Temporal Spatial Decomposition and Fusion Network for Time Series Forecasting 1stLiwang Zhou

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Temporal Spatial Decomposition and Fusion

Network for Time Series Forecasting*

1st Liwang Zhou

Zhejiang University

China

21731005@zju.edu.cn

2nd Jing Gao

Anhui University

China

jingles980@gmail.com

Abstract—Feature engineering is required to obtain better

results for time series forecasting, and decomposition is a cru-

cial one. One decomposition approach often cannot be used

for numerous forecasting tasks since the standard time series

decomposition lacks ﬂexibility and robustness. Traditional feature

selection relies heavily on preexisting domain knowledge, has no

generic methodology, and requires a lot of labor. However, most

time series prediction models based on deep learning typically

suffer from interpretability issue, so the ”black box” results

lead to a lack of conﬁdence. To deal with the above issues

forms the motivation of the thesis. In the paper we propose

TSDFNet as a neural network with self-decomposition mecha-

nism and an attentive feature fusion mechanism, It abandons

feature engineering as a preprocessing convention and creatively

integrates it as an internal module with the deep model. The self-

decomposition mechanism empowers TSDFNet with extensible

and adaptive decomposition capabilities for any time series,

users can choose their own basis functions to decompose the

sequence into temporal and generalized spatial dimensions.

Attentive feature fusion mechanism has the ability to capture

the importance of external variables and the causality with target

variables. It can automatically suppress the unimportant features

while enhancing the effective ones, so that users do not have to

struggle with feature selection. Moreover, TSDFNet is easy to

look into the ”black box” of the deep neural network by feature

visualization and analyze the prediction results. We demonstrate

performance improvements over existing widely accepted models

on more than a dozen datasets, and three experiments showcase

the interpretability of TSDFNet.

Index Terms—time series,interpretability, long-term predic-

tion, deep learning

I. INTRODUCTION

Time series forecasting plays a key role in numerous ﬁelds

such as economy [1],ﬁnance [2], transportation [3], meteo-

rology [4], It empowers people to foresee opportunities and

serves as guidance for decision-making. Therefore, it is crucial

to increase the generality of time series models and lower

modeling complexity while maintaining performance. In the

ﬁeld of time series forecasting, multi-variable and multi-step

forecasting forms one of the most challenging tasks. Errors

may accumulate as the forecast step increases.At present,

there is no universal method to handle the problem of multi-

variable and multi-step time series prediction. One time series

usually calls for its speciﬁc feature engineering and forecasting

model, due to the complexity and diversity of real world time

series, which usually requires data analysts to have specialized

background knowledge.

Feature engineering is usually used to preprocess data

before modeling. In the ﬁeld of feature engineering, time

series decomposition is a classical method to decompose a

complex time series into numerous predictable sub-series, such

as STL [37] with seasonal and trend decomposition, EEMD

[24] with ensemble empirical mode decomposition, EWT

[25] with empirical wavelet transform. In addition, feature

selection is another important step. For complex tasks, some

auxiliary variables are usually needed to assist the prediction

of target variables. The reasonable selection of additional

features is crucial to the performance of the model, because

the introduction of some redundant additional features may

degrade the performance of the model. How to choose the

appropriate decomposition methods and important additional

features is also a challenging problem for data analysts.

On the other hand, despite the fact that numerous models

have been put forth, each one has drawbacks of its own.

The majority of deep learning based models are difﬁcult to

comprehend and produce unconvincing predictions. However,

models like ARIMA and xgboost [26], which have sound

mathematical foundations and offer interpretability, cannot

compete with deep learning-based models in terms of per-

formance.

Therefore, it is necessary to break the traditional practice

and devise a new way to handle these problems. In this study,

a novel neural network model called TSDFNet is developed

based on the self-decomposition mechanism and attentive fea-

ture fusing mechanism. Decomposition and feature selection

are integrated as internal modules of the deep model to lessen

complexity and increase adaptability. The data’s high-order

statistical features may be captured by this model’s robust

feature expression capabilities, which make it applicable to

datasets from a variety of domains.

In summary, The contributions are summarized as follows:

•We proposed Temporal Decomposition Network (TDN),

which is extensible and adaptive.it decomposes time

series over temporal dimension and allows users to cus-

tomize basis functions for speciﬁc tasks.

•We proposed Spatial Decomposition Network (SDN),

which creatively uses high-dimensional external features

as decomposition basis functions to model the relation-

ship between external variables and target variables.

arXiv:2210.03122v1 [cs.LG] 6 Oct 2022

•We proposed Attentive Feature Fusion Network (AFFN),

which has the ability of automatic feature selection and

can capture the importance and causality of features.

In this way, users can avoid the trouble of feature

selection and use arbitrary basis functions in the self-

decomposition network without worrying about the loss

of model performance caused by introducing invalid

features.

•TSDFNet obtains interpretable results on datasets in mul-

tiple ﬁelds, and has signiﬁcantly improved performance

compared with many traditional models.

II. RELATIVE WORK

The ﬁeld of time series prediction has a rich history, and

many outstanding models have been developed. The most

well-known conventional methods include ARIMA [6] and

exponential smoothing [7]. The interpretability and usability

of the ARIMA model, which turns nonstationary processes

into stationary ones through difference and can also be further

expanded into VAR [8] to address the issue of multivariate

time series forecasting, are the main reasons for its popularity.

Another effective forecasting technique is exponential smooth-

ing, which smooths univariate time-series by giving the data

weights that decrease exponentially over time.

Since time series prediction is essentially a regression

problem, it is also possible to utilize a variety of regression

models.Some machine learning-based techniques, including

decision trees [10] and support vector regression (SVR) [9].

Additionally, ensemble methods, which employ multiple learn-

ing algorithms to achieve better predictive performance than

could be attained from any one of the constituent learning

algorithms alone, are effective tools for sequence prediction.

Examples of these methods include random forest [11] and

adaptive lifting algorithm (Adaboost) [12].

In recent years, deep learning has become popular and neu-

ral networks have achieved success in many ﬁelds [29], [30],

[31]. It uses the back propagation algorithm [32] to optimize

the network parameters. Long Short-Term Memory (LSTM)

[13] and its derivatives shows great power in sequential data,

It overcomes the defect of vanishing gradient of recurrent

neural network (RNN) [14] and can better capture long-

term dependence. Deep autoregressive network (DeepAR)

[15] uses stacked LSTMs for iterative multi-step prediction,

and Deep state-space Models (DSSM) [16] also adopts a

similar approach, utilizing LSTMs to generate parameters of

a predeﬁned linear state-space model. Sequence to Sequence

(Seq2Seq) [17] usually uses a pair of LSTMs or GRUs [18]

as encoder and decoder. The encoder maps the input data

to the hidden space into a ﬁxed-length semantic vector, The

decoder reads the context vector and attempts to predict the

target variable step by step. Temporal convolutional network

(TCN) [19] could also be effectively applied to the sequence

prediction problem, which may be used as an alternative to

the popular RNN family of methods and has faster speed

and fewer parameters compared with RNN-based models with

causal convolution and residual connection. The attention

mechanism [22] emerged as an improvement over the encoder

decoder based [23], and it can easily be further extended into

a self-attentional mechanism as the core of the Transfomer

models [20], [21].

III. METHODOLOGY

The network’s architecture is depicted in Figure 1. It has two

main parts, the ﬁrst of which is a self-decomposition network

that includes TDN and SDN. The feature fusion network

(AFFN), is the additional element.

Fig. 1: Overall structure of TSDFNet

A. Self-decomposing network

The structure of self-decomposition network includes two

decomposition modules, one is time decomposition network

TDN, which adopts custom basis function to decompose se-

quences in time dimension. The other is spatial decomposition

network SDN, which decomposes sequences in generalized

spatial dimensions, using exogenous features as basic func-

tions. Its main objective is to break down complex sequences

into ones that are simple and predictable.

TDN uses multiple sets of pre-trained basis functions with

different parameters to capture signal features, which could be

triangular basis, polynomial basis, wavelet basis and so on.

The architecture of TDN is shown in Figure 2. There are

Nrecursive decomposition units in it. (n+ 1)th unit accepts

its respective input Xnas input and output two intermediate

components Wnand Vn. Each decomposition unit consists of

two parts, Stacked fully connected network Lsmaps data into

hidden space to produce the semantic vector Sn, predicts basis

expansion coefﬁcients both forward and backward through two

sets of fully connected networks Lpand Lqrespectively. The

process is:

Sn=Ls(Xn)(1)

Pn=Lp(Sn)(2)

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TemporalSpatialDecompositionandFusionNetworkforTimeSeriesForecasting*1stLiwangZhouZhejiangUniversityChina21731005@zju.edu.cn2ndJingGaoAnhuiUniversityChinajingles980@gmail.comAbstractFeatureengineeringisrequiredtoobtainbetterresultsfortimeseriesforecasting,anddecompositionisacru-cialone.Onedecomposi...

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