SEAnet: A Deep Learning Architecture for Data Series Similarity Search

Qitong Wang; Themis Palpanas

cs.DBMar 2, 2026

SEAnet: A Deep Learning Architecture for Data Series Similarity Search

Authors: Qitong Wang, Themis Palpanas

Organizations: LIPADE, Université Paris Cité

Abstract

A key operation for massive data series collection analysis is similarity search. According to recent studies, SAX-based indexes offer state-of-the-art performance for similarity search tasks. However, their performance lags under high-frequency, weakly correlated, excessively noisy, or other dataset-specific properties. In this work, we propose Deep Embedding Approximation (DEA), a novel family of data series summarization techniques based on deep neural networks. Moreover, we describe SEAnet, a novel architecture especially designed for learning DEA, that introduces the Sum of Squares preservation property into the deep network design. We further enhance SEAnet with SEAtrans encoder. Finally, we propose novel sampling strategies, SEAsam and SEAsamE, that allow SEAnet to effectively train on massive datasets. Comprehensive experiments on 7 diverse synthetic and real datasets verify the advantages of DEA learned using SEAnet in providing high-quality data series summarizations and similarity search results.

Figures & tables

Panel of Figure 1 — Fig. 1: Case studies where PAA and DFT work or fail to approximate and reconstruct series from RandWalk and Deep1B datasets. In both cases, DEA works to approximate and reconstruct series. All summarizations use the same memory budget.

Panel of Figure 2 — Fig. 2: Replace PAA by DEA for SAX symbolization.

Fig. 3: Workflow of DEA-based approximate similarity search.

Panel of Figure 4 — Fig. 4: The SEAnet architecture and the details of a dilated full-preactivation ResBlock.

Fig. 5: The SEAtrans encoder architecture.

Length	Before Scaling		$\times\sqrt{{256}/{m}}$		$\times\sqrt{{1}/{m}}$
$m$	Mean	Var	Mean	Var	Mean	Var
256	22.605	0.999	22.605	0.999	1.4128	0.0039
128	15.969	0.998	22.583	1.9961	1.4115	0.0078
96	13.820	0.997	22.569	2.6597	1.4105	0.0104
16	5.5692	0.984	22.277	15.743	1.3923	0.0615
8	3.8772	0.967	21.933	30.944	1.3708	0.1209

TABLE I: Mean and Variance of the distribution of pairwise distances between two ideal series. Scaling by

\sqrt{{256}/{m}}

is to preserve SoS by scaling DEA itself. Scaling by

\sqrt{{1}/{m}}

is the case where we scale both series and DEA in loss functions. (Note that for length

256

, scaling by

\sqrt{{256}/{m}}

does not change the original behavior.)

Fig. 6: SEAsam transformation and InvSAX [ 21 ] .

Fig. 7: SEAsam sampling workflow.

layer name	13-layer ( 96 )	15-layer ( 128 )	17-layer ( 256 )
ConvLayer	$\begin{bmatrix}3,96\end{bmatrix}$	$\begin{bmatrix}3,128\end{bmatrix}$	$\begin{bmatrix}3,256\end{bmatrix}$
ConvBlock	$\begin{bmatrix}3,96\\ 3,96\end{bmatrix}\times$ 5	$\begin{bmatrix}3,128\\ 3,128\end{bmatrix}\times$ 6	$\begin{bmatrix}3,256\\ 3,256\end{bmatrix}\times$ 7
Linear	$\begin{bmatrix}96\\ 16\end{bmatrix}$	$\begin{bmatrix}128\\ 16\end{bmatrix}$	$\begin{bmatrix}256\\ 16\end{bmatrix}$
parameters/M	0.585	1.234	5.712
MACs/B	0.053	0.152	1.412

TABLE II: SEAnet encoder architecture specifics for different series lengths. Building blocks ([kernel size, channel number] for the convolutional layer/block, [dimension] for the linear layer) are shown in brackets, multiplied by the numbers of blocks stacked.

Fig. 8: Improvements of employing SoS preservation in terms of 1st BSF tightness (positive values mean SoS is better); 100M datasets.

Fig. 9: Improvements of SEAsam over uniformly random sampling in terms of 1st BSF rightness (positive values mean SEAsam is better); 100M datasets.

Panel of Figure 12 — Fig. 10: Leaf node coverage across different sampling sizes for uniformly random sampling (light gray) and SEAsam (dark red).

	$($ a $)$ Averaged Distance Differences						$($ b $)$ Reconstruction RMS Error
Dataset	PAA	FDJNet	TimeNet	Incept	SEAnet-nD	SEAnet	PAA	TimeNet	Incept	SEAnet
RandWalk	1.3701	0.2794	0.4098	0.6285	0.2976	0.2194	0.3061	0.3354	0.3587	0.2604
F5	2.1152	0.1737	0.2103	0.2836	0.1692	0.1629	0.4214	0.2527	0.2708	0.2433
F10	5.0395	1.1943	1.9063	1.3958	1.1859	1.1672	0.6238	0.6799	0.5041	0.2635
SALD	3.2927	0.6247	0.6928	0.858	0.5748	0.6182	0.5586	0.5883	0.6831	0.5023
Deep1B	8.1095	0.9511	7.8478	0.9511	0.9083	0.9484	0.9207	1.0	0.6368	0.5418

TABLE III: (a) Averaged distance differences between pairs of series in the original and the embedded (PAA, DEA) spaces. (b) Root-Mean-Square error between original and reconstructed series. In both cases, best result (lower is better) is marked in bold, second best is underlined. (Results calculated using 10,000 series SEAsam sampled from datasets of 10-million series.)

Panel of Figure 14 — Fig. 11: Distance scatters of 1,000 SEAsam sampled series pairs across different datasets for PAA (light gray) and SEAnet (dark red).

Panel of Figure 15 — Fig. 12: Nearest neighbors’ coverage vs neighborhood size (higher is better).

Panel of Figure 16 — Fig. 13: Approximate query answers quality: 1st BSF tightness vs dataset size (higher is better)

Panel of Figure 17 — Fig. 14: Average distances among series of the visited leaf nodes vs dataset size (lower is better)

Panel of Figure 18 — Fig. 15: Approximate query answers quality: 1st BSF tightness vs number of series visited; 100M series datasets (higher is better)

Panel of Figure 19 — Fig. 16: SEAnet DEA vs. PAA on kNN classification accuracies of UCR18 dataset. Number of datasets where SEAnet wins-ties-losses compared with PAA are reported.

Panel of Figure 20 — Fig. 17: Convergence procedures measured by compression error (averaged distance difference) $L_{C}$ across architectures on F5 dataset.

Fig. 18: Improvements of SEAsamE over SEAsam in terms of 1st BSF rightness (positive values mean SEAsamE is better); 100M datasets.

Panel of Figure 22 — Fig. 19: Query answers quality upper-bounds: 1st BSF tightness vs number of series visited; 100M series datasets (higher is better).

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Time series representation learning develops compact, transferable features that capture temporal patterns for forecasting, classification, retrieval, and anomaly detection.

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We propose the Deep Distance Measurement Method (DDMM) to improve retrieval accuracy in unsupervised multivariate time series similarity retrieval. DDMM enables learning of minute differences within states in the entire time series and thereby recognition of minute differences between states, which are of interest to users in industrial plants. To achieve this, DDMM uses a learning algorithm that assigns a weight to each pair of an anchor and a positive sample, arbitrarily sampled from the entire time series, based on the Euclidean distance within the pair and learns the differences within the pairs weighted by the weights. This algorithm allows both learning minute differences within states and sampling pairs from the entire time series. Our empirical studies showed that DDMM significantly outperformed state-of-the-art time series representation learning methods on the Pulp-and-paper mill dataset and demonstrated the effectiveness of DDMM in industrial plants. Furthermore, we showed that accuracy can be further improved by linking DDMM with existing feature extraction methods through experiments with the combined model.

Abstract

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