DLGAN : Time Series Synthesis Based on Dual-Layer Generative Adversarial Networks

TL;DR

DLGAN is a novel dual-layer GAN model that effectively synthesizes time series data by capturing temporal dependencies through a two-stage process involving feature extraction and reconstruction, outperforming existing methods.

Contribution

The paper introduces DLGAN, a dual-layer generative adversarial network that decomposes time series synthesis into feature extraction and reconstruction, improving temporal dependency modeling.

Findings

DLGAN outperforms existing methods on four public datasets.

The model effectively captures temporal dependencies in generated time series.

Extensive experiments validate the superiority of DLGAN across various metrics.

Abstract

Time series synthesis is an effective approach to ensuring the secure circulation of time series data. Existing time series synthesis methods typically perform temporal modeling based on random sequences to generate target sequences, which often struggle to ensure the temporal dependencies in the generated time series. Additionally, directly modeling temporal features on random sequences makes it challenging to accurately capture the feature information of the original time series. To address the above issues, we propose a simple but effective generative model \textbf{D}ual-\textbf{L}ayer \textbf{G}enerative \textbf{A}dversarial \textbf{N}etworks, named \textbf{DLGAN}. The model decomposes the time series generation process into two stages: sequence feature extraction and sequence reconstruction. First, these two stages form a complete time series autoencoder, enabling supervised learning on the original time series to ensure that the reconstruction process can restore the temporal dependencies of the sequence. Second, a Generative Adversarial Network (GAN) is used to generate synthetic feature vectors that align with the real-time sequence feature vectors, ensuring that the generator can capture the temporal features from real time series. Extensive experiments on four public datasets demonstrate the superiority of this model across various evaluation metrics.

Tables

Table 1. Table 1. Results on Multiple Time-Series Dataset (Bold indicates best performance)

Metric	Methed	ETTH	Stock	Exchange	Weather
Discriminative Score	C-RNN-GAN	0.497	0.399	0.289	0.487
	WaveNet	0.332	0.232	0.394	0.498
	WaveGAN	0.252	0.244	0.293	0.425
	RCGAN	0.125	0.196	0.317	0.493
	TimeGAN	0.106	0.102	0.209	0.412
	PSA-GAN	0.497	0.469	0.499	0.499
	DLGAN	0.079	0.090	0.104	0.173
Predictive Score	C-RNN-GAN	0.131	0.038	0.179	0.007
	WaveNet	0.347	0.042	0.252	0.527
	WaveGAN	0.156	0.040	0.068	0.019
	RCGAN	0.146	0.040	0.061	0.006
	TimeGAN	0.132	0.038	0.051	0.002
	PSA-GAN	0.253	0.061	0.331	0.484
	DLGAN	0.127	0.037	0.048	0.003

Table 2. Table 2. Results of Ablation Experiments (Bold indicates best performance)

Metric	Methed	ETTH	Stock	Exchange	Weather
Discriminative Score	w/o Temporal Feature Extractor	0.086	0.152	0.155	0.267
	w/o TimeSeries Reconstructor	0.134	0.169	0.163	0.324
	w/o All	0.095	0.181	0.127	0.177
	DLGAN	0.079	0.090	0.104	0.173
Predictive Score	w/o Temporal Feature Extractor	0.133	0.039	0.066	0.003
	w/o TimeSeries Reconstructor	0.177	0.038	0.092	0.002
	w/o All	0.130	0.040	0.054	0.003
	DLGAN	0.127	0.037	0.048	0.003

Equations

$$H_{1:T}^{Real}=encoder(X_{1:T}),$$

$${\hat{X}}_{1:T}^{Real}=decoder(H_{1:T}^{Real}),$$

$$H_{:,d}^{time}=MSA\left(PATCH\left(H_{:,d}\right)+E_{:,d}^{pos}\right),$$

$$H_{t,:}^{dim}=MSA\left(H_{t,:}^{time}\right).$$

$$H_{emb}^{Real}=GRU(H_{:,:}^{dim}).$$

$$H_{emb}^{Fake}=GRU(CA(TF(AvgPool(Z)),TF(Z),TF(Z)),$$

$$CA(Q,K,V)=Softmax(Q\times K^T)\times V,$$

$$y_1=Discriminato{r}_1(H_{emb}^{Real},H_{emb}^{Fake})$$

$${\hat{H}}_{1:T}^{Fake}=Generato{r}_2(H_{emb}^{Fake}),$$

$${\hat{H}}_{1:T}^{Real}=Generato{r}_2(H_{emb}^{Real}),$$

$$y_2=Discriminato{r}_2(H_{1:T}^{Real},H_{1:T}^{Real},H_{1:T}^{Fake}).$$

$$L_R^{AE}=L_{mse}(X_{1:T},{\hat{X}}_{1:T}^{Real}).$$

$$L_R^H=L_{mse}(H_{1:T}^{Real},{\hat{H}}_{1:T}^{Real}).$$

$$L_G=L_{gan}(y_1)+L_{gan}(y_2)+L_{mse}(H_{1:T}^{Real},{\hat{H}}_{1:T}^{Real}).$$

$$L_D=L_{gan}(y_1)+L_{gan}(y_2).$$

Full text

Data synthesis, Time series, Generative adversarial network

††copyright: none††ccs: Security and privacy Data anonymization and sanitization††ccs: Information systems Data cleaning††ccs: Computing methodologies Neural networks

1. Introduction

Traditional manufacturing enterprises accumulate a large amount of industrial time series data in their daily production and operational activities, but often lack the necessary tools for analysis and utilization. To fully exploit the potential of this data, collaboration with technology companies or data analysis firms is often necessary. An ideal collaboration mode involves traditional manufacturing enterprises providing an authentic and effective industrial time series dataset, and the collaborating partner utilizes this data set to develop the corresponding model algorithms and provide feedback. However, due to concerns about protecting trade secrets and user privacy, direct sharing of authentic data with the collaborating partners is typically not permitted (28, ; 29, ; 30, ; 31, ). Facing this contradiction, synthesizing a high-quality dataset with equivalent utility is a preferable solution.

In recent years, generative models have undergone significant development, primarily including those based on Generative Adversarial Networks (GANs)(3, ), Variational Autoencoders (VAEs)(41, ), and Diffusion Models(42, ). Although their impact has primarily been in the field of computer vision (20, ; 21, ; 22, ; 32, ; 33, ) for generating realistic images, researchers have begun to apply them to the field of time series synthesis due to their success in the field of vision. These methods attempt to learn the inherent features and temporal dependencies of time series, generating new time series with similar utility and statistical properties from random sequences.

Existing methods tend to start with random sequences sampled from a particular distribution and perform continuous temporal modeling on them to generate target time series. However, temporal modeling tools such as RNNs (27, ) and their variants LSTM(4, ), GRU(5, ), etc., primarily aim to capture patterns and regularities in input sequence data. Since the input data consists of discrete random sequences that inherently lack significant temporal patterns or regularities, these modeling tools often perform poorly, failing to effectively ensure the temporal dependencies in the generated sequences. Besides, time series often exhibit strong temporal features, such as local dependencies, periodicity, etc. (34, ; 36, ; 37, ; 38, ). The generation process from random sequences to target sequences in these models is typically unsupervised, and also due to the fact that the input data are discrete random sequences, some of the methods that are proven to be effective in time series representation and prediction (11, ; 13, ; 14, ; 15, ; 19, ; 34, ) are difficult to directly apply to the time series generation process, resulting in the models not being able to fully learn the temporal feature of the original time series.

In response to the above issues, we propose a simple but effective generative model Dual-Layer Generative Adversarial Networks, named DLGAN. The model decomposes the time series generation process into two stages: sequence feature extraction and sequence reconstruction. First, these two stages form a complete time series autoencoder, allowing for comprehensive supervised learning on the original time series dataset. This ensures that the model can effectively extract the temporal features from the original time series. Additionally, the feature-reconstruction process ensures the temporal dependencies of the time series reconstructed from the feature vectors. Second, we add two layers of GANs to the above time series autocoding process. The first-layer generative network is responsible for generating temporally extracted feature vectors, ensuring that the generation process can capture the temporal characteristics of real-time series. The second-layer generative network adds an unsupervised training layer to the temporal feature reconstruction process, enhancing the reconstruction process’s ability to interpret and rebuild the temporal feature vectors. The main contributions of this paper are as follows.

• •

The DLGAN model is proposed, which places the time series generation process on a foundation of supervised learning based on the original time series. By combining supervised and unsupervised learning, DLGAN ensures the temporal dependencies of the generated time series.

• •

The time series feature extraction process is applied to the original sequence, while the GAN is used to generate feature vectors that align with the original temporal feature vectors. This approach effectively leverages existing temporal feature extraction methods while ensuring that the generation process also captures the temporal features from the original time series data.

• •

Extensive experiments on four publicly available datasets show that the DLGAN performs better than the state-of-the-art methods on a variety of evaluation metrics.

2. Related Work

The demand for data sharing and the need for data privacy protection often coexist. The critical solution to addressing this issue lies in the synthesis of high-quality synthetic datasets that have the same utility as the original data when confronted with the same task. Earlier research often relied on statistical models, attempting to establish an approximate distribution of real data by identifying correlations between attributes. Synthetic datasets were then constructed by sampling from this approximate distribution (2, ; 35, ). However, capturing the complex relationships between data is challenging, and approximate distributions often struggle to fully replicate the true distribution of the original data. As a result, it is difficult to synthesise high quality synthetic datasets using such methods.

Due to the superior capability of neural networks in capturing data correlations, they have been widely applied in the field of data synthesis. GANs(8, ; 9, ; 10, ; 17, ; 26, ) are undoubtedly among the most widely used models. In recent years, there has also been a rise in time series generation models based on VAEs(43, ; 44, ) and Diffusion Models(45, ; 46, ).

The GAN consists of a generator and a discriminator, the generator generates the target data from random data and the discriminator improves the model performance by discriminating the authenticity of the original and generated data. Benefiting from the extensive research on generative adversarial networks for relational data generation (6, ; 7, ; 23, ; 24, ; 25, ), early time series generative models used the temporal modeling module to perform a simple reconstruction of the generator and discriminator for temporal data generation, for example, Mogren et al.(8, ) used LSTM for reconstruction of generators and discriminators. Additionally, Yoon et al.(9, ) introduced an additional sequence regression prediction process to provide temporal dynamics support for the generated sequences. Jeha et al.(10, ) employed progressive generation and self-attention mechanisms to gradually generate long-range temporal samples.

The VAEs consist of an encoder and a decoder. The encoder maps the original data to a standard normal distribution, while the decoder samples randomly from this distribution to generate target data. Desai et al.(43, ) simply reconstructs the encoder and decoder to make VAE suitable for time series generation. Li et al.(44, ) learns causal graph during the time series generation process and incorporates it into the data generation process.

Diffusion models gradually map original data to a standard normal distribution space by progressively adding noise, and then reverse the diffusion process to transform randomly sampled data from the standard normal distribution back to the original data distribution space. Yuan et al.(45, ) combines seasonal trend decomposition techniques with denoising models to learn the seasonal trends of time series. Shen et al.(46, ) performs seasonal trend decomposition and incrementally models the target sequence from coarse to fine granularity.

In all three types of models, the issue of performing continuous time series modeling on discrete random sequences is very common, which fails to ensure the temporal dependencies of the generated sequences. These models often rely on specific model characteristics to consider partial temporal features. For example, diffusion models naturally possess a coarse-to-fine-grained modeling process, which has led to research into multi-scale temporal feature. However, because feature extraction modules struggle to work effectively with randomly sampled inputs, GANs and VAEs rarely consider temporal feature information.

3. Methodology

In the task of time series synthesis, our goal is to develop a generative model that can effectively capture the features of the original time series and generating high-quality synthetic datasets with temporal dependencies from random inputs. The DLGAN mainly consists of three component modules: Sequence Autoencoder, which maps the original time series into a low-dimensional embedding space, capturing its primary features while providing data patterns that facilitates learning in subsequent modules. Temporal Feature Generator, which uses a temporal feature extractor to extract temporal feature vectors from the original time series and generate synthetic temporal feature vectors aligned with the real temporal feature vectors. Sequence Reconstructor, which combines a supervised autoregressive process to reconstruct the time series from the temporal feature vectors. We will first present the overall architecture of the model, followed by a detailed description of each component module.

3.1. Overall Architecture

The overall architecture of DLGAN is illustrated in Figure 1, which mainly consists of three major components: 1) Sequence Autoencoder, highlighted by a light red background, is given the original time-series data $X_{1:T}=(X_{1},\cdots,X_{T})$, where $X_{t}=(X_{t}^{1},X_{t}^{2},\cdots,X_{t}^{M})$ represents the feature vector of the multidimensional time series at time step $t$, and $M$ is the number of attributes contained in the time series. The encoder generates a hidden sequence $H_{1:T}^{Real}=(H_{1}^{Real},H_{2}^{Real},\cdots,H_{T}^{Real})$, where $H_{t}^{Real}=(H_{t}^{1},H_{t}^{2},\cdots,H_{t}^{N})$ represents the feature vector at time step $t$ of the hidden sequence, and $N$ is the number of attributes included in the hidden sequence. This is followed by decoding to reconstruct $\widehat{X}_{1:T}^{Real}\in R^{M\times T}$. 2) Temporal Feature Generator, highlighted by a light yellow background, the temporal feature extractor receives the hidden sequence $H_{1:T}^{Real}$ for extracting temporal features, generating the synthesised temporal feature vector $H_{emb}^{Real}$. Meanwhile, Generator1 accepts a random sequence $Z$ to generate the temporal feature vector $H_{emb}^{Fake}$, and Discriminator1 discerns the authenticity of the temporal feature vectors. 3) Sequence Reconstructor, highlighted by a light green background, Generator2, also known as the feature reconstructor, receives the temporal feature vectors to reconstruct the hidden series, generating $\widehat{H}_{1:T}^{Real}\in R^{N\times T}$ and $\widehat{H}_{1:T}^{Fake}\in R^{N\times T}$. Discriminator2 is responsible for discerning the authenticity of these reconstructed hidden sequences. After training the model, random sequences are passed through Generator1 and Generator2 to generate $\widehat{H}_{1:T}^{Fake}$, which is then decoded to generate the synthetic time series data.

3.2. Sequence Autoencoder

The autoencoder consists of two major components: the sequence encoder and decoder. The encoder is responsible for mapping the original time series to a low-dimensional embedding space, while the decoder reconstructs the time series from this embedding space. The reason for choosing to map the time series to an embedding space rather than directly using the original data for subsequent training lies in two aspects. On the one hand, time series data often contain considerable noise. Mapping time series to a low-dimensional embedding space makes it easier to capture the intrinsic characteristics of the time series, thereby improving the model’s generalization ability. On the other hand, through joint training, the encoder can also learn a more favorable representation of the time series for the subsequent modules’ training. The encoding and decoding process can be represented as follows:

[TABLE]

[TABLE]

In this case, the encoder and decoder can be implemented using any time series modeling module. Here, we choose to implement them using a deep GRU (Gated Recurrent Unit) network.

3.3. Temporal Feature Generator

Temporal Feature Generator comprises three main components: the Temporal Feature Extractor, Generator1, and Discriminator1. The critical design lies in the Temporal feature extractor’s effective utilization of component analysis of the time series to capture the temporal features of the original hidden sequence $H_{1:T}^{Real}$ and generate the temporal feature vector $H_{emb}^{Real}$. The generator, through adversarial training, is able to map the input random sequence $Z$ to the latent space where the temporal feature vector resides, generating $H_{emb}^{Fake}$. By extracting the process of time series feature extraction from the generator of the generative adversarial network and placing it on the original hidden sequence, we ensure the effectiveness of the temporal feature extraction process. Simultaneously, it avoids performing temporal feature extraction modules on immature time series data generated by the generator.

The detailed structure of the temporal feature extractor is illustrated in Figure2(c. For multivariate time series, the time series of different channels exhibit a certain degree of channel independence while also influencing each other(47, ). Therefore, we first treat the input multivariate time series $H_{1:T}^{Real}$ as multiple univariate time series and perform channel-independent temporal modeling. Subsequently, to capture the cross-channel correlations, the univariate-modeled time series are concatenated and restored as multivariate time series, enabling the capture of correlations between different information channels at the same time step.

In channel-independent modeling, since the temporal features of a time series are often reflected in its dynamic changes, the value at a single time step does not carry rich temporal semantics(11, ; 13, ). Therefore, for the input univariate time series, we select an appropriately sized sliding window to partition the time series into non-overlapping segments, preserving the temporal dynamics while maintaining the local dependencies of the series. Subsequently, we employ a multi-head self-attention mechanism(MSA) to enhance the features, capturing the global dependencies and periodicity of the time series.

[TABLE]

In the above equation, $H_{:,d}$ represents the value of the hidden sequence on data dimension $d$, $PATCH$ is the sliding window partitioning operation. While the self-attention mechanism effectively reduces the reasoning distance between different positions to $1$, capturing the global dependencies of the input, it neglects positional information, which is crucial in the temporal dimension. To address this, we incorporate positional encoding $E_{:,d}^{pos}$ into each patch.

In cross-channel modeling, we merge the time series from different channels while maintaining the patch segmentation. Similarly, we use a self-attention mechanism to capture the dependencies of patches across different channels at the same temporal position. However, unlike in the temporal dimension, there is no explicit positional relationship between channels. Thus, we omit positional encoding, ensuring the modeling aligns better with the characteristics of time series data.

[TABLE]

Although the attention mechanism excels in capturing global dependencies, it fundamentally relies on discrete modeling. Therefore, we employ a deep GRU network for temporal modeling and the extraction of temporal features.

[TABLE]

The detailed structure of the Generator1 is illustrated in Figure2(a. We adopted a trend-first modeling approach followed by detail enhancement to imbue random sequences $Z$ with temporal dependencies. First, we utilized an average pooling window with a stride of 1 to extract relatively smooth trend information. The trend information was then used as the query, while the detailed information served as the key and value. A cross-attention mechanism was employed to construct the synthetic time series, which was further processed by a deep GRU network for temporal feature extraction.

[TABLE]

[TABLE]

Here, $TF$ refers to the vanilla Transformer encoder. Discriminator1 distinguishes between the original temporal feature vectors $H_{emb}^{Real}$ and the synthetic temporal feature vectors $H_{emb}^{Fake}$ to enhance the synthesis quality of Generator1 and the discriminative ability of Discriminator1.

[TABLE]

3.4. Sequence Reconstructor

Sequence Reconstructor mainly consists of Generator2 and Discriminator2. Generator2 , also known as the Feature Reconstructor, is illustrated in Figure2(b. It receives the time series feature vectors outputted by Generator1 and the Temporal feature extractor, adoptting an iterative autoregressive generation approach to reconstruct the target time series step by step. Additionally, we utilized the teacher forcing approach to reconstruct the real sequence, ensuring the model effectively learns the authentic temporal dependencies. Discriminator2 receives three types of inputs: $\widehat{H}_{1:T}^{Real}$ and $\widehat{H}_{1:T}^{Fake}$ generated by the feature reconstructor from $H_{emb}^{Real}$ and $H_{emb}^{Fake}$ respectively, and $H_{1:T}^{Real}$ generated by the encoder from $X_{1:T}$. Adversarial training enhances the generative capability of Generator2 and the discriminative ability of Discriminator2.

[TABLE]

[TABLE]

[TABLE]

4. Training Procedure

During the training process of the model, we utilized two types of loss functions. Firstly, we employed the Mean Squared Error (MSE) loss function $L_{mse}$ as the supervised loss function for time series reconstruction error. For the GAN modules in the model, we utilized the standard GAN loss $L_{gan}$. We trained DLGAN according to the following procedure:

1. (1)

Firstly, we pre-trained the Sequence Autoencoder. We trained the encoder-decoder pair based on the reconstruction loss $L_{R}^{AE}$ of the Autoencoder.

[TABLE] 2. (2)

Next, to ensure the effectiveness of the Temporal feature extractor in extracting temporal feature vectors, we pre-trained the Temporal feature extractor and Feature Reconstructor. The loss error was the reconstruction loss $L_{R}^{H}$ of the embedding sequences $H_{1:T}^{Real}$.

[TABLE] 3. (3)

After the pre-training steps mentioned above, we proceeded with joint training of all modules. Each iteration mainly involved three processes: training the Generators, training the Autoencoder, and training the Discriminators. Firstly, we trained Generator1 and Generator2 using the standard GAN loss. To ensure that the training effectiveness does not solely rely on unsupervised adversarial training, we incorporated a supervised reconstruction loss $L_{R}^{H}$ for the original hidden sequence $H_{1:T}^{Real}$. This ensures that the Generators can learn the feature distribution of original sequences. Therefore, the Generator loss function $L_{G}$ is specifically defined as follows:

[TABLE]

Next, we further fine-tuned the Encoder and Decoder in the Sequence Autoencoder using the reconstruction losses$L_{R}^{AE}$ and $L_{R}^{H}$ from steps 1 and 2. This ensures that the Encoder can generate temporal embedding structures suitable for subsequent module learning. Finally, we trained the Discriminators using the standard GAN loss. Therefore, the discriminator loss function $L_{D}$ can be represented as follows:

[TABLE]

Through the aforementioned training process, random sequences can be synthesized into the target time series dataset via Generator1, Generator2, and the Decoder.

5. Experiments

5.1. Experiment Setup

Dataset. We conducted experiments on four publicly available time series datasets: 1)ETTH (14, )(Electricity Transformer Temperature-hourly), 2)Stock (9, ) (Google Stock data-daily), 3)Exchange (16, ) Excahnge rate data-daily, 4)weather (15, ) Weather data-minutely. These datasets have been widely used in various time series analysis tasks.

Baseline. We selected the following six sequence generation models as baselines: 1)PSA-GAN (10, ), 2)TimeGAN (9, ), 3)RCGAN (39, ), 4)WaveGAN (17, ),5)WaveNet (40, ),6)C-RNN-GAN (8, )

Evaluation Metrics. This paper adopts the synthetic data evaluation metrics from the study (9, ), which mainly include the following three evaluation metrics:

1. (1)

Visualization: Using the t-SNE(18, ), multivariate time series can be mapped to a two-dimensional space for visualizing the distribution of real and synthetic data. By comparing the overlap between the two distributions, the quality of the synthetic data can be assessed. 2. (2)

Discriminative Score: Used to measure the similarity between the original and synthetic data. A posterior classifier based GRU is employed to differentiate between real and synthetic data. The discrimination score is defined as the absolute difference between the classification accuracy and 0.5. A lower discrimination score indicates higher quality of the synthetic data. 3. (3)

Prediction Score: The main idea is that synthetic data should exhibit the same performance as the original data when facing the same prediction task. Train a GRU-based predictor on the synthetic dataset and test it on the real dataset. A smaller prediction error indicates higher quality of the synthetic data.

5.2. Experiment Results

Visualization. The experimental results are depicted in Figure 3. On all four datasets, the synthetic datasets generated by C-RNN-GAN and WaveNet exhibit a significant discrepancy compared to the real data. PSA-GAN, due to its progressive growing mode, may lose some temporal patterns, resulting in a relatively high overlap between its synthetic datasets and the original datasets in the data centre, but it often fails to fully cover the original datasets. DLGAN, TimeGAN, RCGAN and WaveGAN achieve relatively good synthesis results on multiple datasets. However, WaveGAN performs poorly on datasets with insufficient data volume like Stock, while TimeGAN’s synthesis performance deteriorates when dealing with high-dimensional datasets like Weather. RCGAN benefits from benefiting from conditional generation, achieves relatively satisfactory synthetic results. DLGAN achieves satisfactory synthetic results on all datasets.

Discriminative Score and Prediction Score. The experimental results are presented in Table 1. PSA-GAN uses the attention mechanism to capture global dependencies but often overlooks local sequence dependencies. Additionally, the progressive growing mode from coarse-grained modeling to fine-grained modeling may lead to the loss of some multi-period patterns in time series, resulting in less than ideal results. WaveNet primarily learns information from the original dataset, but it overlooks the ability to map random input sequences to the target space, which results in mediocre overall performance. WaveGAN uses transposed convolutions to generate sequence data, including a process where the sequence gradually grows. It maintains consistent data information throughout, leading to better predictive performance compared to PSA-GAN. However, due to the lack of continuity modeling, its discrimination score is not ideal. C-RNN-GAN reconstructs GAN framework using an RNNs, ensuring basic continuity in the generated sequences. However, due to its relatively low model complexity, its performance tends to be unstable. RCGAN benefits from conditional generation and generally outperforms the aforementioned methods, but it still does not consider temporal features inherent in time series. TimeGAN incorporates temporal dynamics support during the generation process, achieving better experimental performance compared to the aforementioned methods. However, its overall performance may deteriorate when handling high-dimensional datasets like Weather. DLGAN fully considers temporal features of original dataset and intentionally injects temporal dependencies into the synthesized sequences, achieving overall better experimental results than the baselines.

5.3. Ablation Experiments

The main purpose of DLGAN is to fully consider the temporal features of time series while learning the mapping relationship from random sequences to target sequences, and generate synthetic time series that genuinely exhibit temporal dependencies. Its gains stem mainly from two aspects: 1) the Temporal feature extractor, which captures temporal features effectively through multi-patch partitioning and a two-stage attention mechanism, thereby enhancing the temporal dependencies of input sequences; 2) time series reconstructor, which uses an iterative self-generation method to reconstruct the time series, explicitly ensuring the temporal dependencies of the synthesized sequences through supervised learning based on original dataset. Therefore, we analyze the effectiveness of these two components by removing them from the model. The experimental results are shown in Table 2. w/o Feature Extractor indicates that we remove the Feature Extractor, and only retained the most basic sequence modeling process to extract time feature vectors. w/o TimeSeries Reconstructor indicates that we remove the feature vector extraction and self-generation processes for time series reconstruction. Instead, we used the sequence data generated by the Temporal feature extractor and Generator1 through temporal modeling as input for Generator2. w/o ALL indicates the simultaneous removal of both components, where the Temporal feature extractor retains only the simplest sequence modeling process and Generator2 takes sequence data as input.

The results of the ablation experiment are presented in Table 2. From the experimental results, it is evident that the complete DLGAN model achieved the best results on all four datasets. However, on some datasets, the w/o All were superior to those obtained by solely removing single mechanisms. The analysis of the structure of the model shows that in order to ensure the temporal dependence of the generated sequences, the temporal feature extraction and reconstruction processes we employed condensed the information of input sequences into temporal feature vectors. While this approach guarantees the temporal dependency of reconstructed sequences, it inevitably results in the loss of some information in the input sequences. Nevertheless, Our model still achieve results that far exceed those of the baselines, demonstrating that even the simplest sequence modeling process can still improve the quality of synthesised time series data through supervised learning based on the original data. This further demonstrates the effectiveness of temporal feature extraction and time series reconstruction mechanisms in ensuring the temporal dependency of the synthesized sequences.

6. Conclusion

In this paper, we propose a simple but effective generative model called DLGAN, which introduces a stacked GAN structure to decompose the time series synthesis process, effectively addressing the issue of insufficient extraction of temporal features in generation processes while learning the mapping relationship from random sequences to target sequences, and explicitly incorporates the temporal dependencies of the original dataset into the synthetic time series through a supervised learning process. Extensive experiments demonstrate that DLGAN outperforms the state-of-the-art methods in time series synthesis tasks, and ablation studies validate the effectiveness of each module in the model. In the future, we will further investigate privacy protection for synthesized time series data and the integrity of the synthesized data distribution patterns to generate higher-quality time series data.