intriguing. Your experiments confirm this phenomenon, which I find to be a valuable finding.  
2. Regarding the KL loss and domain loss, I realize my previous query may not have been clear. From the ablation study, it appears that the domain loss contributes significantly more to the overall performance improvement than the KL loss. The KL loss seems to be an adjustment to align with the authors' previous observations of different domain characteristics. My question is: can domain adaptation tasks be effectively completed with domain loss alone, without relying on the KL loss?  
3. Following up on the previous point, I noticed in your rebuttal that you described the relationship between mutual learning and adversarial learning as "orthogonal." While I agree that these two tasks have different objectives, the term "orthogonal" suggests a strong distinction. Considering that these tasks are closely related, is there any theoretical support for describing them as orthogonal?  

Lastly, I sincerely apologize for the confusion regarding Q4/6. This error was due to my handling multiple paper reviews simultaneously and inadvertently switching pages. I deeply regret any inconvenience this may have caused.