Crossformer: Transformer Utilizing Cross-Dimension Dependency for Multivariate Time Series Forecasting (ICLR 2023)

This is the origin Pytorch implementation of Crossformer: Transformer Utilizing Cross-Dimension Dependency for Multivariate Time Series Forecasting.

Key Points of Crossformer

1. Dimension-Segment-Wise (DSW) Embedding

Figure 1. DSW embedding. Left: Embedding method of previous Transformer-based model: data points in different dimensions at the same step are embedded into a vector; Right: DSW embedding of Crossformer: in each dimension, nearby points over time form a segment for embedding.

2. Two-Stage Attention (TSA) Layer

Figure 2. TSA layer. Left: Overall structure: the 2D vector array goes through the Cross-Time Stage and Cross-Dimension Stage to get corresponding dependency; Middle: Directly using MSA in Cross-Dimension Stage to build the $D$-to-$D$ connection results in $O(D^2)$ complexity. Right: Router mechanism for Cross-Dimension Stage: a small fixed number ($c$) of ``routers'' gather and distribute the information among dimensions. The complexity is reduced to $O(2cD) = O(D)$.

3. Hierarchical Encoder-Decoder (HED)

Figure 3. HED. The encoder (left) uses TSA layer and segment merging to capture dependency at different scales; the decoder (right) makes the final prediction by forecasting at each scale and adding them up.

Requirements

• Python 3.7.10
• numpy==1.20.3
• pandas==1.3.2
• torch==1.8.1
• einops==0.4.1

Reproducibility

1. Put datasets to conduct experiments into folder datasets/. We have already put ETTh1 and ETTm1 into it. WTH and ECL can be downloaded from https://github.com/zhouhaoyi/Informer2020. ILI and Traffic can be downloaded from https://github.com/thuml/Autoformer. Note that the WTH we used in the paper is the one with 12 dimensions from Informer, not the one with 21 dimensions from Autoformer.

2. To get results of Crossformer with $T=168, \tau = 24, L_{seg} = 6$ on ETTh1 dataset, run:

python main_crossformer.py --data ETTh1 --in_len 168 --out_len 24 --seg_len 6 --itr 1

The model will be automatically trained and tested. The trained model will be saved in folder checkpoints/ and evaluated metrics will be saved in folder results/.

3. You can also evaluate a trained model by running:

python eval_crossformer.py --checkpoint_root ./checkpoints --setting_name Crossformer_ETTh1_il168_ol24_sl6_win2_fa10_dm256_nh4_el3_itr0

4. To reproduce all results in the paper, run following scripts to get corresponding results:

bash scripts/ETTh1.sh
bash scripts/ETTm1.sh
bash scripts/WTH.sh
bash scripts/ECL.sh
bash scripts/ILI.sh
bash scripts/Traffic.sh

Custom Usage

We use the AirQuality dataset to show how to train and evaluate Crossformer with your own data.

1. Modify the AirQualityUCI.csv dataset into the following format, where the first column is date (or you can just leave the first column blank) and the other 13 columns are multivariate time series to forecast. And put the modified file into folder datasets/

Figure 4. An example of the custom dataset.

2. This is an hourly-sampled dataset with 13 dimensions. And we are going to use the past week (168 hours) to forecast the next day (24 hour) and the segment length is set to 6. Therefore, we need to run:

python main_crossformer.py --data AirQuality --data_path AirQualityUCI.csv --data_dim 13 --in_len 168 --out_len 24 --seg_len 6

3. We can evaluate the trained model by running:

python eval_crossformer.py --setting_name Crossformer_AirQuality_il168_ol24_sl6_win2_fa10_dm256_nh4_el3_itr0 --save_pred

The model will be evaluated, predicted and ground truth series will be saved in results/Crossformer_AirQuality_il168_ol24_sl6_win2_fa10_dm256_nh4_el3_itr0

main_crossformer is the entry point of our model and there are other parameters that can be tuned. Here we describe them in detail:

Parameter name	Description of parameter
data	The dataset name
root_path	The root path of the data file (defaults to ./datasets/)
data_path	The data file name (defaults to ETTh1.csv)
data_split	Train/Val/Test split, can be ratio (e.g. 0.7,0.1,0.2) or number (e.g. 16800,2880,2880), (defaults to 0.7,0.1,0.2)
checkpoints	Location to store the trained model (defaults to ./checkpoints/)
in_len	Length of input/history sequence, i.e. $T$ in the paper (defaults to 96)
out_len	Length of output/future sequence, i.e. $\tau$ in the paper (defaults to 24)
seg_len	Length of each segment in DSW embedding, i.e. $L_{seg}$ in the paper (defaults to 6)
win_size	How many adjacent segments to be merged into one in segment merging of HED (defaults to 2)
factor	Number of routers in Cross-Dimension Stage of TSA, i.e. $c$ in the paper (defaults to 10)
data_dim	Number of dimensions of the MTS data, i.e. $D$ in the paper (defaults to 7 for ETTh and ETTm)
d_model	Dimension of hidden states, i.e. $d_{model}$ in the paper (defaults to 256)
d_ff	Dimension of MLP in MSA (defaults to 512)
n_heads	Num of heads in MSA (defaults to 4)
e_layers	Num of encoder layers, i.e. $N$ in the paper (defaults to 3)
dropout	The probability of dropout (defaults to 0.2)
num_workers	The num_works of Data loader (defaults to 0)
batch_size	The batch size for training and testing (defaults to 32)
train_epochs	Train epochs (defaults to 20)
patience	Early stopping patience (defaults to 3)
learning_rate	The initial learning rate for the optimizer (defaults to 1e-4)
lradj	Ways to adjust the learning rate (defaults to type1)
itr	Experiments times (defaults to 1)
save_pred	Whether to save the predicted results. If True, the predicted results will be saved in folder results in numpy array form. This will cost a lot time and memory for datasets with large $D$. (defaults to False).
use_gpu	Whether to use gpu (defaults to True)
gpu	The gpu no, used for training and inference (defaults to 0)
use_multi_gpu	Whether to use multiple gpus (defaults to False)
devices	Device ids of multile gpus (defaults to 0,1,2,3)

Citation

If you find this repository useful in your research, please cite:

@inproceedings{
zhang2023crossformer,
title={Crossformer: Transformer Utilizing Cross-Dimension Dependency for Multivariate Time Series Forecasting},
author={Yunhao Zhang and Junchi Yan},
booktitle={International Conference on Learning Representations},
year={2023},
}

Acknowledgement

We appreciate the following works for their valuable code and data for time series forecasting:

https://github.com/zhouhaoyi/Informer2020

https://github.com/thuml/Autoformer

https://github.com/alipay/Pyraformer

https://github.com/MAZiqing/FEDformer

The following two Vision Transformer works also inspire our DSW embedding and HED designs:

https://github.com/google-research/vision_transformer

https://github.com/microsoft/Swin-Transformer